Laboratory Protocols For Evaluating The Fate Of Organic Chemicals In Air and Water


United States
Environmental Protection
Agency
Environmental Research
Laboratory
Athens GA 30605
EPA-600 3 82 022
July 1982
Research and Development
Laboratory Protocols for
Evaluating the Fate of
Organic Chemicals in
Air and Water

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EPA-600/3-82-022
LABORATORY PROTOCOLS FOR EVALUATING THE FATE
OF ORGANIC CHEMICALS IN AIR AND WATER
by

T. Mill, W.R. Mabey, B.C. Bomberger, T.-W. Chou,
D.G. Hendry, and J.H. Smith

SRI International
Menlo Park, California 94025
Contract No. 68-03-2227
Project Officer
James Falco
Technology Development and Applications Branch
Environmental Research Laboratory
Athens, Georgia 30613
Agency
,
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DISCLAIMER
This report has been reviewed by the Environmental Research Laboratory,
U.S. Environmental Protection Agency, Athens, Georgia, and approved for
publication. Approval does not signify that the contents necessarily
reflect the views and policies of the U.S. Environmental Protection Agency,
nor does mention of trade names or commercial products constitute endorse-
ment or recommendation for use.
ction Agency
ii
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FOREWORD
Environmental protection efforts are increasingly directed towards
prevention of adverse health and ecological effects associated with specific
compounds of natural or human origin. As part of this Laboratory's research
on the occurrence, movement, transformation, impact, and control of environ-
mental contaminants, the Technology Development and Applications Branch
develops appropriate transport and transformation measurement protocols,
source information, and environmental data bases for application to models
that assess toxic chemical exposure.

Delineation of the environmental pathways followed by potentially
harmful chemicals is a key element in predicting the effects of pollutants
before extensive damage occurs. This report presents procedures (or proto-
cols) for obtaining rate and equilibrium constant data for use in evaluating
some of the important pathways of chemicals in aquatic and atmospheric
environments.
David W. Duttweiler
Director
Environmental Research Laboratory
Athens, Georgia
ill
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ABSTRACT

Laboratory test procedures (or protocols) have been developed to provide
data useful in evaluating the environmental fate of organic compounds in
natural aquatic systems and in the atmosphere. Screening-level protocols are
described to estimate rate constants for hydrolysis, photolysis, oxidation,
biotransformation, and volatilization processes in natural aquatic systems; a
screening protocol for measurement of partition coefficients for sorption of
organic chemicals to sediments is also described. Detailed test protocols
have been developed for the hydrolysis, photolysis, volatilization, and
sediment-sorption processes to obtain more accurate and precise data for use
in environmental assessments applied to aquatic systems. Screening and de-
tailed test protocols are described for estimating rate constants for the
atmospheric photolysis and oxidation of organic compounds. For each process,
the theory and the present state of knowledge regarding the environment are
reviewed, and some common methods currently in use are critically evaluated.

This report was submitted in fulfillment of Contract No. 68-03-2227 by
SRI International under the sponsorship of the U.S. Environmental Protection
Agency. The report covers the period from October 1977 to January 1980.
After peer review, the report was revised under EPA Contract No. 68-03-2981,
October 1981.
iv
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CONTENTS
Foreword . . .
Abstract . . .
Acknowledgments
1. Introduction
2. Hydrolysis in Water
3. Photolysis in Water
4. Oxidation In Water
5. Atmospheric Chemistry
6. Aquatic Biodegradation
7. Volatilization from Water . . . ,
8. Sorption of Organics on Sediments
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ACKNOWLEDGMENTS
The assistance, advice and comments of the EPA project officer,
Dr. James Falco of the Environmental Research Laboratory, Athens, Georgia,
have been of great value in preparing this report, as were the comments of
other EPA personnel, including Drs. Arthur Stern and Asa Leifer of the Office
of Toxic Substances, Dr. George Baughman of the Athens Laboratory, and Dr.
Marcia Dodge of the Environmental Sciences Research Laboratory, Research
Triangle Park, North Carolina.

Dr. Dale G. Hendry, the author of one chapter in this report and co-
author for two other chapters, died in June 1981. Dr. Hendry's death is a
personal as well as a professional loss to his coworkers at SRI and to his
colleagues in the scientific community. His research in oxidation chemistry,
photochemistry, and atmospheric chemistry was instrumental in developing the
procedures and background sections in this report.
vi
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CHAPTER 1. INTRODUCTION
The Toxic Substances Control Act of 1976 (P.L. 94-469) requires that the
EPA evaluate all new chemicals for their possible adverse effects on the
environment before manufacture and use are permitted. The act also provides
that the manufacturers of new chemicals provide the EPA with laboratory and
other test data on fate and effects for specific chemicals that may con-
stitute a possible hazard to a biological population. To be useful to the
EPA, test data must be developed under conditions that allow meaningful
interpretation in the context of environmental transport and transformation
processes.

There is general consensus among experienced investigators that, at this
time, predictions of environmental pathways for chemicals are most reliably
and economically obtained from laboratory evaluation of the physical,
chemical, and microbiological processes important in the environment. With
the appropriate data, this approach can provide information on the fate of
specific chemicals in a wide variety of aquatic and atmospheric environments.
Therefore, it is essential that the EPA develop guidelines and specific pro-
cedures for carrying out laboratory tests for use in fate assessment.

This report was prepared by SRI International (formerly Stanford Research
Institute) for EPA under contract No. 68-03-2227 to evaluate existing test
procedures and recommend test protocols for the following environmental pro-
cesses:

Hydrolysis in water
Photolysis in water
Oxidation in water
Atmospheric chemistry
Aquatic biodegradation
Volatilization from water
Sorption of organics on sediments.
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1.1 GENERAL CONSIDERATIONS

In individual sections of this report, we discuss kinetics, test
methods, and recommendations for test protocols for each of the seven
specific chemical or physical processes listed above. This section out-
lines the relationship between laboratory experiments and environmental
processes and some basic requirements for laboratory test procedures
intended to be used for environmental assessment.

The foundation for use of laboratory data for environmental assessment
is based on the following assumptions:

• The rate of transformation or transport of a chemical in
or from an environmental system is the sum of the rates of ^
known individual chemical, physical, and biological processes.

• The rate or equilibrium constants for these processes can be
measured independently in the laboratory.

• The laboratory data for individual processes can be integrated
and extrapolated to the appropriate set of environmental conditions
using simple or computer models.

Theee same assumptions are also implicit in the use of models to describe
photochemical smog, agricultural run-off, and other enviro'iunental processes
with varying degrees of complexity. The success of any effort to model or
assess the transport and transformation of a chemical in the environment
thus depends on two factors: (1) availability of reliable rate or equili-
brium data, usually developed in the laboratory, and (2) a reliable method
for using such data in an environmental assessment.

This second factor refers specifically to extrapolation or scaling
methods that accurately combine environmental variables, such as pH, wind
velocity, or microbial cell count, with the process affected by the variable.
Since a specific equilibrium or rate process can be measured quite accurately
usually to within ± 10%, whereas values of environmental variables can vary
dramatically and are rarely known to within more than a factor of two, the
accuracy of fate estimates is usually limited by the accuracy of the environ-
mental descriptors, not the laboratory data.

For example, the efficiency of a photochemical processs can be measured
fairly easily with an accuracy of ± 10% in the laboratory and applied to the
calculation of the rate of photolysis in sunlight at a specific time and
location using sunlight intensity data from the literature. However, the
This assumption implicitly neglects interactive processes that would
accelerate or retard a specific transport or loss process; their
importance probably is not great in most environmental systems.
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photolysis in sunlight is variable and uncertain owing to random fluctuations
in light intensity from cloud cover, backscatter, and light absorption by
other chemicals. In this example the net rate of the process follows a
relation

Rate c* <(>I

where is the efficiency of the process (quantum yield) and I is the intensi-
ty of sunlight. Since the standard error ratio in rate is related to the sum
of standard error ratios for $ and I (section 3.6.8) there is a significant
advantage in measuring $ as accurately as possible in the laboratory, to the
point where the error in is reduced to about one-fifth the error in I.

1.2 CRITERIA FOR SELECTION OF SUITABLE TEST METHODS

Although many experimental procedures have been described to measure
rate and equilibrium constants for processes analogous to those found in the
environment, for several reasons most procedures are inapplicable for develop-
ing data useful for fate assessment. One reason is that some procedures give
only qualitative information about the process and thus can be used only to
judge whether the reaction occurs or not. Another reason is faulty design
of the experimental procedure, which prevents control of some important
variables and hence gives data that are affected by some other, unsuspected
and more rapid process. An example of this situation is found in measure-
ments of loss of a highly insoluble chemical from water at elevated tempera-
ture, where the loss is thought to be caused by hydrolysis but actually is
caused by volatilization.

A third reason is that some procedures are used in the laboratory under
conditions for which no satisfactory extrapolation is possible to a specific
environmental situation. A good example is the measurement of the rate of
biotransformation of a chemical dissolved in a natural water, and where only
the loss of chemical or evolution of carbon dioxide is monitored. In this
case, the necessary data to quantitatively link these results to an aquatic
environment — for example, information on the lag phase and cell counts — are
lacking and no reliable extrapolation is possible.

Thus, the scientific criteria for judging the suitability of a test
procedure for environmental assessment are the quantitative character of the
data, the use of proper controls to ensure the applicability of the data for
the intended process, and the availability of reliable scaling or extrapola-
tion procedures.

Apart from the purely scientific validity of specific laboratory tests,
the generality and complexity or sophistication of tests must also be con-
sidered in evaluating available methodologies, especially if such tests are
intended as protocols for regulatory use. Thus, a test procedure that
requires use of a complex and expensive Fourier transform magnetic reso-
nance spectrometer is not likely to be adopted as a protocol for industry-
wide use. Preferred test methods are those generally carried out by
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experienced laboratory personnel with instruments commonly found in well-
equipped analytical and physical chemistry laboratories. Each procedure must
be evaluated for the balance between speed, accuracy and cost.

To achieve both economy and reliability in environmental assessment, we
need to consider the use of screening tests in exposure assessment. Usually,
only one or two environmental processes control the persistence and fate of a
specific chemical in aquatic or atmospheric environments. Thus in many
cases, testing costs can be significantly reduced through rapid screening
tests designed to give approximate values of rate constants or equilibrium
constants for comparison of competing rate processes in simple assessment
models.* Processes not significant in this assessment usually can be elim-
inated from further evaluation, with savings in cost and simplification of
subsequent detailed assessment. In subsequent sections of this report, we
evaluate and recommend both screening and detailed tests for each process.

In the preparation of these protocols, we have assumed that a valid ana-
lytical method is available for analysis of the chemical being tested. Ana-
lytical procedures and techniques are usually selected by the equipment avail-
able and by the properties of the chemical (that is, susceptibility to anal-
ysis by flame ionization or electron capture detectors, or absorbance, etc.)
If special analytical devices or procedures are used, the experimental
approach should be carefully examined to determine whether the protocol is
affected. It is also expected that suitable controls (or blanks) will be
performed for each protocol with each chemical to identify any adventitious
processes that would introduce artifacts into the data obtained. Control
experiments are designed with considerations of both the fundamentals of the
process which the protocol is intended to quantify, and the adventitious pro-
cesses which may complicate the experimental data.
By a simple model we mean a well-mixed single compartment in which the
overall rate of transformation of the chemical is easily calculated
using the simple relation
k = ki + k2 + k
t n

where kt is the observed rate constant and ki, ka, and 1^ are simple
first-order rate constants for individual environmental processes.
Sorption may not be included in this preliminary assessment.
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CHAPTER 2. HYDROLYSIS IN WATER

T. Mill, W. R. Mabey, and D. G. Hendry
2.1 INTRODUCTION 6
2.2 SUMMARY 6
2.3 CONCLUSIONS 7
2.4 RECOMMENDATIONS 7
2.5 SCREENING TESTS 7
2.5.1 Purpose 7
2.5.2 Deatailed Procedure 7
2.5.3 Criteria for Screening Test 8
2.5.4 Rationale 9
2.5.5 Scope and Limitations 9
2.6 DETAILED TESTS 9
2.6.1 Purpose 9
2.6.2 Estimation of Half-Life from Screening Studies 9
2.6.3 Evaluation of Rate Constants for Hydrolysis 10
2.6.4 Exact Temperature Dependence Measurement 12
2.6.5 Approximate Measurements of Temperature Dependence .... 14
2.6.6 Rationale 15
2.6.7 Scope and Limitations 15
2.6.8 Error Analysis 16
2.7 BACKGROUND 20
2.7.1 Definition of Hydrolysis 20
2.7.2 Kinetics 21
Rate Laws 21
Rate Constants 23
Effect of Structure on Reactivity 23
Effect of Temperature 28
Effects of Ionic Strength and Buffer Salts 29
Effect of Solvent Composition 30
Effects of Metal Ion Catalysis 31
2.7.3 General Environmental Considerations 32
Effects of Ion Concentration, Temperature, and pH . . . . 32
Review of Literature on Hydrolysis in Natural Waters . . 32

REFERENCES 39
APPENDICES
2.A A GENERAL SOLUTION FOR THE HYDROLYSIS REACTION RATE EQUATIONS . 41
2.B TEMPERATURE EXTRAPOLATION 43
2.C KINETIC ANALYSIS OF PARALLEL FIRST-ORDER REACTIONS 47
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2. HYDROLYSIS IN WATER
2.1 INTRODUCTION

The deliberate and accidental introduction of many hundreds of differ-
ent organic chemicals into major streams and rivers in this country is well
documented. Reactions of some of these chemicals with the water is one
possible process that transforms them into new structures with properties
that are very different from their precursor molecules. Therefore data on the
rate constants for hydrolysis of chemicals having a hydrolysable function are
necessary to evaluate the importance of hydrolysis as a dominant pathway for
transformation of some chemicals.

This section evaluates methods available for obtaining the data needed
to calculate rates of hydrolysis or half-lives under conditions found in
aquatic systems. From these methods we have selected a few to use as screen-
ing and detailed test protocols for hydrolysis.

2.2 SUMMARY

Screening and detailed test protocols for hydrolysis of chemicals in
water have been prepared to enable an investigator to select chemicals with
half-lives of one year or less and estimate hydrolysis rate constants and
half-lives for most chemicals at any environmental pH and temperature. Only
chemicals with half-lives of less than one year are considered for detailed
study.

The test protocols are based on a large body of experimental data for
hydrolysis together with detailed kinetic analysis of the process. The
recommended test protocols meet the criteria of quantitation, accuracy, and
applicability to experimental systems and are cost-effective and simple to
use for a wide range of chemical structures. Background data on hydrolysis
kinetics and a review of studies of hydrolysis rates of some pesticide
chemicals in buffered and natural waters are presented to demonstrate that,
in nost natural waters, only pH and temperature affect rates of hydrolysis.
All investigations to date show that hydrolysis rates in buffered and
natural waters are the same within experimental error.
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2.3 CONCLUSIONS

Present knowledge of the theory and experimental aspects of hydrolysis
reactions provide a sound basis on which to propose hydrolysis protocols.
The recommended protocols for screening and detailed studies represent a
balance between the economic need to minimize laboratory work and the
scientific requirements for sufficient and accurate data. The screening
protocol can be used to identify chemicals that have half-lives of less than
a year. The detailed protocol can be used to determine data necessary to
calculate rate constants and half-lives for hydrolysis at any pH and tempera-
ture encountered in aquatic environments.
2.4 RECOMMENDATIONS

The protocols should be tested in the laboratory for applicability to
several chemicals of environmental concern. Initial studies should include
chemicals from classes with known pH-rate profiles, such as esters or alkyl
halides. A dibutyl phthalate and ethylene dibromide would be two such
chemicals.

For chemicals in classes whose pH-rate profiles are unknown, we recom-
mend that general pH-rate profiles be established for the class of compounds.
Data from protocols carried out for specific chemicals can then be refer-
enced to the known profiles.

Validation of laboratory tests should be carried out using limited field
tests (enclosed ponds) and a simple model.
2.5 SCREENING TESTS

2.5.1 Purpose
This screening protocol is intended to identify chemicals with half-
lives of less than 1 year during hydrolysis at 25°C for simple environmental
fate assessment applications.

2.5.2 Detailed Procedure
Solutions should be prepared using sterile, pure water and Reagent
Grade (or purer) chemicals. Buffer solutions should be prepared according to
the following procedures:

• pH 3.0: 50 ml of 0.10 M KHCaH,.0,, is mixed with 22.3 ml of
0.10 M HC1 and diluted to 100 ml.

• pH 7.0: 50 ml of 0.10 M KH2PO<. is mixed with 29.1 ml of 0.10 M
NaOH and diluted to 100 ml.

• pH 11:0: 50 ml of 0.05 M NaHC03 is mixed with 22.7 ml of
0.100 M NaOH and diluted to 100 ml.
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• For each chemical being tested reaction mixtures should be pre-
pared in each of the three buffer solutions without the use of
heat. The chemical should be at a concentration less than one-
half its solubility in water and at less than 10~3 M. If neces-
sary, 1 volume percent acetonitrile may be added as cosolvent if
the chemical is too insoluble in pure water to permit reasonable
handling and analytical procedures. Acetonitrile is stable enough
up to 80°C to permit its use as a cosolvent; above 80°C, 1%
ethanol in water is the recommended solvent for hydrolysis tests.

• Sealed ampoules or stoppered (no grease) volumetric flasks con-
taining the reaction mixtures should be placed in a constant
temperature bath at 25 ± 1°C in the dark. Solutions should be
analyzed for the concentration of chemical and at t = 0, 44 and
88 hr. Wherever possible, an analytical procedure should be used
that provides a precision within ± 5%.

2.5.3 Criteria for Screening Test
The solution at pH 7 is both a control solution and one point on the
pH rate profile curve (see Section 2.6.2). If no loss of chemical is noted
in 88 hr in this solution, any losses noted in the solutions at pH 3 and 11
are probably due to hydrolysis. Significant loss of chemical from the pH 7
solution may indicate the intervention of some other loss process such as
sorption, volatilization, or biological transformation. These possibilities
should be checked before proceeding with additional analyses or calculations
(see Section 2.6.3). If hydrolysis does occur at pH 7 and if more than 75%
of the chemical has hydrolyzed after 2 hr, the hydrolysis half-life will be
less than 1 hr. In this case the chemical will not persist in the aquatic
environment, and detailed hydrolysis studies are then not necessary.

Providing that the control solution data are satisfactory, the loss
rates from the pH 3 or 11 solutions may be interpreted in a straightforward
manner; if more than half the initial concentration of chemical has
hydrolyzed at either pH 3 or 11, or both, in 88 hr, the chemical is expected
to have a half-life of less than 1 year at pH 5 or 9, respectively, or both
(see Section 2.7). As a check on the reliability of the percent loss of
chemical at 88 hr, the loss at 44 hr should be more than 29% if the half-life
is less than 1 year.
The basis for this screening study is that most chemicals hydrolyze
at pH 3 or 11 at rates that are one hundred times as fast as at pH 5 or 9,
respectively; thus, a measured half-life of less than 88 hr at pH 3 or 11 is
equivalent to a half-life of less than 8800 hr or one year at pH 5 or 9,
respectively. If more than 75% of the chemical has hydrolyzed after 2 hr,
the half-life is less than an hour.
If the environmental hydrolysis half-life is found to be less than a
year, detailed hydrolysis studies are recommended for the chemical. This
recommendation is based on a screening test, however, and detailed studies
may not be necessary if other screening data show the chemical has low
toxicity or is more rapidly transformed by other processes.
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2.5.4 Rationale
The screening test described above is a simple, rapid procedure for
qualitatively evaluating hydrolysis rates and half-lives; it requires common
laboratory chemicals and equipment and minimal time, assuming that a valid
method is available or can be developed for analysis of the chemical in
water. The test is designed to identify those chemicals that have environ-
mental half-lives of more than or less than a year at pH 5 or 9 at 25°C. These
are limiting conditions encountered in most freshwater systems because at pH
5 or 9, acid- and base-promoted reactions can have significant rates, and
25°C is higher than the average temperature of most aquatic systems. Thus,
this screening test is conservative in subjecting a maximum number of com-
pounds to detailed studies.

2.5.5 Scope and Limitations
The screening test for hydrolysis at pH 3, 7, and 11 is designed to
separate chemicals into three groups: those with hydrolysis half-lives
(1) greater than one year at pH 5 and/or pH 9, (2) less than a year but more
than 1 hour at pH 5 and/or pH 9, and (3) less than 1 hour at pH 7. The test
procedure is simple,but correct interpretation requires that the chemical be
dissolved in water and have no functional group that ionizes in the pH
region 3 to 11.

2.6 DETAILED TESTS

2.6.1 Purpose
The objective of this test protocol is to provide a uniform pro-
cedure for accurate measurement of rates of hydrolysis and estimation of rate
constants (k^) under conditions that will enable the investigator to estimate
a rate constant for hydrolysis at any pH and temperature commonly encountered
in environmental water bodies—usually pH 5-9 and 5-30°C. Therefore, some
information concerning the dependence of k^ on both pH and temperature must
be developed from which to estimate values of the acid> base and neutral
hydrolysis rate constants, k , lo, k. and their Arrhenius activation param-
eters. A B IN

2.6.2 Estimation of Half-Life from Screening Studies
Screening studies provide a basis for a quick estimate of the life-
time (and rate constant of the chemical in hydrolysis) at any pH. From the
loss of chemical measured at 88 hr at any pH, the half-life is

tt/hr = (88) x 0.69/ln(C /C88)
-5 O
and the rate constant is

1^/hr"1 = ln(Co/C88)88

where Co and C88 are the concentrations of chemical at time 0 and 88 hr,
respectively.
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If hydrolyses observed at pH 3 and 11 are due only to the acid and base-
promoted reactions, respectively (Section 2.7.2), then the half-life at any
intermediate pH can be estimated by using the multiplication factors shown
below:

Acid Multiply Base
Reaction Half-life Reaction

pH By pH

3 1 11

4 10 10

5 102 9

6 103 8

7 10" 7

This interpolation tends to give estimated half-lives that, are too long be-
cause it assumes that no other hydrolysis process contributes to the overall
rate; the half-lives estimated in this way are useful only in planning
detailed experimental studies. As an additional aid to selecting conditions
where the reaction rate is conveniently rapid, the half-life at any tempera-
ture may be approximated by assuming that the measured half-life will double
(or be halved) for each 10°C decrease (or increase) in temperature.

2.6.3 Evaluation of Rate Constants for Hydrolysis
The rate of hydrolysis should be measured at pH 3, 7, and 11 at the
same temperature, preferably 25°C, using the procedure described in
Section 2.5. Rates of hydrolysis should be fast enough so that 60-70%
hydrolysis is effected in not more than several weeks' time. For these
experiments, temperature control should be ± 0.1°C or better. Each reaction
mixture should be analyzed at regular intervals to provide a minimum of six
time points between 20% and 70% hydrolysis of the chemical. Control exper-
iments are also needed as indicated in Section 2.5.1. If hydrolysis is too
slow at 25°C to conveniently follow the reaction to high conversion in
several weeks but still rapid enough to measure 20-30% conversion, the
accuracy of the data will be improved if more data points are taken between
10 and 30% conversion; fifteen to twenty time-points are preferable. If the
reaction is too slow to measure a significant reaction in several weeks, a
higher temperature should be used; see Section 2.6.4 below for procedures
for temperature extrapolation.
10
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To demonstrate that the hydrolysis reaction is a first-order
reaction over the interval of 10-60% conversion, two concentrations of
chemicals should be used that differ by about a factor of ten.

Rate constants for hydrolysis (k^) can be evaluated from the con-
centration-time data in several ways. The simplest procedures are (1) to
plot the log of concentration of chemical against time using semi-log paper
(the best straight line through the points will have a slope equal to
-kh/2.3),and (2) to more precisely and accurately evaluate k^, fit the data
by linear regression analysis to the equation ln(Ct/Co) = -k^t, where C and
C are the concentrations of chemical at times t and 0.

Marked curvature in a plot of log C versus time or a low correlation
coefficient indicates that a non-first order process is taking place and ad-
ditional experiments may be necessary.

Since k^ is the composite rate constant (see Section 2.7.2).

k, = k.(H+) + k + k_(OH-) (2.1)
h A N B

The values of kA, k_, and k.. are readily obtained from the values of k, mea-
J*.TTIT"JII*" "
sured at pH 3, 7, and 11:*

— lr -1-1 n~*V H
(3) Ti(7) Vll)J (2.2)
k = 10 Ik, - k. + 10 k, I (2.3)

kN = kh(7) - 10"^kh(3) + kh(ll)J (2'4)
The overall rate of hydrolysis and the composite rate constant k^
may be calculated at any pH by using eq 2.1 and the values of k^, kg, and
kjj. Eq 2.1 also shows that if kA or kg are less than 10 k^, the reaction
will be pH independent from pH 3 to 7 or 7 to 11, respectively. Under these
conditions, eqs 2.2 to 2.4 predict that k^ and kg < 0.1 k^; that is, the equa-
tions are not sensitive enough to detect the true values of k^ or kg. This
limitation is not serious, however, since as a practical matter, neither pro-
cess will contribute more than 1% to the overall rate in this pH region.

For example, if the values of k^ at pH 3, 7, and 11 are assumed to be
2.1 x 10"1, 1 x 10-2, and 2 x 10"2 hr"1, respectively, solving for kA, kN, k_
using eqs 2.2 to 2.4givesk = 2 x 102 M"1 hr"1, k^ = 1 x 10~2 hr-1, and
A IN
*
See Appendix 2.A for general solution to eq. 2.1 for any three pH values.
11
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kg = 10 M"1 hr"1, respectively. The value of k^ at say pH 8.7 can be
calculated by substitution in eq 2.1 together with the values of H+ and OH~
at pH 8.7 (at 25°): H+ = 2.0 x 10'9 M; OH~ = 5.0 x 10~6 M

k, = 2 x 102 (2 x 10-9) + 1 x 10~2 + 10 (5 x 10"6) = 1.0 x 10~2 hr'1

2.6.4 Exact Temperature Dependence Measurement
Many chemicals hydrolyze too slowly at 25°C to allow measurement of
their rates conveniently in less than a few months. In these cases some
elevated temperature must be chosen to provide rates that are rapid enough to
be measured with accuracy and convenience but not so high as to cause other
problems such as volatilization or loss of solvent. Rate constants ku, k^,
kfl, and kg evaluated at an elevated temperature must be extrapolated to
25°C or some lower temperature to be useful in environmental assessment. The
temperature dependence of any discrete hydrolysis process may be expressed by
the Arrhenius relation*

1 A ~E/RT
k = Ae

where A is the entropy term, E is the activation energy, and R is the gas
constant 1.987 cal deg"1 mol"1. Between any two temperatures, the following
relationship holds

I
At a pH where hydrolysis occurs by a combination of two or more processes,
temperature dependence is more complex
[OH-3
Since A and E for each process are usually different, no analytical solution
to the composite equation is possible. Moreover, although approximations to
the temperature dependence of k^ at one pH are possible and useful in limited
ways (see below) , the exact solution of the temperature dependence relation
for each process — in which values of EA, Eg, EN, AA, and AN are calculated
from the data obtained at several pH values and temperatures — is the most
satisfactory method for calculating kh at any other temperature and pH.* To
evaluate E and A for each process requires knowing the rate constants for the
three processes k^, kjj, and kg at two or more temperatures; from these data
and the Arrhenius relationship, values of A and E for each process can
usually be calculated and used to calculate rate constants for hydrolysis at
other temperatures and pH values of interest for environmental assessment.
Temperature is in degrees Kelvin.
Another form of the temperature dependence relationship is used in Section
2.6.8 and Appendix 2.B that does not require explicit calculation of E and A,
but both procedures require separation of Ic into the constituent rate constants
or
12
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To determine the temperature dependence, rate constants k^ are
measured at pH 3, 7, and 11* at (where possible) 25°C and two higher or lower
temperatures (controlled to + 0.1°C) at least ten degrees apart, k^ is
evaluated and kA, kg and kN are calculated frc.m k^ at each temperature using
eqs 2.2 to 2.4. A and E are estimated for each process by plotting log k
versus 1/T and taking the best straight line through the three data points,
or by fitting the data by regression analysis to the equation In k = A-E/RT.

For example, the rate of hydrolysis of an ester was assumed to have
the following values of k^ at 25°, 40°, and 55°C, and at pH 3, 7, and 11:*
Temp
°C pH 3 pH 7 pH 11

25 3.00(-7) 1.12(-7) 1.20(-4)

40 1.58C-6) 7.98(-7) 3.17(-4)

55 7.8K-6) 4.95(-6) 7.71(-4)
(Values in parentheses are
exponents of 10.)

Equations 2.2 to 2.4 were used to calculate values of k , k.,, and k^ at each
temperature:

Temp kA' V kB'
8C (sec-1) M-1 sec-1 M-1 secj
25 2.00(-4) 1.00(-7) 1.20(-1)

40 8.14(-4) 7.66(-7) 3.16(-1)

55' 2.86(-3) 4.87(-6) 7.66(-l)

Regression analysis on the three sets of three rate constants at three
temperatures gave values of E^, Ejg, and Eg: E^ = 17.224, EJJ = 25.156, and Eg
12.000 kcal mol"1. Corresponding values of log A are: log A. = 8.9355, log
A = 11.4503, and log A = 7.88016 in units of mol-1 sec-1 or sec-1.
pH of buffered solutions should be checked at temperature and adjusted
to the correct pH if necessary (Section 2.7.2).
Experimental errors are deleted from this example; estimation of the
probable errors in this procedure are given in Section 2.6.8 on Error
Analysis. These kinetic data were selected to illustrate the use of the op-
tional estimation methods and are not derived from any actual measurements.

13
-------
These values of A and E can be used to recalculate values of k with a
4% error and to calculate new values of the rate constant k^. For example we
can calculate kh and the half-life for this ester at 15°C (288°K) and pH 5.2.

log k (15°C) - 8.9355 - 17.224/6 = -4.1511
A
kA = 7.06 x ID'3 M-1 sec-1 (6 = 4.57T)

log kjjdS'C) = 11.4503 - 25.155/9 = -7.6621

k^ - 2.177 x 10-8 sec'1

log kgCLS'C) = 7.8802 - 12.000/6 =-1.2372

kg = 5.791 x ID'2 M-1 sec'1

At pH 5.2 [H+] - 6.3 x 1Q-6 M and since at 15°, K - 4.57 x 10~1S (see
Section 2.6.2), [OH~] - 7.26 x lO"10 M. W
7.06 x 10~5(6.3 x 1Q-6) + 2.177 x KT8 + 5.79 x lQ-a(7.26 x 1Q-10)

5°) = 2.181 x 10-8 sec"1

tj^ - 368 days

2.6.5 Approximate Measurements of Temperature Dependence
The foregoing procedure may be approximated at a fixed pH by
assuming that the temperature dependence of k^, which can be measured to give
an apparent activation energy, E^, is linear with e~l/T and can be used to
extrapolate kjj to a new temperature at the same pH. However, since k^ is not
actually linear in e~^/T, owing to the presence of more than one kind of pro-
cess, the value of E^ will vary with the temperature range used to calculate
its value. Thus, for example, in the hydrolysis of the above ester at pH 7,
where the base-promoted reaction makes a significant contribution to the over-
all rate, values of E^ change from 15.04 to 16.19 kcal mol"1 between 25 and
55°C. Nonetheless, for short temperature intervals, the use of an E^ for ex-
trapolating kn leads to only small errors. A comparison is obtained by calcu-
lating the value of kh at 15°C* and pH 3 by using (1) the exact solution given
in 2.5.2.4 and (2) the approximation of E, .

(1) ^(15°) at pH 3 - 7.06 x 10"8 + 2.18 x 10~8 + 5.79 x 10~13

- 9.24 x 10-8 sec~x

(2) E, calculated from the values of Eh at pH 3 and 25 and 55° is 21.10

kcal mol"*.
Temperature measurements are assumed to be accurate to ± 0.1°C but actual
temperatures are cited to two significant figures only.

14
-------
From Eh and kh at 25° and pH 3
3.00 x 10~7/3.446

8.70 x 10-8 sec-1
The error in using the approximation is only 20% over this range; thus, for
many temperature measurements' made close to 25°C and not over 60°C, the use
of Eh for extrapolating to any temperature between 60 and 10°C should give a
satisfactory result. However, this approximation method has a serious
limitation in that values of k^ cannot be calculated at pH values other than
those for which temperature measurements have been made. If measurements have
been made, at several pH values and temperatures, then in view of the small
amount of additional work needed to calculate the exact value of E for each
process from the same data, we recommend using the exact method described in
Section 2.6.4.

2.6.6 Rationale
The foregoing detailed procedure is intended to provide
accurate kinetic information concerning the effect of pH and temperature on
the rate constant for hydrolysis. The procedure requires that close atten-
tion be paid to control experiments, temperature and pH regulation, and cal-
culation of individual rate constants from experimental data. Hydrolysis ex-
periments in duplicate are recommended for three pH values and at three
temperatures for a minimum of nine experiments. However, some latitude may
be possible, particularly for reactions that are rapid at or near 25°C, where
extrapolations to other temperatures of concern in assessment procedures are
necessarily short.

2.6.7 Scope and Limitations
The foregoing detailed test protocol is intended to provide the
quantitative information necessary to estimate rate constants for hydrolysis
of most chemicals dissolved in water under a variety of conditions found in
aquatic environments. These data will provide estimates of rate constants
and half-lives at any pH and temperature of concern for environmental assess-
ment with an accuracy of greater than a factor of two in most cases. Some
exceptions should be noted however.

Although many chemicals exhibit limited rate dependence on pH
because of the relative unimportance of one or more of the hydrolysis pro-
cesses in the pH region of prime interest (see Figures 2 through 5 in Section
2.6.2), we recommend that pH measurements always be carried out at three pH
values near 3, 7, and 11 in order to check the consistency of the rate data.
While intervention of other unsuspected processes can be partly anticipated
and minimized through proper experimental design (e.g., sealed and sterile
containers to eliminate volatilization and biodegradation, respectively) ,
other chemical processes such as pyrolysis, rearrangement, or elimination may
become important for some chemical structures at elevated temperatures.

15
-------
Initial evidence for such processes will usually be found by
formation of different products at high temperatures. Additional evidence
for these processes will be found by data analysis for the temperature
dependence of k^, kjj, and kg; if other processes intervene significantly,
these rate constants will probably exhibit nonlinear dependence on e~l/T.

The effect of competitive rate processes on hydrolysis rate
data will be to increase k at elevated temperatures and decrease k when ex-
trapolated to environmental temperatures; that is, values of E will be
increased. If the products are stable the simplest method to correct hy-
drolysis data for intervention of additional rate processes is to measure
only the rate of formation of products from hydrolysis rather than loss of the
starting compound. Hydrolysis rate data obtained in this way over a range of
pH and temperature should be relatively free of this source of error. How-
ever, kinetic analysis of data for formation of products versus time for
parallel first-order reactions is different from that for analysis of data for
loss of starting chemical versus time or for a simple first-order process (see
Appendix 2.C).

Another limitation on the scope of this protocol is found in
measurements of the rates of hydrolysis of chemicals that reversibly ionize
or protonate in the pH range of interest. Rates of hydrolysis of these com-
pounds will often have unusual pH-rate profiles owing to competition between
the reactions of the charged and uncharged forms:

H20 + HAY ~—"AY~ + H30+

AY~ A + Y~

HAY —- HA+ + Y~

The net effect is that the pH-rate profile for HAY will be more complicated
than the typical curve and will often have a minimum or maximum, and the
exact features cannot be decided a_ priori. Should there be any question con-
cerning the possible importance of this effect in hydrolysis of an ionic
chemical having a pKa or pKb in the pH region of 3-11, additional measure-
ments should be made to define the pH-rate profile.

2.6.8 Error Analysis
Estimation methods for error analysis of the test protocol are
based on certain assumptions concerning the accuracy of specific measurements
and the relationships between variables. The test protocols proposed here
require measurements of concentrations of the chemical as function of time at
3 pH values and two temperatures that differ by at least 10°.
• The error analyses that follow are based on the basic kinetic
rate laws cited in Section 2.6.3

l^ - ln(Co/C)/t

16
-------
kh = kA[H+] + S + V°H~]

11 i * -E/RT
V *N °r kB = Ae

Error Analysis for Ic : The estimate of the rate constant k^ is
related to the measured variables, concentration and time, by the following
regession equation. (Statisticians often designate the estimate of k as k,
but we will ignore the distinction in this discussion.)

. _nZtlnC- [Et][ZlnC] ,, ..
*h nZt2 - [It]2 (2'5)

where C is concentration of chemical measured at time t. This version of the
regression equation does not require that ln(C/CQ) = 0 at t = 0; that is, the
line is not forced through the origin and any significant departure from the
origin indicates bias in values of C at t > 0.

The intercept C , the concentration at t = 0, is obtained from
the equation

In/C \ = i-IlnC - k. (-It) (2.6)
\ oj n n n

The preferred measure of error in experiments of this kind is the standard er-
ror, a,* used here in the form a2 or the variance. The variance of k, from n
measurements is given by
a _ 1 [nlflnC]2 - [ZlnC]2
C -^2[ nZt2 - (Zt)

Equation (2.7) shows that a varies with — and ^ -7— and directly with a(C).

Estimation of Errors in k , k. , and k : For the recommended pH
values of 3, 7, and 11, equations 2.2-2.4 can be applied; hence, the variances
in k., k,., and k^ are given by

aa(kA) = I06a$ + 106a2 + 10-2a2t (2.8)
i(kN) = 10~8a2 + a2 + 10-8a?x (2.9)
2 4 - (2'7)
a2(kB) = 10-2af + 106af + K^o2! (2.10)
*
The standard error may be expressed as the standard deviation, (k ± cr), the
error ratio, a/k, or percent error (a/k) x 100.

17
-------
where al is a (\ at pH = 3)

a* is °2(\ at pH = 7)

a?! is o2(k_ at pH = 11)

Similar relationships hold for other pH values (see Appendix 2. A).

Estimation of Errors in Temperature Extrapolation of Rate
Constants kA, k^, and kg: When kA, kN, and kg have been deter-
mined at each of two temperatures, TI and T2, extrapolations of k., k^, and
k^ to a lower temperature T0 can be made by the relation

k(T0) - [kT1](1 + a)/[k(T2)]a (2.11)
where k may be k^, kN or kg, T0' + 0,>'«To>]' (2.U)
which applies only when a(k)/k < 0.4.

Error Analysis for Hydrolysis Kinetic Data: Effect of Reaction
Variables on the Error Ratio: Error equation (2.7) has been
used to estimate the standard error in kfo at 25°, 40°, and 55° based on the
assumption that the standard error in individual concentration measurements
for a chemical is ± 4 percent (a/c = 0.04) for all data points and that data
points are evenly distributed with time for one half-life. Under these condi-
tions, the error ratio o/k depends in the following way on the number of
sample points

a/k - 0.20(n - l)is[n(n + 1) ]~** (2.13)
where n is the number of samples. When n > 5, the error ratio changes nearly
with the square root of the number of sample points. For seven points,
(a/k) = 0.065; for fourteen points (a/k) - 0.050.

The value of (a/k) is more sensitive to the length of sampling
time, since, from eqn 2.7,

18
-------
a2
and
a *j —
We have assumed that seven data points were used for each rate measurement;
as a result a/k^ = 0.065 for values of k^ at all pH and temperatures. If two
half-lives were used instead of one for the standard reaction time, a/k =
0.033; or, analogously, if the precision of the concentration measurement were
doubled, a/k ^ 0.03.

We have used equations (2.8)-(2.10) to evaluate a2 for k^, kjj,
and kg at 25°, 40°, and 55° based on a value of a/k = 0.065 for kh at all pH
values and temperatures (seven points evenly distributed and one half-life).
Values of a2 were converted to a/k and are listed below.
Temperature o/k
kA
25 0.10 0.07 0.065

40 0.14 0.065 0.065

55 0.20 0.065 0.065
The magnitude of the error found in either kA, kjj or kg depends on the rela-
tive contributions of each rate process to the measured value of k^ at each
pH at one temperature; the relative importance of each process to the total
rate changes with temperature (see Section 2.6.4). In this case the larger
errors in kA are due to the relatively small contribution of kA at all pH
values and to its decreasing importance with increasing temperature relative
to kfl (lower value of EA than EN). Nonetheless, the error ratios (a/k) often
are the same as the error ratio (a/C) of k^ and close to the error ratio of an
individual measurement (0.04).

The effect on the error ratio of changing the measurement
strategy was also evaluated. For a set of six concentration data points each
having a precision of 4 percent (standard error) but distributed unevenly at
one-minute intervals, three at the beginning and three at the end of one half-
life, the error ratio for kA was about two-thirds as large as for the case of
evenly distributed data points. Less improvement was found for k^j and kg
where uneven distribution of data points resulted in 25 and 20 percent reduc-
tions in a/k for kN and IL, respectively.

19
-------
Temperature Extrapolation Error: Extrapolation of rate
constants at 40° and 55° to 25° were carried out using equations (2.11) and
using values of a2 from both measuring strategies, (2.12). Values of
(a/k), calculated from a2 and k, are listed below

q/k(extrapolated to 25°)
k_ even 7 pts 3 pts initial, 3 pts final

kA 0.37 0.19

k^ 0.16 0.12

k_ 0.16 0.13
o

The extrapolation of our idealized sets of data to 25° leads to errors ranging
from 19 to 37 percent in estimating k^; similar but smaller errors are ob-
tained for kjj and kg.

In general, the reductions in errors achieved by using uneven
sampling times at the beginning and at one half-life are not large enough to
justify recommending the practice; indeed, doubling the total measurement time
or reducing the measurement error will reduce the error in k^ more than use of
an uneven sampling strategy. Moreover, the need to ensure that the process
being measured actually follows a first-order relation provides additional ar-
gument for using an even sampling time strategy.

2.7 BACKGROUND*

2.7.1 Definition of Hydrolysis

Hydrolysis refers to a reaction of a compound with water, usually
resulting in the net exchange of some leaving group (-X) with OH at a re-
action center:

RX + H20 *- ROH + HX

The mechanism of the reaction may involve a cationic or anionic intermediate,
and the hydrolysis rate may be promoted or catalyzed by acidic or basic
species, including anion (OH~) and hydronium ion (H30+ or H+). The promotion
of the reaction by H30+ or OH~ is referred to as specific acid or specific
base catalysis, as contrasted to general acid or base catalysis encountered
with other cationic or anionic species, respectively.
*Much of this material has been excerpted from a recent publication on hy-
drolysis of organic compounds in water (Mabey and Mill, 1978).

20
-------
For this protocol we consider only specific acid or base catalysis
together with the neutral water reaction. The concentration of H30+ or OH
is directly measured by the pH of the solution (see Section 2.7.2), an easily
measured variable for aquatic systems. Although other chemical species can
be involved in hydrolysis reactions, their concentrations in aquatic systems
are usually quite low and their effects are minimal (see Section 2. 7. 3) .

2.7.2 Kinetics

Rate Laws
The rate law for hydrolysis of chemical RX usually can be put in the
form

kB[OH~][RX] + kA[H+][RX] + kN'[H20][RX] (2.14)

where kjj, kA, and kN* are the second-order rate constants for acid- and base-
catalyzed and neutral processes, respectively. Since the concentration of
water is nearly constant and much greater than the chemical RX, kN*[H20] is
a constant (kN) . The pseudo-first-order rate constant kn is the observed or
estimated rate constant for hydrolysis at a specific and constant pH and
temperature. Eq (2 .14) assumes that the individual rate processes for the
acid, base, and neutral hydrolyses are each first order in substrate. With
only a few exceptions, this is the case, and

t^ = kB[OH~] + kA[H+] + kjj (2.15)

From the autoprotolysis water equilibrium [eq (2.16)] eq (2.15) may be
rewritten as eq (2.17).

[H+][OH~] = K (2.16)
w

+ kA[H+J +kN (
From eq (2.17), it is evident how pH affects the overall rate: at
high or low pH (high OH~ or H+) one of the first two terms is usually
dominant, whereas at pH 7 the last term can often be most important. How-
ever, the detailed relationship of pH and rate depends on the specific values
of kg, kA, and kN. At any fixed pH, the overall rate process is pseudo first
order, and the half-life of the substrate is independent of its concentration:

tj^ - 0.693/1^ (2.18)

Eq (2. 17) is conveniently expressed graphically as three equations —
one each for the acid, base, and neutral hydrolysis reactions — in which log
kh is plotted against pH. The curves obtained are especially useful for
describing the effect of acid or base on the rate of hydrolysis. Figure 2.1
depicts a typical log k, versus pH plot for compounds that undergo acid-,

21
-------
CO

-------
water-, and base-promoted hydrolysis. It is obvious from eq (2.17) that the
upper curve in Figure 2.1 is a composite of three straight lines — (a) log k
= log kA - pH; (b) log kh = log kN, and (c) log kh = logtkgl^) + pH— with
slopes - 1, 0, and +1, respectively. The lower curve results when k^ «
] and kB[OH~].
Most log kh vs pH curves are found to have one or two areas of
curvature corresponding to pH values where two kinds of rate processes con-
tribute to the overall hydrolysis rate. The pH at which the two processes
contribute equally to k^ is given by the intercept, I. Thus in Figure 2.1
the intercept IAN corresponds to a value of pH where kA[H+] = k^; similarly,
INB corresponds to kg [OH ] = k^. In cases where k^, kg, or kjj = 0, only one
intercept is observed. Values of pH corresponding to I may be calculated
readily from the values of k , k^, and k :
INB ' -1°8(kBKw/kN) (2'20)

1^ = -[log(kBKw/kA)]/2 (2.21)

Rate Constants
The second-order rate constants kjj ' , kA, and kg for hydrolysis are
in the units of concentration"1 time"1; for solution kinetics the specific
units are commonly molar"1 seconds"1 (abbreviated M"1 s"1, or M"1 sec"1).
The concentration of pure water is 55.5 M and is essentially unchanged after
hydrolysis of dilute solutions of chemicals so that kN*(55.5) = kjj. 'The units
of kfl are then time"1 (sec"1 or s"1). The units of k^ and kg are commonly
M"1 sec"1. Units of kh, the observed rate constant for hydrolysis, are time"1.

Effect of Structure on Reactivity
pH-rate profiles for several classes of hydrolyzable organic
chemicals are shown in Figures 2.2 through 2.5. These curves indicate the
relative importance of acid, base, and neutral hydrolysis processes for these
chemicals, their absolute rate constants (k, ) , and half-lives estimated from
1^, all at 25°C.

Comparison of these curves shows how different structures respond to
acid or base promotion: alkyl halides have no acid-promoted reaction, whereas
epoxides are nearly insensitive to base-promoted reactions. However, carbonyl
derivatives such as esters, amides, or carbamates undergo both acid- and base-
promoted processes. Some carbamates and esters also undergo neutral hydrolysis.

Among alkyl halides , k^ (= kjj) spans six orders of magnitude between
methyl fluoride and _t-butyl chloride, but most epoxides have a kjj very close
to 1 x 10~6 sec"1; esters and amides exhibit significant differences in k^
depending on the steric and electronic properties of substituents at the re-
active center. In general, esters hydro lyze about 1,000 times as rapidly as
23
-------
Z/l.
'3dll dIVH
o
c.
I
•o

-------
Z/l.
•o
§
E
CN
E
CM
•o
CO
<
I-
g-
A

A
o
(N
I
to
0)
•a
•H
X
o
D.
W
to
•H
cn
O
M
•o
>>
33
CM

0)
D
so
601
25
-------
2/1,
'3dH d~IVH
I
ID
CM

CM
CM
in
o
CM
CM
O=0
O
0=0
o
0=0
a
1/1
CN
CO
t-l
s
3
bO
•H
tu
60,
26
-------
Z/l,
J1VH
CM
(M
Ifl
CM
CM
8
CM
o
CM
CM
<
I-
X X
o
LO
CM
tn

-------
amides at the same pH. Half-lives at pH 7 and 25°C for hydrolyzable chemicals
vary from several hundred centuries for some amides to only a few minutes for
tertiary halides and aromatic epoxides .

Effect of Temperature
The effect of temperature on the rate constant for a specific hy-
drolysis process can be expressed in several ways, all of which are variants
of the general relation (where T is in degrees Kelvin)

log k = -A/T + B log T + C (2.22)

There is no uniform practice for expressing values of A, B, or C; different
investigators have used different versions of eq (2.22), usually in more
familiar Arrhenius or absolute rate theory format.

log k = log A - E/RT Arrhenius (2.23)

log k - log(kT /h) - AH*/RT + AS*/R Absolute (2.24)
Rate Theory

We choose to use the Arrhenius form to express the temperature
dependence of k because of its simpler form and application.. While some ac-
curacy (e.g., heat capacity terms) is gained by using eq (2,22), most ex-
perimental data are not precise enough to justify the use of the three-term
expression. Units of A are the same as for k, units of E are in kcal/mole or
kjoule/mole (1 kjoule = 4.18 kcal) , and units of K are M2 .

KW varies with temperature (Harned and Owen, 1958) and follows the
relation log K = -6013.79 - 23.6521 log T + 64.7013
w T

Temperature ,°K -logK
-- * ' — v w

273 14.943
283
293
298
303
313
323
333
14.535
14.167
14.000
13.833
13.535
13.262
13.017
A temperature correction should be applied in all calculations involving
or [OH~].
28
-------
Effects of Ionic Strength and Buffer Salts
The effects of ionic strength on hydrolysis reactions are difficult
to predict: they can lead either to rate acceleration or retardation, de-
pending on the substrate, the specific salts, and their concentration. Salt
effects of this kind are associated with changes in activity coefficients of
ionic or polar species or transition states with significant charge
separation; no bond making or breaking is involved in such interactions.

Table 2.1, which lists some effects of different nonnucleophilic
salts on the hydrolysis of several kinds of compounds, shows that in most
cases rather massive amounts of these salts cause only 30-40% changes in rate
constant.
TABLE 2.1. SALT EFFECTS IN HYDROLYSIS REACTIONS

a
Compound Salt, M Solvent, t, &C k/k

t-BuBrLiBr, 0.106590/10 acetone-water,1.44

323

Y-Butyrolactone Nad, 0.51 0.10M HC1, 25 1.08

NaCIO,., 0.40 0.10M HC10,., 25 0.95

CH3C02Et LiCl, 2.00 0.15M HCIO^, 25 1.35

NaClO^., 2.00 0.15M HC10,., 25 1.00

CH3C02Me NaCl, 0.100 0.01M NaOH, 35 0.96

k/k is the ratio of rates with (k) and without (k )
sal?.
Another effect of nucleophilic added salts is to accelerate the rate
of hydrolysis by a general acid- or general base-promoted process (where H+
or OH~ promoted reactions are specific acid or base processes) . Some ar.ions
can effect displacement of leaving groups more rapidly than water (k^) and in
doing so catalyze hydrolysis via the sequence

RX + A~ — RA + X~

RA + H20 i—- ROH + HA

(HA + X~ J A~ + HX)

The use of nucleophilic anions such as phosphate or acetate at 1.0 M to 0.01
M to buffer hydrolysis reactions in the pH range 5-9 is a common and useful

29
-------
practice. The general acid- or base-catalyzed term kG[A ] added to eq C2.15) tc
give

\^ = kB[OH"] + kA[H+] + kjj + kG[A*] (2.25)

can often be as large as the specific acid or base terms because both [H ]
and [OH ] are relatively low in the buffered region. As a result, the value
of kjj may increase significantly in the presence of buffer salts. Table 2.2
lists values for \S.Q relative to k^ for specific ions in displacement reactions.
However, the fact that primary and secondary salt effects aliso may be
important makes it difficult to predict the overall direction or magnitude of
such rate changes.
TABLE 2.2. NUCLEOPHILICITY CONSTANTS (n) FOR DISPLACEMENT REACTIONS
. . a
Anion n
Cl
soiT
NO 3
HCOl
HPO*~
OAc~
H20
3.04
2.5
1.03
3.8
3.8
2.72
0.00
aFrom the Swain-Scott relation logC^/k^) = ns, where s is a substrate-
dependent constant that varied from 0.75 to 1.5; s for MeBr is 1.00
(Swain and Scott, 1953) kg and kfl refer to specific rate constants
for anion and water, respectively.
Effect of Solvent Composition
Chemists have commonly used mixed organic and water solvents to
obtain concentrations of organic chemicals that make laboratory work con-
venient. Methanol, ethanol, dioxane, dimethyl sulfoxide, and acetone have
been often used as cosolvents with water. While extrapolation of rate data
from mixed solvents to pure water can be accomplished with moderate success
for some hydrolytic reactions by use of empirical relationships such as the
Winstein-Grunwald equation, the extrapolation contributes additional un-
certainty. Additionally, the meaning of pH in such mixed solvent systems
becomes questionable and requires what amounts to a double extrapolation to
conditions of pH in pure water.

30
-------
The effect of solvent composition is most pronounced in those re-
actions in which charge separation is well developed in the transition state,
as, for example, in solvolysis of t-butyl chloride. In ethanol-water
mixtures this hydrolysis is purely solvolytic—that is, no effect of acid or
base is noted. Table 2.3 summarizes values of kjj, which increases by a
factor of nearly 10* on going from 90% ethanol to water.
TABLE 2.3. EFFECT OF SOLVENT COMPOSITION ON THE RATE OF HYDROLYSIS OF
t-BuCl IN ETHANOL/WATER AT 25°Ca
Percent
ethanol k,., s"1
90
70
50
40
0
1
9
4
1
1
.7K-6)
.14(-6)
.03C-6)
.26(-4)
•0(-2)b
*From Hughes (1935).
Estimated from data in Table 4.1 of
Mabey and Mill (1978).
Effects of Metal Ion Catalysis
A number of alkaline earth and heavy metal ions catalyze hydrolysis
of a variety of organic esters (Bender, 1963; Martell, 1963). The principal
function of the metal ion appears to be to increase the effective concentra-
tion of H0~ at pH levels where its concentration would otherwise be neg-
ligible (Martell, 1963; Buckingham and Engelhardt, 1975). This explanation
is by no means universally applicable, especially to enzyme-like processes
where prior complexation seems a necessary prelude to bond cleavage.
Nonetheless, the kinetic features of several kinds of ester hydrolyses are
similar, and they follow the same rate law

where k^, kjj, and kg have their usual significance, kj^ is the metal ion
catalysis constant, M is the total metal ion concentration, and KA is the
equilibrium constant for dissociation of the hydrated metal ion complex
M(H20)2+:

M(H20)*+ 3=: M(HaO)_,(OH)+ + H+
-------
Kinetic analysis of several metal ion-catalyzed reactions indicates that at
the concentrations of Cu or Mg ion found in aquatic or soil systems, the
contribution of these reactions to the total rate of hydrolysis would be
negligible.

2.7.3 General Environmental Considerations

Effects of Ion Concentration, Temperature, and pH
The preceding discussion shows that only ionic concentration,
temperature, and pH will affect rates of hydrolysis in most natural waters.
A review of water analyses for several hundred rivers indicates that the con-
centrations of inorganic salts in most aquatic environments are usually too
low to have any effect of hydrolysis rates. Similarly, the concentrations of
ions that can promote hydrolysis through catalytic mechanisms are generally
so low that the catalyzed reaction rates will not compete with the specific
acid- and base-promoted and neutral hydrolysis reaction rates. Furthermore,
metal ions present in aquatic environments are probably complexed to natural
organics and are not even available as catalysts at the low concentrations
observed in water analyses.

Temperatures commonly encountered in aquatic systems range from
freezing in some lakes during winter to 30°C in some ponds during summer.
Since hydrolysis rates can vary by factors of 2 to 5 with each 10°C change,
hydrolysis rates in the environment may vary seasonally by an order of
magnitude. For compounds that do not show pH-dependent hydrolysis rates,
temperature will be the major factor influencing their hydrolysis rates.

The pH values of natural waters can range from about pH 5 to 9, but
they are usually close to 6.5 and result from several naturally occurring
buffer systems. Eq 2.1 shows that for acid- or base-promoted reactions, a
change of one pH unit will change the rate by an order of magnitude (at a
maximum). Thus, for an ester hydrolysis (see Figure 2.4), the hydrolysis
rate may increase by four orders of magnitude as the pH increases from 5 to 9.

Review of Literature on Hydrolysis in Natural Waters
A wealth of information has been published on the hydrolysis of a
wide variety of organic compounds. However, most of the hydrolysis
literature relating to environmental behavior concerns pesticides,
particularly phosphorous esters. Much of this literature is incomplete for
the range of either pH or temperature studied. Controls are seldom carried
out (or at least reported) nor are precautions taken to eliminate adventitious
processes such as volatilization or biodegradation. Effects of buffer salts
and added organic solvents are often unrecognized.

Another problem with some reported studies is lack, of data on effect
of pH on the hydrolysis rate constant. Without such data, calculation of rate
constants or half-lives at other pH values is not possible. In some studies
the presence of buffer catalysis causes high hydrolysis rates, which intro-
duces errors in the pH rate profile. When acid- and base-catalyzed processes
are important, it may be difficult to determine whether a rate constant at an
intermediate pH is due to a contribution from a neutral hydrolysis process or
to buffer catalysis.

32
-------
Few studies have been conducted that compare rates of hydrolysis of
chemicals in buffered and in natural waters. This knowledge is critical to
understanding hydrolysis in the environment. Results of some limited studies
suggest that hydrolysis rates are the same in natural and buffered waters at
the same pH and temperature; that is, naturally occurring organic and in-
organic materials present in low concentrations in natural waters do not
catalyze hydrolysis reactions.

Wolfe et al. (1977) studied the hydrolysis of methoxychlor in buf-
fered waters and in two natural waters. Hydrolyses were carried out in buf-
fered waters in the pH range 3 to 12 and at four temperatures between 45° and
85°C; below pH 8, the hydrolysis rate was found to be independent of pH. Rate
constants at 27°C were calculated by extrapolation of these data. Hydrolysis
reactions were carried out at 858C in waters from the Oconee River (Athens,
Georgia), pH 6.6, and from the Alabama River (Birmingham, Alabama), pH 7.2.
Wolfe and coworkers found that reactions in the buffered and natural waters
obeyed first-order kinetics and that there was no detectable difference in the
hydrolysis rates between the two types of waters. At 85°C and below pH 8, the
first-order (neutral) hydrolysis rate constant was about 5.2 x 10~5 s"1, cor-
responding to a half-life of about 3.7 hr.

Zepp et al. (1975) investigated the hydrolysis of
2,4-dichlorophenoxyacetic acid esters (2,4-D) in buffered waters and in water
from the Withlacoochee River (pH 8.1). They report that the hydrolysis rate
measured in this water agreed well with the rate calculated from data
obtained from experiments in buffered waters. The pH rate profile calculated
from this data is presented in Figure 2.4.

Wolfe et al. (1977a) measured the hydrolysis of malathion in buf-
fered waters and in a natural water sample from the Withlacoochee River in
southern Georgia (pH 8.2). The experimentally determined half-life in the
river water was,22 hr, in good agreement with the half-life of 20 hr cal-
culated from data obtained from experiments in the buffered waters.

Smith et al. (1977) investigated the hydrolysis of methyl parathion
in buffered waters, in four natural waters, and in one distilled water solu-
tion containing 9.5 ppm humic acid. These data are summarized in Tables 2.4
and 2.5; the pH-rate profile is given in Figure 2.6. The good agreement
among the data in solutions below pH 8, where the neutral hydrolysis is
dominant, indicates that natural waters do not catalyze hydrolysis of methyl
parathion. In the early phase of the study, which used waters containing
0.067 M phosphate buffers, there was evidence of buffer catalysis. Subse-
quent use of acetate, borate, and phosphate buffers at 0.01 M concentrations
eliminated the effect of buffer catalysis.

Weber (1976) has studied the hydrolysis of parathion in seawater.
Data for the hydrolysis at 70°C in solutions that contain less than 10 ppm
parathion are given in Table 2.6. Although it is difficult to reconcile the
data with all the experimental variables in each experiment, by analogy to
methyl parathion the half-life should be independent of pH up to about pH 8.
From the data in Table 2.6, it appears that the rate of parathion hydrolysis
is.increased by increasing the ionic strength of the solution. Also, by

33
-------
TABLE 2.4. FIRST-ORDER RATE CONSTANTS k
FOR HYDROLYSIS OF METHYL PARATHIONa
AS A FUNCTION OF pH

3
5
6
7
8
9
10
11
PH
.00
.00
.00
.00
.00
.00
.00
.25
kh x 107
(sec-1)
6.
6.
8.
7.
9.
16.
67.
747
80
45
08
44
27
37
70
(±
(±
(±
(±
(±
(±
(±
(±
0.
0.
0.
0.
0.
1.
1.
26)b
33)
52)
24)
17)
39)
1)
166)
Experiments used 26 yg ml"1 (1.0 x 10"'' M)
methyl parathion at 40°C. Solvent was 1%
acetonitrile in buffered distilled water.
TABLE 2.5. FIRST-ORDER RATE CONSTANTS kh FOR
HYDROLYSIS OF METHYL PARATHION IN NATURAL WATERS3

Natural water source
Lake Tahoe
Lake Taho e
Coyote Creek
Distilled water with 9.5
ppm humic acid^
Aucilla River
Searsville Pond
PH
7
7
7
5

6
7
.6
.6
.8
.25

.07
.5
12
6
7
5

6
6
kh x 107
(sec'1)
.41
.31
.54
.99

.10
.83
(±
(±
(±
(±

(±
(±
1.
0.
0.
9.

0.
0.
44)b'C
36)
21)
53)d

81)
08)
Except where noted, experiments used 26 yg ml"1
(1.0 x 10"'* M) methyl parathion at 40°C. Solvent was 1%
acetonitrile in filtered natural water.
Standard deviation.
jO.26 yg ml"1 methyl parathion was used.
2.60 yg ml"1 methyl parathion was used.
34
-------
ra
3

T3
01
2/l»'3dlTd1VH

en
n
a>
c
00
PI
N
2 S
I
a
DOT
Ol
0)
Ij
4J 3
en
•H O
TJ «
33
•a u
0) T3

0) rH 4J
<4-l rH O
"4-1 -H >,
3 4J O
& w u
•H
CO *• ^
.O ^-s C
u"t O
J3 • CU
4-1 CN
•H 0)
3 0) rH
en ja
4J Cfl
C H
•H
>
05
o «
PH CO 01
4-1 CO
..s *
u o
-3- S-i O
4-i in o

-------
TABLE 2.6. HYDROLYSIS HALF-LIVES OF PARATHION IN VARIOUS AQUEOUS REACTION
MEDIA AT 70°C.

Reaction media
Estuarine
Seawater,
water, salinity 25.7gl~1
salinity
32.5gl~1
Seawater + concentrated HC1
Distilled
Distilled
Distilled
Buffer I,b
Buffer II,
water
water +
water +

30 g I-1 NaCla
dilute NaOH
total salt 30 g I'1
c total
salt 0.6 g I"1
PH
7
8
•v 1
5
5
8
7
7
Half-life (hr)
.8
.0

.9
.5
.6
.9
.5
30
17
19
39
21
22
15
31
.0
.2
.3
.2
.0
.7
.7
.8
± 0.
± 0.
± 0.
± 1.
± 0.
± 0.
± 0.
± 0.
9
3
5
3
7
6
2
7
j*0.514 M NaCl, ionic strength = 0.5.
Contains 0.063 M Na2HPO<., 0.003 M KH2PO,., and 0.313 M NaCl, ionic strength
= 0.5.
CContains 0.002 M Na2HPO<. and 0.001 M KH2POA, ionic strength = 0.007.
TABLE 2.7. HYDROLYSIS OF ZECTRAN IN BUFFERED AND NATURAL WATER.

Buffered waters
PH
5.94
Temperature
ki x 103
t^ (days-
Temperature
kt x 103
t^ (days"
Temperature
ki x 103
t, (days-
, 10°C
(days-1)
x)
, 20°C
(days-1)
x)
, 28°C
(days"1)
l)
6
105
15
46
19
37
.6
.1
.0
.5

.3
PH
7.00
9.2
75.5
27.0
25.7
100
6.9
pH
8.42
20
35.4
160
4.6
550
1.3
Natural
Solution A,
pH 8.2
12
59.3
76
9.1
470
1.5
waters
Solution B,
pH 8.2 - 8.4
12
58.
110
6.
540
1.

3
a
See text for sources.
36
-------
analogy to the previously discussed work on methyl parathion, some buffer
catalysis effect may be present in the experiment in which the solution desig-
nated Buffer I was used (see Table 2.6). Although the effects operative in
the hydrolysis of parathion in Weber's studies are complex, there appears to
be no clear evidence that seawater possesses any particular catalytic effect
other than ionic strength.

Matthews and Faust (1977) have reported the hydrolysis of Zectran,
4-dimethylamino-3,5-xylyl methyl carbamate, in buffered waters at pH values
of 5.94, 7.00 and 8.42, and in water from the Musconctcong River, a stream in
CentralNew Jersey (pH ^ 8). The hydrolysis experiments were carried out at
three temperatures—10°C, 20°C, and 28°C. Two solutions of the natural
waters were prepared—one was filtered through a Millipore 0.45-ym filter
(Solution B) and the second comprised half filter-sterilized water and half
untreated river water (Solution A). The data are presented in Table 2.7.

From the data reported, it is impossible to construct a pH-rate
profile in terms of a neutral and base-promoted hydrolysis. Moreover, since
0.05 M phosphate buffers were used, buffer catalysis is suspect. Because the
hydrolysis rate constants were nearly the same in the unsterile and filter-
sterilized water, biodegradation was not occurring. The slightly faster hy-
drolysis of 20°C in the sterile water compared to the unsterile water was
noted and could not be explained by the authors; it is probably an ex-.
perimental artifact.

If we assume that the hydrolysis rate at pH 8.42 in buffered water
contained a minimal contribution from buffer catalysis, then the hydrolysis
rate constants in the river water are in good agreement, which shows that no
significant catalysis is occurring in the natural water.

The carbamate Sevin (N-methyl-1-naphthylcarbamate, also called
Carbaryl) has also been the subject of hydrolysis studies, and of a
controversy regarding the effect of natural waters on hydrolysis rates.
Karinen et al. (1967) studied the hydrolysis of Sevin in seawater. In ex-
periments carried out in the dark (Sevin is also light sensitive), in
distilled water, in autoclaved seawater, and in filtered seawater similar
degrees of transformation of Sevin were found after 4 days. All waters were
adjusted to pH 7.8 with phosphate buffer. The authors reported only that .the
amount of Sevin hydrolyzed at 17°C, 20°C, and 28°C was 44%, 55%, and 93%,
respectively. From the datum point at 20°C, we can calculate a half-life of
3.5 days.

A study on the hydrolysis of Sevin in 0.01 M phosphate buffers at
20°C over a pH range of 7 to 10 was conducted by Aly and El-Dib (1971), and
they report a half-life of 1.3 days at pH 8. Citing a paper by Fukoto et al.
(1967), which indicates that phosphate buffer does not affect hydrolysis rates
of nitrophenyl carbamates, Aly and El-Dib concluded that the ionic strength
of seawater was responsible for the slower rate of Sevin hydrolysis in sea-
water reported by Karinen.

A subsequent paper by Wauchope and Haque (1973) also reported the
hydrolysis of Sevin in NaOH solutions at pH values of 9 - 10. These authors

37
-------
claim that the rate constants obtained in phosphate buffers by Aly and El Dib
were too high, and concluded that there "... was little difference in
carbaryl hydrolysis rate constants in NaOH solution versus seawater."

This apparent conflict in data shows several points commonly en-
countered in literature information, all of which arise from too few ex-
periments or, at least, insufficient data that are reported. Assuming that
the pH values of the studies of Karinen and Aly/El-Dib were actually 7.8 and
8.0, respectively, as reported, and that the reaction is a base-promoted
process, then the first-order rate constant at pH 7.8 should be 0.63 of that
at pH 8.0. Correcting the datum point of Karinen at pH 7.8 to 8.0 gives a
half-life of 2.2 days, compared to 1.3 days reported by Aly and El Dib. This
difference, less than a factor of two for measurements in two different
laboratories, seems relatively small.

Neither Aly and El-Dib (1971) nor Wauchope and Hague (1973) attempted
to repeat the same experiments reported by the previous investigator. All
three papers neglect in some way to describe adequately the experimental pro-
cedures used and the data obtained. Therefore, it is not possible to make the
comparisons necessary to resolve the discrepancies.
38
-------
2.8 REFERENCES

Aly, 0. M., and M. A. El-Dlb. 1971. Studies on the Persistence of Some
Carbamate Insecticides in the Aquatic Environment - I. Hydrolysis of
Sevin, Baygon, Pyrolan and Dimetilan in Waters. Water Research 5: 1191-
1205.

Bender, M. L. 1963. Metal Ion Catalysis of Nucleophilic Organic Reactions
in Solution. Advan. Chem. Ser. 37: 19-36.

Buckingham, D. A., and L. M. Engelhardt. 1975. Metal Hydroxide Promoted Hy-
drolysis of Carbonyl Substrates. J. Am. Chem. Soc. 97:5915-5917.

Fukoto, T. R., M.A.H. Fahmy, and R. L. Metcalf. 1967. Alkaline Hydrolysis,
Anticholinesterase, and Insecticidal Properties of Some Nitro-Substituted
Phenyl Carbamates. J. Agr. Food Chem. 15(2):273-281.

Harned, H. S. and R. B. Owen. 1958. The Physical Chemistry of Electrolytic
Solutions, Reinhold Publishing Corp., New York, pp. 638 and 645.

Hughes, E. D. 1935. Mechanism of Substitution at a Saturated Carbon Atom.
Part V. Hydrolysis of t-Butyl Chloride. J. Chem. Soc. London. 255-
258.

Karinen, J. F., J. G. Lamberton, N. E. Stewart and L. C. Terriere. 1967.
Persistence of Carbaryl in the Marine Estuarine Environment. Chemical
and Biological Stability in Aquarium Systems. J. Agr. Food Chem. 15(1):
148-156.

Mabey, W. R., and T. Mill. 1978. Critical Review of Hydrolysis of Or-
ganic Compounds under Environmental Conditions, J. Phys. Chem. Ref.
Data 7(2):383-415.

Martell, A. E. 1963. Metal Chelate Compounds as Acid Catalysts in Solvolysis
Reactions. Advan. Chem. Ser. 37:161-173.

Matthews, E. W., and S. D. Faust. 1977. The Hydrolysis of Zectran in Buf-
fered and Natural Waters. J. Environ. Sci. Health, B12(2): 126-146.

Smith, J. H., W. R. Mabey, N. Bohonos, B. R. Holt, S. S. Lee, T.-W. Chou,
D. C. Bomberger and T. Mill, 1977. Environmental Pathways of Selected
Chemicals in Freshwater Systems. Part II. Laboratory Studies.
EPA-600/7-78-074.

Swain, C. G., and C. R. Scott. 1953. Quantitative Correlation of Relative
Rates. Comparison of Hydroxide Ion with Other Nucleophilic Reagents
Toward Alkyl Halides, Esters, Epoxides and Acyl Halides. J. Am. Chem.
Soc. 75:141-147.
39
-------
Wauchope, R. D., and R. Hague. 1973. Effects of pH, Light and Temperature
on Carbaryl in Aqueous Media. Bull. Environ. Contam. Toxicol. 9(5):257-
260.

Weber, K. 1976. Degradation of Parathion in Seawater. Water Research 10:
237-241.

Wolfe, N. L., R. G. Zepp, J. A. Gordon, G. L. Baughman and D. M. Cline.
1977a. Kinetics of Chemical Degradation of Malathion in Water. Environ.
Sci. Technol. ll(l):88-93.

Wolfe, N. L., R. G. Zepp, D. F. Paris, G. L. Baughman and R. C. Hollis. 1977.
Methoxychlor and DDT Degradation in Water: Rates and Products. Environ.
Sci. Technol. 11(12):1077-1081.

Zepp, R. G., N. L. Wolfe, J. A. Gordon and G. L. Baughman. 1975. Dynamics
of 2,4-D Esters in Surface Waters. Hydrolysis, Photolysis and Vaporiza-
tion. Environ. Sci. Technol. 9(13):1144-1150.
40
-------
*
Appendix 2.A

A GENERAL SOLUTION FOR THE HYDROLYSIS

REACTION RATE EQUATIONS
Using determinations of k. at three values of pH(say pH = x,

x + y and x + y + z), the first order reaction rates are obtained by solving

the equations

v i n~xi, j. i j. i n~14 + xi
) = 10 kA + kN + 10 kg

+ y) = 10~(X + y)kA + k + 10'14 +(x + y\ (2.A.1)
AN &

+ y + z) = I0"(x + y + z)kA + k, + 10~14 +(x + y + z\
for kA, kj^.
The solution of these equations is

kA " I {10X (1 ~ 10~Z) kh(x) ~ 1C)X (1 ~ 10~y ~Z) ^i^ + y)

+ 10X ~ z (1 - 10~y)kh(x + y + z)j (2U.2)
- 10
~2z
)kh(x) + (1 - 10~2y ~2Z)kh(x + y)
-10~Z(1 - lO'^lCx + y + z)
kg = i {l014-x-2y-2(l-10-2)kh(x)-1014-X-y-2(l-10-y-2)kh(x + y)

+ 1014~X~y~2(l-10"y)kh(x+y+z)>

where B - 1 - 10~y - 10~Z - 10~2y~2z + 10~2y~Z + 10~y~2z
*This appendix was prepared by Francis W. Dresch of the Statistical Analysis

and Computation Department.
41
-------
If the lowest pH is 3 and the increments are at least 2—that is,
ifx>2, y>2, z> 2—3 = 1 and other factors such as 1 - 10"^ are close
to one. The solution can then be written more simply as

x) - 10Xk (x + y) + 10X ~ Zk, (x + y + z)

kN --10~ykh(x) + k^x + y) -10~zkh(x + y + z) (2.A. 3)
i i «14-x-2y-z, , s , -14-x-y-z, ... . , , _14-x-y-z. , . , s
k^ = 10 J k,(x) ~ 1° k,(x + y) + 10 ' k,(x+y+z)

For the recommended values of pH at 3, 7, 11 we have x=3, y=z=4 and
these equations become those given in Section 2.6.3, equations 2.2 and 2.4.
For this case, the variances are related by equations 2.8 through 2.10 given
in Section 2.6.8.

In general, the coefficients in the variance equations are the squares
of those in the equations for the relations among the k's. The coefficients
in (2.A.3) must be squared to obtain relations among the variances. Thus we
have in general

a2(k.) = 102x a2(x) + 102x a2(x+y) + 102x~2z a2(x+y+z)
A

a2(kN) = 10~2y a2(x) + a2(x + y) + 10~2z a2(x + y + z) (2.A.4)
2f. . ,n28-2x-4y-2z 2. . . . _28-2x-2y-2z 2, . .
a (1O - 10 * a (x) + 10 J a (x+y)
where a2(x) - a2[kh(x)]

a2(x + y) = a2[kh(x + y)]

and a (x + y + z) = O2[kh(x + y + z)] .
42
-------
*
Appendix 2.B

TEMPERATURE EXTRAPOLATION
1. Extrapolation to Lower Temperatures

From the Arrhenius relation for either k , k , or k^

k(T) = Ae-E/RT = A(e-E/R)1/T = AP^

—E/R
where P = e . For two measured temperatures T.. and T-» we have
k(T2)/k(T1) -

or p = [k(T2)/k(Tl)]TlT2/(Tl~T2)

If T is the extrapolation temperature and T < TI< Ta, we have

k(TQ)/k(Ti) =
or k(TQ) = k(Ti) [k(T2)/k(Ti)]'T2(Tl-To)/To(T2-Tl)
where a = T2^Tl~To^ > 0. We thus have finally :

T0(T2-Ti)

k(T) = [kCTO]1 + a!k(T2)]~a (2.B.2)
which is applicable to each of the rate constants k. , Ic,, k

2. Expected Value and Standard Error of Extrapolated Rate Constants

If errors in measurement of the logarithm of the concentrations are

normally distributed with zero mean and constant standard error a, the
*This appendix was prepared by Francis W. Dresch of the Statistical Analysis

and Computation Department

43
-------
statistical errors in the estimates lc of the rate constant: also follow a
normal distribution because these estimates are linear functions
of the logs of the concentration. Moreover, the estimates k , £ , and £. are
also normally distributed since these are each linear functions of the relevant
kjs for each measured temperature. However, the extrapolating formula (2.B.2)
above does not lead to a normal distribution for k(T ) even though k(Ti)and
k(T2) are normally distributed. The expected values°for k(T ) and a[k(T )]
o o
can be calculated from series expansions as follows:
E[k(TQ)] = E[k(T1)1'KX k(T2)"a] = EUCT!)1"**] E [k(T2)"a] (2.B.3)

because observations at T are independent from those at T,, . Similarly
E[k(TQ)2] = EtkCT^2^2] E[k(T2)~2a] (2.B.4)

and a2[k(TQ)] = E[k(TQ)2] - {E[k(TQ)]}2

= E[k(T1)2a+2]E[k(T2)~2a]- {Etkdi)1"^]} 2{E[k(T2)"a]} 2 (2.B.5)
The series expansion is needed to estimate the expected value of (in general
not integer) powers of a normally distributed variable k [either k(Ti) with
exponents 1 + a and 2a + 2 or k(T2) with negative exponents-a and -2or] . If k
is normally distributed with mean y and standard error a, we are interested in
"
E(km) = -—=-! (y+a x)m e" T X dx = J== (1 + - x) e 2 dx (2.B.6)
V 27T -L
This could be evaluated in terms of moments of x it m is a positive integer
by expansion of
by the binomial theorem. For noninterger m or negative m the binomial expan
sion becomes an infinite series, which converges only for
To employ the series expansion we must truncate the normal distribution
symmetrically at a point L, cutting off the distribution for x>Land x < - L.
The values are then defined to be

E(km)
where — LaL. IfL= 2, for example, we must exclude k's for which
the k < 2 a(£)' Under these conditions we have
44
-------
E(km) =
where E(x )
L 2 x

xn e dx,
_1 x 2
dx
2n
Evidently E(x ) = 0 for n = 0, 1, 2, . . .

Integration by parts for even n gives

, 2n»
E(x )
,_ i \ T-. / 2n— 2. 2n—
(2n - 1) E(x ) -cL
where c = \/ —
VST
- i 2

2 X dx
Thus E(x ) = E(0) -cL-l-cL
E(x4)

etc.

We thus have
E(km)
3E(x2) - c L3 = 3 - c(L3 + 3L)
E[k(TQ)]
£

I-
r

jo
(1 - c L) +...]
(l - c D-f..
a2 2

-i (1 - c L) +...|
(2.B.8)

(2.B.9)
(2.B.10)

(2.B.11)

(2.B.12)

(2.B.13)
(2.B.14)

(2.B.15)
:.B.i6)
and the bias in k(T ) from use of equation (2.B.2) is of the order of
ct(q
(1 - c L)<
J+ pa[k(T
k(T.
ffl
(2.B.17)
Similarly by use of (2.B.3), (2.B.5), (2.B.14), and (2.B.15) we have
45
-------
a[£(T)]
K(TQ)
= (1 - c L) < (a + 1)'

i- \ 2n
2 [~a[k(T2)P21
+ a
(2.B.18)
p
where terms Involving y
|2n
of order 2 n > 2

have been neglected. Note that for L = 1.95996 for which

2
L i x
dx =0.95, c = 0.12304 and 1 - c L = 0.75884
-L
For L = 3.09023 for which
L
L
dx = 0.998,
c = 0.0067477 and 1 - c L = 0.97915.
46
-------
Appendix 2.C

KINETIC ANALYSIS OF PARALLEL FIRST-ORDER REACTIONS*
For the reactions
k2 ^

k3
A - >-D
the loss of A and appearance of B, C, and D can be formulated as
d[A]/dt = (ki + k + kg) [A] = k[A]

In[A /A ] = kt

° A A -kt
At = Aoe

However since

d[B]/dt - kilA]

d[B]/dt = kxA e"kt
o
Then
Similarly, for C and D
and
[B]t - (k1[Ao]/k)(l-e"kt)
[C]t - (ka[Ao]/k)(l-e~kt)
From Frost, A. A., and R. G. Pearson, Kinetics and Mechanism (John Wiley and
Sons, New York, 1967) p. 148.

47
-------
[D]t = (k3[Ao]/k)(l-e~kt)

[B] t/[C] t = ki/ka

[BJt/[D]t = kx/ks

Since all products vary exponentially with the same rate constant k, all
products have the same half-life

tt = In 2/k
•*i

despite having different rate constants.

The rate constants kx, ka or k3 may be evaluated from a plot of concen-
tration of product against l-e"^ where k for loss of reactant is evaluated
in the usual way. The slope of the straight line (for B) is kx[A ]/k.
48
-------
CHAPTER 3. PHOTOLYSIS IN WATER

W. R. Mabey, T. Mill, and D. G. Hendry

3.1 INTRODUCTION 51
3.2 SUMMARY 51
3.3 CONCLUSIONS 52
3.4 RECOMMENDATIONS 52
3.5 SCREENING TESTS 53
3.5.1 Purpose 53
3.5.2 Procedure 53
3.5.3 Criteria for Screening Tests 53
3.5.4 Rationale 56
3.5.5 Scope and Limitations 56
3.6 DETAILED TESTS 57
3.6.1 Purpose 57
3.6.2 Direct Photolysis Half-Life from e\, L\, and Data 57
3.6.3 Measurement of Absorption Coefficients, e^ 62
3.6.4 Lx Data 64
3.6.5 Measurement of Reaction Quantum Yield 65
Photochemical Apparatus for Procedures Ql and Q2 65
Procedure Ql: High Optica-1 Density Actinometer 65
Procedure Q2: Low Optical Density Actinometer 67
Procedure Q3: Sunlight Actinometer 68
3.6.6 Rationale 69
3.6.7 Scope and Limitations 69
3.6.8 Error Analysis 69
Error Analysis for kz 70
Error Analysis for I0xr 71
Error Analysis for kp 71
Error Analysis for $ 72
Error Analysis for k 72
3.7 BACKGROUND ? 74
3.7.1 Definition of Photolysis 74
3.7.2 Kinetics of Photochemical Processes 74
3.7.3 Kinetics in Solution 75
Light Absorption and Energy Relationships 75
Quantum Yield 76
Rate Laws and Constants 77
Basic Photochemical Rate Equation 7.7
Environmental Photolysis Rates 80
3.7.4 Effects of Environmental Variables 82
Temperature Effects 82
Solvent Effects 82
Light-Screening Effects of Natural Organics 82

49
-------
3.7.4 Effects of Environmental Variables (continued)
Chemical Effects of Natural Organics and Oxygen 83
3.7.5 Photochemical Equipment 86
Sunlight Experiments 86
, Laboratory Experiments 87
Design of Apparatus 87
Light Sources 88
Light Filter Systems 88
Reaction Cells and Solutions 89
3.7.6 Actinometers and Actinometry 91
3.7.7 Light Sources to Simulate Sunlight 92
3.7.8 Sunlight Intensity Variations 93
3.8 REFERENCES 96
APPENDICES

3.A CALCULATION OF LX VALUES 98
3.B INTEGRATION OF EQUATION (3.40) 102
50
-------
3. PHOTOLYSIS IN WATER
3.1 INTRODUCTION

The effects of sunlight on biological systems and in weathering of materials
has long been recognized. The variations in sunlight with season, time of day,
and latitude govern many aspects of human life and agriculture. One of the
early applications of photochemistry was by the armies of Alexander the Great,
who used the rate of fading of dyed rags exposed to sunlight to measure time.
More recently the chemical literature has provided ample evidence that photol-
ysis of chemicals does occur in the atmosphere to produce photochemical smog;
photochemical processes are also important in soil and aquatic systems. These
protocols are designed to determine the rates of photolysis of chemicals in
aquatic environments.

3.2 SUMMARY

Screening and detailed test protocols for direct photolysis of chemicals
have been prepared to enable an investigator to estimate the photolysis rate
constants and half-lives for chemicals in pure water or shallow depths of clear
natural waters. Only chemicals with half-lives of less than three months are
considered for detailed studies.

The test protocols are based on an extensive body of experimental and
theoretical literature on photolysis together with a detailed kinetic analysis
of direct photolysis. The recommended test protocols meet the criteria of
quantitation, accuracy, and applicability to experimental systems and are cost
effective and simple to use for a wide range of chemical structures. The theory
and experimental procedures described in the literature are reviewed for the
direct photolysis protocol. Indirect photolysis processes are also discussed,
but only a screening test for indirect photolysis is recommended. The processes
involved in indirect photolyses need to be studied further before a detailed
test for indirect photolyses can be recommended.

The screening tests for direct and indirect photolyses of chemicals and a
direct photolysis of a reference chemical (actinometer) are performed in sun-
light experiments. The detailed test requires laboratory studies to obtain
the following data:

• Absorption coefficients, e^: The protocol requires e^ data at specified
wavelengths to determine the ability of the chemical to absorb light
within small, specific intervals around these wavelengths.
• Reaction quantum yield, : The detailed protocol requires the measure-
ment of the reaction quantum yield for the chemical in air-saturated,

51
-------
pure water to measure the efficiency with which a photochemical
process converts absorbed light into chemical reaction.

The rate of loss of a chemical is given by

where L^ is a term proportional to the light intensity in the wavelength inter-
val A averaged over a 24-hour Calendar) day, and kp£ is the first-order photol-
ysis rate constant in units of day"1. Data for L^ as a function of decadic
latitude and four season dates are given in Tables 3.2-3.5, Section
3.6. The rate constants kg apply to shallow depths of water (less than
0.5 meter) with very low absorbances (< 0.02) in the solar spectral region
290 nm to 825 nm.
3.3 CONCLUSIONS

Present knowledge of the theory and experimental aspects of direct photol-
ysis reactions provides a sound basis on which to propose protocols for
evaluating photolysis in water. The recommended screening and detailed studies
for direct photolysis reactions represent a balance between the economic need
to minimize laboratory work and the scientific requirements for sufficient and
accurate data. The direct photolysis screening test is used to identify
chemicals that have photolysis half-lives of less than three months in pure
water. The detailed protocol can be used to measure the data necessary to
manually calculate rate constants and half-lives for photolysis in clear water
at shallow depths. The data can also be used to calculate direct photolysis
rate constants in other aquatic environments, using a computer program
available from the EPA-Athens Environmental Research Laboratory.

A screening test is also recommended to determine the effect of other
substances present in natural waters on the photolysis rate of the chemical.

3.4 RECOMMENDATIONS

The protocols should be tested for applicability to several chemicals of
environmental concern. Sunlight actinometers for use in the screening protocols
should be selected from candidate chemicals and then validated for several
seasons and latitudes. Although some data are available for validating the
detailed protocol, the protocol should be tested using chemicals with a wider
range of structure and reactivity.

Research is needed to determine what effects substances present in natural
waters may have on photolysis rates, with an emphasis on the role of various
sensitized and photo-initiated free radical processes in accelerating photolyses.
Research is also needed on the effect natural substances may have on quenching
or retarding photochemical processes.

52
-------
3.5 SCREENING TESTS

3.5.1 Purpose

This screening test protocol is intended to identify chemicals with
photolysis half-lives of less than three months.

3.5.2 Procedure

Solutions of chemical and an actinometer should be prepared using
sterile, air-saturated, pure water and Reagent Grade (or purer) chemicals.
Reactions mixtures should be prepared with chemicals at concentrations at less
than one-half their solubility in water and at concentrations such that, at any
wavelengths above 290 nm, the absorbance is less than 0.02 in the photolysis
cell. If the chemicals are too insoluble in pure water to permit reasonable
handling or analytical procedures, 1-volume % acetonitrile may be added to water
as a cosolvent.

A solution of chemical should also be prepared in a natural water that
has a measurable absorbance in the solar spectrum region above 290 nm. The
natural water sample should be freshly collected (within 5 days of the photol-
ysis experiment) and refrigerated until use. The natural water should be
sterilized by filtration through a 0.22-um filter; filtration also provides a
reaction solution that is free of particulate so that reaction kinetics can be
conducted in a homogeneous solution.

Solutions of chemicals and actinometer in sealed ampoules or stoppered
flasks (with no greased joints) should be placed outdoors in sunlight beginning
in early morning; whenever possible, these tests should be made in clear weather.
The location should be free of excessive reflections from walls and windows
and without morning or afternoon shadows. The tubes should be placed at an
angle of about 30° from vertical. The reaction tubes should be placed in a
transparent housing thermostated to maintain a constant temperature (± 2°C),
preferably around 25°C. If possible, sunlight experiments should be done in
summer to take advantage of longer sunlight periods and warm weather, in which
case a housing is unnecessary.

Solutions should be analyzed for concentration of the chemical after 6
hours, 2 days (48 hours), 10 days (240 hours), and 4 weeks (672 hours). When-
ever possible, an analytical procedure should be used that provides a precision
within ± 5%. Solutions of the chemical and a standard should be maintained in
the dark and analyzed at the above reaction times as controls on the sunlight
experiments. Once 80% loss of the chemical is found, additional analyses of the
chemicals are not necessary; the standard should be taken to two half-lives re-
action time (i.e., 25% remaining standard).

3.5.3 Criteria for Screening Tests

If no loss of chemical or actinometer is found in the dark control
solutions, any loss of chemical in the solutions in sunlight is assumed to be
due to direct photolysis. Any loss of chemical or actinometer in the dark
control solutions may indicate the intervention of some other loss process,

53
-------
and the possible importance of other transport or transformation processes
should be checked before concluding that photolytic processes are occurring.

If the control solution data are satisfactory, the loss of chemical and
actinometer should be interpreted in the following manner: If less than 20%
of the chemical is lost after exposure to sunlight for four weeks, the chemical
will have a photolysis half-life in water of over three months under all en-
vironmental sunlight conditions. If more than 20% is lost: within 4 weeks, the
data for 20% to 80% conversions may be used to calculate photolysis half-lives,
t, as follows:
tr(ln 2)
(In l/Xr) (3<2)
where Xj. is the fraction of initial concentration remaining at time tr. The
experimental half-life for the chemical is designated t£e.

The half-lives determined in this protocol are relevant to the day mid-
way between the beginning and termination of the photolysis experiment and,
therefore, represent an "average" half-life for the chemical during a certain
time period. Obviously, the longer the experiment, the greater the change
in half-lives during the experimental time period. Therefore, all photolysis
half-lives that are reported should carry appropriate information on the dura-
tion of the experiment.

Since sunlight photolysis half-lives will vary with the time of year
and day and with weather conditions, the experimental half-life for the chemical
must be adjusted to a reference time of year, which is chosen to be the "winter
date" (see Section 3.6.4). To do this, the measured photolysis half-life of
the actinometer should be calculated according to equation (3.2) and is desig-
nated tip. The half -life expected for the actinometer at the same midex-
periment date should be determined from Figure 3.1 at the decadic latitude
nearest the location of the experiment and is designated t:Sc; the half-life
for the actinometer at winter date is also determined from a figure such as
Figure 3.1 and is designated tgcw. The half-life for the chemical in winter,
t£w, may then be estimated by equation (3.3):

sc sew
tcw
L s_ , ce)
. se ^.se \ % /
cw
If tjj is less than one day, the chemical is considered to be nonper-
s is tent and no further detailed studies are required. If t£w is greater than
one day, but less than three months, detailed studies should be made to further
define the rate parameters for photolysis of the chemical in sunlight. For
54
-------
60
50
£ 4°
re
T3
30
20
10
WINTER
DATE
JAN
MAR
MAY JUL
MONTH OF YEAR
SEP
NOV

SA-4396-75
FIGURE 3.1 ANNUAL VARIATION OF PHOTOLYSIS HALF-LIFE OF METHYL PARATHION
ACTINOMETER
This figure does not include half-lives at summer and winter solstices.
55
-------
example, a measured half-life for a chemical at 40° latitude is 30 days in April
(April 1 to 31), and in the parallel experiment the measured half-life of methyl
parathion (the actinometer) was found to be 18 days. Figure 3.1 shows that the
average half-life for methyl parathion should have been 11 days in April (April
15); the half-life for methyl parathion at the winter date (Figure 3.1) is 32
days. The half-life estimated for the chemical for the winter date is then
estimated by

11 32
•Tg x -=-jr x 30 = 33 days
The half-life for photolysis of a chemical in the natural water should
be calculated using equation (3.2) and the datum point from the experiment in
natural water. This half-life, ti nw, should be compared with the half-life
measured in pure water in sunlight, t£e, to determine whether the presence of
natural materials in water either retard or accelerate the photolysis rate of
the chemical. The use of this information in an environmental assessment is
discussed in the detailed protocol (Section 3.6.2).

3.5.4 Rationale

The screening test described above is a simple procedure for quantitative-
ly evaluating sunlight photolysis of a chemical at a specific time of year and
latitude, with a less accurate but still useful calculation used to determine
how the photolysis may vary with the time of year. The test requires common
laboratory chemicals and equipment and a location where the experiments can
be performed in sunlight with reasonable temperature control. Sunlight is used
as the irradiating source because of its obvious relevance as well as its low
cost in comparison to artificial light sources. Simultaneous photolyses of a
chemical and a sunlight actinometer provide a means of evaluating the sunlight
intensities incident on the samples during the reaction time. Simultaneous
photolyses of a chemical in pure water and in natural water provide a direct
comparison to determine the effect natural substances may have on the photol-
ysis rate of the chemical.

3.5.5 Scope and Limitations

The screening test for direct photolysis in pure water is designed to
separate chemicals into two groups: those with half-lives of less than three
months for which detailed studies are recommended, and those with photolysis
half-lives of more than three months. The test procedure is simple and inex-
pensive but does require that the chemical be dissolved in water to obtain
valid photochemical kinetic data. Additionally, if the chemical ionizes or
undergoes structural changes within the environmental pH region of 5 to 9,
photochemical reactions should be performed in the pH regions where the dif-
ferent ionized species structures are present.
56
-------
3.6 DETAILED TESTS

3.6.1 Purpose

The objective of this test protocol is to provide a uniform procedure
for calculating the rate constant for photolysis based on laboratory measure-
ments in a manner that will enable investigators to estimate sunlight photoly-
sis rate constants (kpg) at any decadic latitude and season date (for example,
midwinter at 40° latitude) . The rate constants kp|r apply to environmental
conditions of shallow depths (less than 0.5 meter; of natural waters with very
low absorbances (< 0.02) in the solar spectral wavelength region 296 to 825 nm.

3.6.2 Direct Photolysis Half-life from e>, L^ , and ft Data

The rate constant kpjr, in units of day"1, for direct photolysis of
chemical at a specific latitude and season date is calculated from equation
(3.4)
kpE - *Z£ALA (3'4)
where is the reaction quantum yield, e^ is the extinction coefficient of the
chemical at the wavelength A, and L^ is the term proportional to the sunlight
intensity in the wavelength interval A. Values of L^ for solar radiation from
296 to 825 nm are given in Tables 3.1 through 3.4; e^ and
-------
TABLE 3.1. LX VALUES FOR LATITUDE 20°N
X Center
299
304
' 309
314
319
323
340
370
406
430
460
494
537
588
638
691
747
800
Spring
3.5K-4)
2.5K-3)
8.09(-3)
1.8K-2)
2.82(-2)
2.83(-2)
3.29(-l)
4.24(-l)
8.41(-1)
1.17
1.47
1.88
2.68
2.80
2.80
3.15
3.10
2.50
Summer
4.44C-4)
3.15(-3)
9.6K-3)
1.97C-2)
3.02(-2)
3.03C-2)
3.47(-l)
4.47(-l)
8.83(-l)
1.23
1.55
1.98
2.81
2.96
2.90
3.38
3.15
2.70
Fall
2.74(-4)
2.20(-3)
6.89C-3)
1.48(-2)
2.33(-2)
2.33(-2)
2.68(-l)
3.45(-l)
6.96(-l)
9.80(-1)
1.24
1.58
2.30
2.35
2.42
2.70
2.47
2.26
Winter
1.47(-4)
1.47(-3)
5.34(-3)
1.15(-2)
1.88(-2)
1.88(-2)
2.2K-1)
2.86(-l)
5.97(-l)
8.40(-1)
1.06
1.36
1.95
2.03
2.07
2.36
2.65
1.60
Units of LX are 10~3 einsteins cnT2 day-1. Multiplication of LX by EX in
units of M^1 cm"1 gives rate constant in units of day"1.
58
-------
TABLE 3.2. L, VALUES FOR LATITUDE 30°N
X Center
299
304
309
314
319
323
340
370
400
430
460
494
537
588
638
691
747
800
Spring
2.30(-4)
2.13C-3)
7.26(-3)
1.65(-2)
2.64(-2)
2.69(-2)
3.20(-1)
4.14(-1)
8.27(-l)
1.15
1.45
1.85
2.64
2.74
2.76
3.15
3.04
2.50
Summer
3.65(-4)
2.32(-3)
9.02(-3)
1.92(-2)
3.02(-2)
3.04(-2)
3.74(-l)
4.37(-l)
9.07(-1)
1.34
1.59
2.03
2.89
3.03
3.00
3.38
3.26
2.80
Fall
1.35(-4)
1.44(-3)
4.84(-3)
1.16(-2)
1.89(-2)
2.30(-2)
2.23(-l)
2.84(-l)
6.23(-l)
8.50(-1)
1.09
1.39
2.00
2.07
2.09
2.36
2.36
1.90
Winter
4.10(-5)
6.50(-4)
2.76(-3)
7.55(-3)
1.3K-2)
1.34(-2)
1.70(-1)
2.19(-1)
4.75C-1)
6.69(-l)
8.50(-1)
1.10
1.57
1.63
1.67
1.95
1.83
1.60
59
-------
TABLE 3.3. L, VALUES FOR LATITUDE 40°N
X Center
299
304
309
314
319
323
340
370
400
430
460
494
537
588
638
691
747
800
Spring
1.09C-4)
1.37(-3)
2.96(-3)
7.99(-3)
1.38(-2)
1.42(-2)
1.78(-1)
2.30(-1)
5.26(-l)
6.76(-l)
8.90(-1)
1.15
1.69
1.73
1.78
1.69
1.91
1.60
Summer
2.49(-4)
2.32(-3)
7.93(-3)
1.81(-2)
2.9K-2)
2.97(-2)
3.54(-l)
4.58(-l)
9.7K-1)
1.28
1.43
2.04
2.92
3.05
3.00
3.49
3.26
2.90
Fall
1.09(-4)
1.37(-3)
5.35(-3)
1.38(-2)
2.31(^2)
2.39C-2)
L.08(-l)
3.84(-l)
7.9K-1)
1.11
1.39
1.78
2.52
2.62
2.60
5.29
2.92
2.50
Winter
5.38(-6)
1.56(-4)
1.02(-3)
3.79(-3)
7.53(-3)
8.10(-3)
7.52(-2)
1.47(-1)
3.38(-l)
4.80(-1)
6.10(-1)
7.75C-1)
1.12
1.16
1.19
1.56
1.35
1.16
60
-------
TABLE 3.4.
VALUES FOR LATITUDE 50°N
X Center
299
304
309
314
319
323
340
370
400
430
460
494
537
588
638
691
747
800
Spring
3.71(-5)
7.10(-4)
3.55C-3)
7.30(-3)
1.84(-2)
1.96(-2)
2.66(-l)
3.48(-l)
7.24(-l)
1.02
1.29
1.65
2.34
2.40
2.44
2.82
2.81
2.30
Summer
7.88(-6)
1.75(-3)
6.53(-3)
1.63(-2)
2.67(-2)
2.77(-2)
3.43(-l)
4.44(-l)
9.04(-1)
1.26
1.60
2.04
2.90
3.04
3.00
3.49
3.26
2.90
Fall
1.52(-4)
2.25(-4)
1.29(-3)
4.39(-3)
8.64(-3)
9.20(-3)
1.24(-1)
1.66(-1)
3.65C-1)
5.17C-1)
6.60(-1)
8.50C-1)
1.22
1.25
1.31
1.51
1.47
1.24
Winter
4.00(-7)
1.57C-5)
1.78(-4)
1.20(-3)
2.93(-3)
3.68(-3)
6.29(-2)
8.21(-2)
1.96(-1)
2.75C-1)
3.5K-1)
4.44C-1)
6.30(-1)
6.40(-1)
6.90(-1)
7.99C-1)
7.98(-l)
6.90(-1)
61
-------
combining L. values in Tables 3.4 and 3.1, respectively, with measured $ and e,
values using equation (3.4).

By choice of the appropriate L^ data, direct photolysis rate constants
and half-lives may also be calculated for other latitude and date specific
conditions. Although even more site and time specific data could be generated
by interpolation between the decadic latitudes and four season dates for which
L\ data are given in Tables 3.1-3.4, such calculations do not seem warranted
in view of the assumptions already included in the L^ data presented and the
ambient variations that influence the actual photolyses in aquatic environments.
For most environmental assessments, the L^ data for the decadic latitude and
season date nearest the site and time of interest will be adequate (Varia-
tions in photolysis rates with latitude and date are discussed in Section 3.7.8.)

The rate constants kp£ and the half-lives calculated using the above
procedure should be used in environmental assessments in conjunction with the
half-lives measured in the screening tests for chemical in the pure and natural
water in the following way: If the rate constants calculated and measured in
pure water do not agree to within 50% of each other, further studies may be
necessary to resolve the discrepancy. Possible sources of this discrepancy
may be quantum yield is not constant over the entire wavelength region,
the absorption of chemical has not been accurately or completely included
in the calculation or adventitious loss processes such as volatilization may
also have been occurring during the experiments and were not detected by the
control experiments.

If the rate constants calculated and measured for the pure water solu-
tions of a chemical agree within ± 50%, the pure water rate constants kg should
be compared with the screening test experiment data for the natural water. If
the rate constant in the natural water is more rapid than the rate constant for
pure water, the pure water photolysis rate constant may be taken as the minimum
photolysis rate in a natural water (i.e., photoreactions in natural waters may
be faster than in pure water due to photosensitized or photoinitiated free
radical reactions). If the rate constant in the natural water is slower than
in pure water, then the pure water rate constant should be used in an environ-
mental assessment with the warning that the photolysis rate in natural waters
may be slower; an appropriate rate constant may be taken as the screening test
photolysis rate constant measured in the natural water.

3.6.3 Measurement of the Absorption Coefficients, e,
A
The absorption coefficients of the chemical should be determined
for the wavelengths listed in the first column of Table 3.5.. If
the chemical is too insoluble in pure water for a reliable absorbance measure-
ment, either acetonitrile or methanol may be used as a cosolvent. The amount
of cosolvent used should be the minimal amount required to achieve a
concentration that allows an accurate measurement of absorption coefficients
above 290 run. Particular care should be used to measure the extinction coef-
ficients in the absorption "tail" of the spectrum as well as in the more intense
absorption regions, since tailing absorptions may contribute significantly to
the overall light absorption by the chemical in the solar spectrum region. In
some cases, cells of longer pathlengths can be used to measure absorbances of
chemicals that absorb light weakly even in saturated solutions; such cells are

62
-------
TABLE 3.5. WAVELENGTH CENTER AND INTERVALS FOR L)
(in nm)
X Center-1
299
304
309
314
319
323
340
370
400
430
460
494
537
588
638
691
747
800
Interval
From
296.3
301.3
306.3
311.3
316.3
321.3
325.0
355.0
385.0
415.0
445.0
475.0
512.5
562.5
612.5
662.5
718.8
775
Range
To
301.3
306.3
311.3
316.3
321.3
325.0
355.0
385.0
415.0
445.0
475.0
512.5
562.5
612.5
662.5
718.8
775
825
AX
5.0
5.0
5.0
5.0
5.0
8.8
30.1
30.0
30.0
30.0
30.0
37.5
50.0
50.0
50.0
56.3
56.3
50.0
founded off to unit wavelength.
63
-------
also useful in measuring the absorption tails of some chemicals. If the ab-
sorption curve within the interval around wavelength X (see Table 3.5) is rea-
sonably flat, EX may be determined from the absorbance at X. If a large change
in absorbance occurs within the interval, an averaged absorbance should be
used to calculate e^. The table presenting the e^ should state the method by
which the EX data were obtained (i.e., "based on average of the two absorbances
at boundary of interval").

The absorption coefficients e. should be calculated from the Beer-
Lambert law
e. = A,/(£[C].) (3.6)
where AX is the absorbance at wavelength X, £ is the cell pathlength (in cm),
and [C] is the chemical concentration (in M); the units of e, are then M"1 cm"
For compounds of very low solubility, precautions should be taken to
ensure that a homogeneous solution is used for absorbance measurements.
Filtration of the chemical solution through a 0.22-ym filter or centrifugation
to remove particulate are two ways to obtain homogeneous solutions. The
absence of particulates can be verified by the failure of the solution to scatter
a collimated beam of light.

When measuring absorption spectra for determining absorption coefficients,
always run a solvent versus solvent spectrum to establish the baseline before
measuring the spectrum of the chemical. At wavelengths where the absorbance
is indistinguishable from baseline noise, the values of e^ should be entered
as zero. In practice, the usual lower limit of absorbance measurement is about
0.01 absorbance unit (optical density); for a 10~2 M concentration of chemical
in a 10-cm cell, this is equivalent to a measurable value of EX of 0.1 M"1 cm"1.
When making such absorption measurements, use matched cells. When using long
pathlength cells, make replicate measurements of absorbance and calculations
of absorption coefficients to ensure that no instrumental or cell effects in-
troduce artifacts into the absorption data.

3.6.4 L, Data

The LX data used in equation (3.1) (see Table 3.1-3.4) are proportional
to the average light flux (in units of einsteins liter"1 day"1) that is available
to cause photoreaction in the wavelength interval X over a 24-hour day at a
specific latitude and season date. The LX values were obtained using the
computer program described by Zepp and Cline (1977), where the season date LX
values were defined by the angle of declination of the sun at -20° for winter,
-10° for fall, +10° for spring, and +20° for summer. The actual dates for a
specific year that correspond to the angle of declination can be found in the
American Ephemeris and Nautical Almanac. For the year 1978, the season dates
for winter, spring, summer, and fall correspond to January 21, April 16, July
24, and October 20, respectively. The derivation of the LX data is discussed
in Appendix 3.A. The LX values cover the solar spectral region from 296 nm
to 825 nm in 18 wavelength intervals.

64
-------
3.6.5 Measurement of Reaction Quantum Yield

The reaction quantum yield obtained by this method is subject to a potentially
large, but as yet undetermined, error due to assumptions and the extended cal-
culation required to calculate .

Photochemical Apparatus for Procedures Ql and Q2

Several different designs of the photochemical apparatus for quantum
yield measurements are possible, and the one used will depend on the equipment
available and to some extent on the light source and filter systems chosen for
the measurement. The apparatus used must have a light source, appropriate
filters, sample holder and cells such that solutions of chemical and actinometer
can be reproducibly irradiated with a uniform and constant amount of light
limited to a discrete wavelength region and at a reasonably constant temperature
(25 ± 2°C). If quantum yields are to be routinely measured, a section of the
laboratory should be set aside and a permanent apparatus assembled using a
merry-go-round reactor (MGUR) or an optical bench (FOB). Two such possible
apparatuses are discussed in Section 3.7.5.

The apparatus is designed so that the chemical is irradiated in a wave-
length region where the chemical has an absorption coefficient that can be
measured precisely. Experimental work is simpler if the wavelength region
selected is one where the chemical has a large absorption coefficient. Often,
however, the choices of wavelength regions will be determined largely by the
light sources and light filter systems available or practical in a particular
laboratory. Since some solution filter systems are more complex or less stable
than others, and solutions are certainly more difficult to work with (but less
expensive) than glass light filters, there is considerable latitude in setting
up the photochemical apparatus. To avoid incurring a systematic error of
between 10% to 50% due to temperature fluctuations, the temperature should be
controlled to within ± 2°C in the reaction cell, and preferably around 25°C.

In addition to the information and discussion presented in Section 3.7.5,
deMayo and Shizuko (1976), Murov (1973), and Calvert and Pitts (1966) have given
excellent reviews and evaluations of equipment and components available for
measuring quantum yields.

Procedure Ql: High Optical Density Actinometer

Procedure Ql, the preferred method for measuring <£, uses established
actinometric procedures for measuring the light intensity flux entering a cell
in a MGRR or a FOB. Procedure Ql is performed in two steps.
In Step 1, a solution of the actinometer chemical with a known quantum

a>
65
yield at the irradiating wavelength ( ) is prepared at an optical density
3.
-------
greater than 2 and placed in a cell or cells on the MGRR or FOB. The
actinometer solution is photolyzed and analyzed to determine actinometer con-
centration, taking at least six time points. No data points should be taken
after the optical density falls below 2.

The light intensity flux term, I0xr> entering the reaction cell can then
be evaluated by either of two treatments:

(1) The concentration of the chemical, C , is plotted versus the time t,
with the slope equal to a constant k2 = alo^r, where C^ is the con-
centration of chemical at time t.
(2) A more accurate and precise value of kz is obtained by a fit of the
data by linear regression analysis to equation (3.7)

Ct = V = 'Vox*!' (3'7)
The zero-order rate constant kz is in units of einsteins liter"1 sec~l
in photochemical light intensity and equal to M sec"1 in chemical
concentration. The Ioxr term is then obtained from division of kz
by the known reaction quantum yield,
-------
The reaction quantum yield is then calculated from k using equation (3.9):

* - 2-3-1 (3-9)
where IQ^r is the quantity measured above, e^c is the absorption coefficient
of chemical at wavelength X, and I is the effective cell pathlength. The value
of the effective cell pathlength must be either known or determined independent-
ly, since the quantity T-o^r measures the total light entering the solution and
is independent of pathlength. A discussion of effective cell pathlength and
its experimental determination is given in Section 3.7.5.

Procedure Q2; Low Optical Density Act inometer

Procedure Q2 is simpler than Ql but suffers from the lack of
actinometers that can be easily analyzed at low concentrations. Future develop-
ment of appropriate dilute solution actinometers for use in Q2 offers promise
for measuring reaction quantum yields rapidly and accurately.

Procedure Q2 is performed by preparing dilute aqueous solutions of an
actinometer with a known quantum yield a and chemical whose quantum yield is
to be measured. The absorbance of both solutions should be less than 0.02 in
the irradiating wavelength region. The solutions are photolyzed in identical
cells in a MGRR or POB and analyzed for concentration of actinometer or chemical
at reaction times between 10% and 80% loss of initial concentration for each
species.

The rate constants kpa and kpc for direct photolysis of actinometer and
chemical, respectively, can then be evaluated in two ways:

(1) Plot the log of the concentration of chemical against time using semi-
log paper, with the best straight line through the points having a
slope equal to k /2.3.
(2) Fit the data by linear regression analysis to the equation

ln(C/CQ) = -k t,

where Ct and C0 are the concentrations of chemical at times t and 0,
respectively.

The quantum yield is then calculated from equation (3.10):
(3.10)
67
-------
where e^a and e^c are the absorption coefficients for actinometer and chemical,
respectively, at the irradiating wavelength A. Procedure Q2 is then simpler
than Ql in that it does not require measurement of the light intensity flux or
knowledge of the effective pathlength of the reaction cell.

Procedure Q3: Sunlight Actinometer

Procedure Q3 requires photolysis rate constants kpg for chemical and ac-
tinometer measured in sumultaneous experiments in sunlight. The same procedures
and conditions used in the screening experiments apply in measuring rate constants
in sunlight, except that at least five data points should be taken between 10%
and 80% reaction of chemical and actinometer, with at least one point in each
photolysis taken after two half-lives have occurred. Appropriate times for
taking sample data points can be determined from the screening test data.

Data for loss of chemical during photolysis should be fit by regression
analysis to the equation ln(C/C0) = -kpt, where C and Co are the chemical or
actinometer concentrations at times t and 0, respectively. The increased number
of data points provides a more precise rate constant kpg than in the screening
experiment and verifies that the photochemical reaction is first order in the
chemical.

If the photolysis rate constant kpg measured for the actinometer is within
± 50% of the value predicted from Figure 3.1 for the corresponding time of year
and latitude, the reaction quantum yield <(> for photolysis of chemical can be
estimated as follows. From equation (3.1), the sunlight photolysis rate
constants for chemical and actinometer are
kpcE = *2LX£Xc (3'U)
and
kpaE
Since the photolyses were conducted simultaneously, L^ values are the same.
Subtracting and rearranging then gives

"X ' - ZLX(£Xc - EXa> (
where kpcE and kpa£ are the measured sunlight photolysis rate constants; exc
and e, are the absorption coefficients at wavelength X for chemical and
68
-------
actinometer, respectively; and a is the known reaction quantum yield for the
actinometer. L^ data used in equation (3.13) should be chosen for the
season date and latitude nearest the date and latitude where the sunlight ex-
periments were performed.

3.6.6 Rationale

The foregoing detailed photolysis procedure is intended to provide ac-
curate kinetic information concerning the photolysis rates of chemicals in
shallow depths of clear water. The procedure requires close attention to
control experiments and some temperature control in conducting the photolysis
experiments. Data obtained from laboratory measurements of the reaction quantum
yield and the absorption coefficients at specified wavelengths are then used
with data from Tables 3.1 through 3.4 to calculate photolysis rate constants
and half-lives at specific season dates and decadic latitudes.

3.6.7 Scope and Limitations

The foregoing detailed test protocol is intended to provide the quanti-
tative information necessary to calculate rate constants for chemicals dissolved
in water exposed to sunlight at four season dates and at the decadic latitudes
of 20°, 30°, 40°, 50° within the continental United States. The rate constants
calculated according to the procedure described above pertain to shallow depths
of clear water., Information from the screening tests in pure and natural waters
can then be used to determine whether photolyses in natural waters will be
faster or slower than those estimated for the shallow, clear water conditions.
The calculation of the sunlight photolysis rates constants and half-lives as-
sumes a constant reaction quantum yield over the entire absorption spectrum of
the chemical in the region 296 to 825 nm.

3.6.8 Error Analysis

Estimation methods for error analysis of the test protocol are based on
certain assumptions concerning the accuracy of specific measurements and rela-
tionships between variables. The test protocols proposed here require measure-
ments of concentrations of chemical as a function of time from which rate
constants for photolysis are calculated using standard kinetic relationships.
The discussion of error analysis follows the same sequence as the test protocol,
beginning with measurement of kz in the actinometer experiment through the
calculation of the environmental photolysis rate constant k „:

k = C/t
Z
I ,r = k
oX z
k = ln(C/C )/t
P o
69
-------
= k /2.3e,I
p A
V

Error Analysis for k

The estimate of the zero-order rate constant kz measured in the
actinometer experiment is related to the measured variables,, concentration and
time, by the following regression equation

. _nZtC- [Zt][ZC]
z nZta - [Zt]2

where C is concentration of chemical measured at time t. This version of the
regression equation does not require that (C/CO) = 1 at t = 0; that is, the
line is not forced through the origin, and any significant departure from the
origin indicates bias in values of C at t > 0.

The intercept C , the concentration at t = 0, is obtained from the equa-
tion
ln(C ) - -EC - k (-It) (3.16)
o' n z n
The preferred measure of error in experiments of this kind is the standard er
ror, a.* The standard error in k, from n measurements is given by
( . / 1 fnZ[C]2 - [ZC]a
CT(kz) \n-2[ nZta - (Zt)2 ~
Equation (3.17) shows that a varies approximately with —p arid directly with
/n
*
The standard error may be expressed as the standard deviation, (n ± o), the
error ratio, a/k, or percent error (a/k) x 100.

70
-------
Error Analysis for I ,r
« OA—

The equation used to calculate I ,r is
I ,r = k.
(3.18)
The standard error ratio is given by
ro2(<|> ) a2(k
a. .
(3.19)
For example, when the standard deviations in $ and k are both ± 5%, the error
ratio is
[(0.05)2 + (0.05)2]1* - 0.071
or a percent standard deviation of ± 7.1% in I ,r.

Error Analysis for k

The estimate of the rate constant kp is related to the measured variables,
concentration and time, by the following regression equation.
nZtlnC- [Zt][ElnC]
(3.20)
where C is concentration of chemical measured at time t. This version of the
regression equation does not require that ln(C/Co)= 0 at t « 0; that is, the
line is not forced through the origin and any significant departure from the
origin indicates bias in values of C at t > 0.

The intercept, C , the concentration at t = 0, is obtained from the
equation
ln(C ) - -ZlnC - k (-Et)
on p n
(3.21)
71
-------
The preferred measure of error in experiments of this kind is the standard er-

ror, a.* The standard error in k from n measurements is given by
1 [n£[lnC]2 - [ElnC]2 , 2 P , __,
7—TTfri /v^* - (k ) (3.22)
n - 21 nit - (It) p J
Equation (3.22) shows that a varies approximately with -r~ and directly with

o(C). /n

Error Analysis for is

= [(0.05)a + (0.04)2 + (0.07)2 + (O-OS)2]^ - 0.108
or a percent standard deviation of ± 10.8% on .

Error Analysis for k

The sunlight photolysis rate constant k is calculated from
pa
(3.25)
The standard error may be expressed as the standard deviation form, (k ± a),

the error ratio, a/k, or percent error (a/k) x 100.

72
-------
The error ratio for k _ is then
pE
-I*
(3.26)
where for each interval X,
a2(ex) a2(Lx)|
T— +
(3.27)
The second term in equation (3.26) can be substituted by the terms in equation
(3.27) where, if we assume the standard error ratio in e, is ± 0.04 and in L,
± 0.10, then
a2(e L )
, T\a = [(0.04)2 + (0.10)2] = 0.0116
and
0.0116(exLx)2
Substitution of error ratios for and e,L, in equation (3.26) then gives
A A.
0.0116
pE
Multiplication of the last term by <|>2/2 and substitution of k_E2 for 2(£exLx)2
gives
73
-------
a(k )
PE = Q.1081 + ;- > > 0.108
PE
3.7 BACKGROUND

3.7.1 Definition of Photolysis

Photochemical transformation of chemicals can occur when energy in the
form of light is absorbed by a molecule, placing it in an excited state from
which reaction can occur. For these protocols we have chosen to define photo-
chemical reactions as those processes that involve reaction of the excited
state of the molecule of the chemical being evaluated for persistence.

Direct photolysis of chemicals occurs when the chemical molecule itself
absorbs light and undergoes reaction from its excited state. Indirect photol-
ysis occurs when another chemical species, called a sensitizer, absorbs light
and the sensitizer transfers energy from its excited state to another chemical,
which then undergoes reaction. This protocol includes photosensitized processes
in a screening study, but not in a detailed study, since the quantitative details
of photosensitized reactions in the environment are not yet established.

3.7.2 Kinetics of Photochemical Processes

There are many types of photochemical reactions, including oxidation,
reduction, hydrolysis, substitution, and rearrangement. Molecules may undergo
several of these reactions competitively depending on the structure and
substitution of functional groups of the molecule as well as on the reaction
conditions (such as, phase, solvent, other reactants, dissolved oxygen, wave-
length of light, temperature). Since direct and sensitized photolyses may pro-
ceed through the same excited state of the molecule, the products of the photo-
reaction may often be the same. Several general references on photochemistry
include Calvert and Pitts (1966), Turro (1967), Crosby (1972), and Murov (1973).

In practice it is possible to measure the rate constant for a photochemical
reaction or a reaction quantum yield without knowing the type of reaction that
is occurring. For environmental applications, data from measurements made
under environmentally relevant conditions, such as air-saturated water, at or
near 25°C, and at wavelengths above 290 nm, can be used to predict probable
loss rates in sunlight without additional knowledge of the chemistry. However,
some knowledge of the photochemistry, including the effects of oxygen, pH, and
temperature and the products formed, are useful in planning detailed photo-
chemical studies and in providing an overall fate assessment.
74
-------
3.7.3 Kinetics in Solution

Light Absorption and^ Energy Relationships

The Beer-Lambert law for light absorption relates the incident light,
Io, on a solution of chemical, to the light emergent from the solution, I, ac-
cording to equation
Iog10 (I /!)= eC& = Absorbance (3.28)
where e is an absorption constant characteristic of the light-absorbing chemical,
C is the concentration of chemical in solution, and SL is the pathlength of the
cell containing the solution. Equation (3.28) may also be rewritten in the
exponential form
1=1 10- (3.29)
o
The amount of light absorbed, I , is then
3.
I - IQ - I = I (1 - 10-eC*) (3.30)
In this discussion, the absorption of light in a solution will be confined to
a single narrow wavelength region X; an additional term, a^, called the light
attenuation coefficient will be used to account for unknown substances other
than the chemical in solution that contribute to light absorption:
The a^ parameter is conveniently defined as a composite of the absorption
constant and concentration(s) of the unknown substance(s) dissolved in water
of 1 cm pathlength, and is in units of cm"1.
75
-------
The absorption of light by a chemical results in formation of an excited
state of the molecule, with the energy (E) of the initial excited state
determined by the wavelength X of the absorbed light
hv = • (3.32)
where E = energy (ergs)
h = Planks constant (6.62 x 10~27 erg-sec)
v = frequency of light absorbed (cm"1)
c = velocity of light (3.00 x 10s meter see"1)
X = wavelength of absorbed light (nm)
The unit of light on the molecular level is called a photon or quantum. In
molar terms, equation (3.32) is then
(3.33)
where N is Avogadros number, 6.02 x 1023 molecules or quanta per mole. A mole
of quanta is called an einstein. Some energies corresponding to wavelengths X
are given in Table 3.6.

In photochemical kinetics, the rate at which the photons are delivered
to a reaction system directly determines the photolysis rate of a chemical.
The most useful unit of light flux for kinetic equations are einsteins cm~2
sec'1 nm~x. Specification of a light pathlength then allows the light flux to
be expressed in volume units, einsteins cm~3sec~l nm-1, by simple division.

Units of einsteins cm"2 sec"1 nm"1 should be clearly contrasted to the
energy units of watts cm"2 nm-1, which are commonly reported in the literature
for meterological data; the watt is defined as joule sec"1 and is wavelength
dependent (see Table 3.6). The conversion of watts cm"a nm" l to einsteins cm"a
sec"1 nm'1 is given by equation 0.34).

Keinsteins cm"2 sec"1 nnr1) - Kwatts cm"a nm-1) x X x 3.03 x 103' (3.34)
Quantum Yield

The Grotthus-Draper law states that "only light absorbed by a molecule
can bring about a photochemical change." The Stark-Einstein law modified this
statement in accord with quantum theory to state that "a molecule which under-
goes a photochemical change does so as the result of the absorption of a single
quantum of energy." However, often less than one mole of chemical reacts for
each einstein of light absorbed as a result of radiationless transitions,
phosphorescence, or fluorescence. In a few cases each einstein of light ab-
sorbed results in reaction of more than one mole of chemical as a result of

76
-------
TABLE 3.6. WAVELENGTH-ENERGY RELATIONSHIPS

(Wavelength
Ultraviolet

Violet
Blue
Green
Orange
Red
X, nm
200
300
350
400
450
500
600
800
kcal mole"1
143.0
95.3
81.7
71.5
63.6
57.2
47.7
35.8
kJ mole l
598.5
399.0
341.8
299.3
266.1
239.4
199.5
149.8

energy = 2.86 x 10*(A"1) kcal mole-
3energy = 1.20 x lO'CX"1) kJ mole"1
chain reactions. A few rare cases are also known where a molecule absorbs two
quanta before reaction (double photon reactions). Direct absorption of light
is not required,' however, if another light-absorbing molecule can transfer part
of its excitation energy to effect a sensitized reaction.

This variable efficiency of the photochemical process has led to the
definition of the efficiency of photochemical reactions expressed as a reaction
quantum yield (j>:

, _ Number of moles chemical reacted . .
Number of einsteins absorbed ^ '

Since the term quantum yield is also applied to other photochemical processes
including fluorescence, phosphorescence, and sensitizations, the term "reaction
quantum yield" should always be explicitly stated.

Rate Laws and Constants

Basic Photochemical Rate Equation: Knowledge of the light incident on
a reaction system IQ, the absorption constant for a chemical undergoing reaction

77
-------
t^, and the quantum yield then provide the complete basis for expressing the
kinetics of photochemical reactions.

The equation describing the rate of photolysis of a chemical in solution
at wavelength A is
where A is the area (in cm2) exposed to the incident light intensity Io^ (in
einsteins cm~a sec"1), V is the volume of solution (in liters), Fs^ is the
fraction of light absorbed by the system, and FC^ is the fraction of absorbed
light that is absorbed by the chemical in the system.

F . - 1 - 10~(ctA + EAC)* (3.37)
(3.38)
For a given reaction cell, the term (A/V) is a constant, which is designated r
in this discussion.* Equations (3.36), (3.37), and (3.38) are combined to
obtain:
For use in kinetic studies, the differential equation (3.39) requires
integration into a form that expresses the concentration of chemical C as a
function of time t . For the case when a. « e,C, equation (3.39) simplifies
to
It = <()IoAr(1 ~ 10~exC^ = a(-1 ~ e"bC) (3'40)
In practice, the terms A, V, and £ have useful measurable dimensions only for
cells with planar windows; A and I lose obvious dimensional relationships
when round cells are used. This problem is discussed in Section 3.7.5.
78
-------
where a = loxr
b = 2.3ex^
Integration of equation (3.40) then gives equation (3.41X (see Appendix 3.B for
details of this integration)
ebC-l _ e-ab(t - to)
bC-l
(3.41)
where C and C0 are the concentrations of chemical at times t and t .
= 0, equation (3.41) can be simplified further:
When t
bC_i
e j_
bC -1
= e
-abt
(3.42)
or
In
bC ,
e -1
bC-l
= - abt
(3.43)
A plot of tote1*0-1) against t gives a straight line with a slope equal to
-ab. Since a is equal to I0xr and b is known, either or the light intensity
flux I0xr may be calculated if the other quantity is known. Equation (3.40)
may be further simplified if limiting conditions are chosen so that £\C%. is
either very small or very large. When eCH < 0.02, the term lO~cC!i ^ 2.3efc[C]
and the rate expression becomes first order
dC
(3.44)
= kp[C]

Integration of equation (3.44) gives the usual first-order expression
-kpt
(3.45)
and a plot of -ln[C.] versus t gives k .
79
-------
When the incident light is nearly completely absorbed by the solution,

e[CH > 2.0, equation (3.40) again simplifies since KT2-0 = 0.01, (1 - 0.01)

"v- I, and equation (3.40) becomes
dC
-T-
dt
,
oX
(3.46)
Integration of equation (3.46) gives the zero-order relation
C -C = k t
o z
(3.47)
Equation (3.47) is used commonly to evaluate the incident flux in a photochemical

experiment where the standard chemical or actinometer absorbs all light incident

on the cell during the course of the reaction. When k is measured in this way,

then from equation (3.46)
I ,r
oX
k
-------
Since at very low concentrations in natural waters the chemical absorbs only
a small fraction of the light (a, » e C), equation (3.49) further simplifies
to
f = +-JT2.3*ex[C] (3.51)
This same result is obtained if a. « e>C. Equation (3.51) can be used to
estimate the photolytic rate constant kp under environmental conditions if ap-
propriate data are available. The composite term Io^ &/D is related to the man-
ner in which sunlight enters and passes through a water body; Zepp and Cline
have analyzed the reflection and refraction of light at the water-air interface
in terms of light intensity, light pathlength and vertical water depth for use
in a computer calculation of environmental photolysis rates (see Appendix D).
From their program, we have prepared a compilation of light intensity terms,
L^ = 2.3 Iox&/D, for four seasonal dates at each specific decadic latitude at
shallow water depths. The L^ data are in units of einsteins-cm liter"1 day"1
to provide a smoothed rate constant that takes into account diurnal fluctuations
in sunlight intensity. With substitution of L , equation (3.51) then simpli-
fies to
kp = «exLx (3.53)
and
ln([C]/[cg) =-k t (3.54)
where kp is actually the product of a rate constant for light absorption and
the quantum yield (k = <|>k ) .
p a

Equations (3.52) and (3.53) refer to the rate of photolysis at one
wavelength; to determine the total rate constant for photolysis in sunlight,
kpE, equation (3.54) may be used to evaluate kp£ from experiments in sunlight
(Section 3.6.5) or equation (3.53) may be used to calculate kpE by gumming the
terms for e^L^ at each wavelength for which the product £\L^ > 0, assuming <|>
is constant over all wavelengths :
kp£ = 4>IexLx (3.55)
81
-------
3.7.4 Effects of Environmental Variables

Temperature Effects

The effect of temperature on photochemical processes in solution has
usually been considered minimal since reactions occurring from the electronic
excited state were assumed to have little or no activation energies. However
many photochemical reactions do have activation energies of 3 to 7 kcal mole"1
(Barltrop and Coyle, 1975). For a reaction with an energy of. activation (E&)
of 5 kcal mole"1, the rate constant will change by a factor of 2.5 going from
0°C to 30°C. Over the same temperature range, rate constants will vary by
factors of 4 and 1.6 for Ea = 7.5 and 2.5 kcal mole"1, respectively. Therefore,
some reliable temperature control to +2°C is necessary to achieve accurate
measurement of photochemical rate constants and quantum yields, especially in
outdoor screening experiments where large ambient temperature effects are common.

Solvent Effects

While extensive information is available regarding the effects of solvents
on photochemical reactions, this discussion will be limited to water as the
major solvent because of the obvious environmental application. Ordinarily, .
water is unreactive in free radical reactions and does not act as a sensitizer.
Water does react in photonucleophilic reactions, sometimes called photohydrol-
ysis reactions; the mechanistic details of these processes have not been
established, and the reactions may be pH dependent (Crosby et al., 1972). Other
studies have shown that photolyses of some polynuclear aromatic hydrocarbons
are much faster in aqueous solutions than in organic solvents (Smith et al.,
1978,) but the information available is not sufficient to determine the exact
role of water in these reactions. In view of the differences between the re-
activity of water and organic solvents, environmentally relevant experimental
studies should be performed in water as the major (> 98%) solvent, and, if
possible, the only solvent.

However, since the solubilities of most organic chemicals in water are
low enough to be a major problem in practical laboratory studies, the choice
of an appropriate cosolvent needs careful examination. Many-organic solvents
are themselves immiscible with water and are therefore obviously poor cosolvents.
Soluble cosolvents such as some ethers and alcohols (i.e., dioxane, tetrahy-
drofuran, ethanol, methanol) are subject to radical hydrogen transfer reactions
and would be unsuitable for some photochemical reactions. Other solvents, such
as acetone, are photosensitizers and should be avoided. Our careful considera-
tion of common and practical cosolvents indicates that only acetonitrile comes
close to being an ideal cosolvent for use in photochemical studies and is the
only cosolvent recommended in these protocols.

Light-Screening Effects of Natural Organics

The rates of photolysis of chemicals in aquatic environments will also
be affected by the natural substances present in these waters. Some properties

82
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of light transmitted in natural waters have been discussed by Kirk (1977), Zepp
and Cline (1977), and Hutchinson (1957). The substances present in natural
waters may serve as light absorbers or as photochemical excited state quenchers
or sensitizers.

In waters that have high optical densities owing to naturally occurring
substances such as humic and fulvic acids, light may be absorbed and therefore
not available to cause photoreaction of chemicals. To account for such a light-
screening effect in natural waters, the computer program of Zepp and Cline
(1977) has the capacity to include the a^ term (equation 3.49) to account for
the attenuation of light by natural substances in water. The kinetic data
calculated using the program are then expressed as the average rate constant
(or half-life) for a chemical for the specified depth of the water body. Ob-
viously, the averaged photolysis rate will decrease with increasing depth of
the water when the natural water absorbs appreciable light; of course, when the
depth parameters are set to calculate near surface photolysis rate constants
(oi,SL - 0) , the rate constants for natural and pure water are the same.
A

The fractional reduction in photolysis rate constant in a natural water
compared with a pure water over a wavelength interval can be determined in the
following manner: for a very dilute solution of a chemical in pure water, the
photolysis rate constant for the chemical is given by

k = 2.3<(>I .re.£ (3.56)
p O A A

In a natural water where a^ » e,C, and from equation (3.39), the rate constant
for the chemical in the natural water k is
pa
c = <>I ±-^[1 - 10 A ~) (3.57)
pa T oA a,
A
Division of equation (3.57) by equation (3.56) then gives the ratio of rate
constants, which is the light-screening factor S:
k , ..-.-ouJl
_DOC _ 1 - 10 X
b k " 2.3u.A U
P *

Figure 3.2 shows how S varies »vith the quantity ou i,where a. is the absorbance
of the natural water in a 1-cm cell.

Chemical Effects of Natural Organics and Oxygen

Dissolved or suspended organics may accelerate or retard photolyses by
chemical processes that assist, compete, or interfere with the direct reaction.

83
-------
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
I I I I I
0.1 0.2 0.3
0.4 0.5 0.6
ABSORBANCE (at)
0.7 03
0.9 1.0

SA-43M-78
FIGURE 3.2 PLOT OF LIGHT-SCREENING FACTOR, S, AGAINST ABSORBANCE FUNCTION
(SEE SECTION 3.7.4)
84
-------
Oxygen can also play a role in these reactions. A chemical that is unreactive
on photolysis in pure water can be photolyzed in natural water; for example,
aldrin to give dieldrin [Ross and Crosby (1975)], dimethylfuran to give di-
acetylethylene (Zepp et al., 1977) and cumene to give oxidation products (Mill
et al. , 1977) .

Some discussion of the various indirect photolysis processes is useful
to fully appreciate the role that photochemistry plays in the transformation
of chemicals in the environment. One mechanism for indirect photolyses is a
photosensitized reaction in which a sensitizer S (a compound or substance other
than the chemical of interest) absorbs light, undergoes intersystem crossing
from singlet to triplet excited state, and then transfers th^e excited state
energy to the chemical, which undergoes reaction from the 3C species:

, *
S - *• 1S
3S* + C - S + 3C
i *
3C - » Products
The products of such sensitized reactions are often the same as if the chemical
had absorbed the light itself in a direct photolysis process
1 * 3 *
1C *• 3C
*
3C —*- Products
Thus, solvents (or cosolvents) that are sensitizers should be avoided in con-
ducting photolyses to evaluate direct photolysis rate constants.

There is no unambiguous evidence that triplet-sensitized reactions of
organics occur in natural waters. One reason for their possible unimportance
is the rapid quenching of many triplets by oxygen with or without formation of
singlet oxygen (102).

3S* + 302 +• *S + ^a
85
-------
Zepp et al. (1977) showed that 10"12 to 10~13 M ^2 was formed in a variety of
natural waters with modest quantum yields ( ^ 0.01). Some triplets from
carbonyls (n-ir) are not as susceptible to quenching and may participate in free
radical oxidations (Mill et al., 1977)
Subsequent reactions of 102 and R- can form peroxides and other oxidation
products. Thus, indirect reaction of triplets from natural organics seems
clearly established.

The efficient quenching of some triplets by oxygen is also a possible
source of retardation of some photolysis. For example, quinoline undergoes
photolysis 2.3 times as fast in the absence of oxygen (Smith et al., 1978).

For the foregoing reasons, the photolysis protocols recommended in
Sections 3.5 and 3.6 explicitly require use of air-saturated solutions of
chemicals. Such conditions are relevant to shallow depths of pure water, and
as long as the concentration of oxygen in the water (2.7 x lO'14 M) is constant,
the effect of oxygen on the photolysis rate will be included in the reaction
quantum yield and photolysis rates that are measured.

3.7.5 Photochemical Equipment

Sunlight Experiments

Numerous investigations of photolyses in sunlight have been described,
but no uniform procedure is used. However, careful consideration of some
variables that affect experimental results suggests some reasonable precautions
for such experiments. Ideally, photolyzed solutions should be exposed in a
sunlit location free from reflections from walls and windows and without morning
or afternoon shadows. Solutions should be contained in a housing protected
from weather; a greenhouse constructed of thin borosilicate glass,
thermostated at about 25° ± 2°C, would be suitable for such sunlight experiments.
In no case should solutions be exposed to freezing conditions.

Although large-diameter dishes with flat transparent tops (like petri
dishes) most closely simulate the light conditions incident on a water body,
such vessels are difficult to seal, and can lose both chemical or water through
volatilization. Condensation of water or chemical on the lid may also serve
to distort or absorb sunlight. These problems would be especially troublesome
for experiments carried out for long reaction times, and would also make sampling
difficult. Reasonable substitutes for reaction dishes are round borosilicate
glass tubes, which can be prepared, sealed, and exposed to sunlight; one tube
can be used for each time-datum point. The tubes should be placed in a rack
at an angle of about 30° from vertical and positioned so that all tubes receive
equal sunlight irradiation. If more accuracy is desired, the simultaneous
photolysis of a solution of a nonvolatile, photoreactive chemical in a glass
dish and glass tubes will provide reaction rates from which a tube correction

86
-------
constant can be calculated for use in studies on other chemicals. One study
has found that photolyses in tubes are less than a factor of two faster than
in dish containers (R. G. Zepp, private communication). Also, judging from the
good agreement between photolysis rate constants measured in experiments using
glass tubes and calculated from quantum yields and absorbance spectra (Smith
et al. , 1978), the glass tubes are quite satisfactory for environmental studies.

Laboratory Experiments

Design of Apparatus: The apparatus used to measure photochemical kinetics
in the laboratory is usually of either the merry-go-round reactor or the optical
bench design. Both designs provide for constant and even irradiation of a
solution at a fixed distance from the light source and allow for interposition
of a light-filter system between the light source and reaction solution. The
general features of each design are described below, with the main components
(light source, reaction cells, and light filters) described in separate sections.
For both designs, the apparatus should be appropriately housed to shield
laboratory personnel from exposure to uv light and to exclude extraneous light
sources that could contribute to photoreaction of chemicals.

In the optical bench system, the light source is located at the end of
the bench, usually with a housing around the light with an aperture to direct
the light beam. The light then passes through glass filters or through a cell
containing filter solutions that may transmit only one wavelength band. Filter
solutions in the cell may be circulated through a cooling system, and the glass
filters should be cooled with a stream of air to prevent heat buildup, which
may crack the filters or cells. The reaction cell containing the solution of
chemical is mounted coaxially with the lamp on the bench so that the filtered
light enters the window of the cell. The reaction cell should be temperature-
controlled to ± 2°C by circulating constant temperature water through side walls.
A sufficient volume of reaction solution should be used to permit removal of
samples for analysis without significantly altering the volume of the reaction
solution in the cell. Details of construction of reaction cells may be found
in Calvert and Pitts (1966) and deMayo and Shizuka (1976). Commercially
available optical benches are preferred to ensure proper alignment of the com-
ponents of the optical train, but simple "home-made" benches have been described
(Andre et al., 1977).

The design of the merry-go-round reactor (MGRR) has been described in
tbe literature (Moses et al., 1969; Murov, 1973; deMayo and Shizuka, 1977), and
several designs are commercially available. The most common and practical
design has the light source at the center of the MGRR in an immersion well with
reaction solutions in tubes arranged in a ring around the light source. The
ring rotates around the light source to give even irradiation of the reaction
tubes. Glass filters may be inserted between the light source and the reaction
tubes. Filter solutions may also be contained in the immersion well containing
the light source or in a glass "donut" that surrounds the light source. To
dissipate heat from the lamp, the MGRR may be immersed in a water bath or a
stream of air may be passed through the space between light and filters; filter
solutions can be circulated to an external cooling source. The design of the
MGRR usually dictates that cells (cylindrical or square) of small volume can
be used, with one cell used for each datum point measured.

87
-------
The MGRR has the advantage over the optical bench that a number of samples
can be irradiated at one time, and the apparatus takes up little laboratory
space. The disadvanges of the MGRR are that it requires a larger initial in-
vestment to purchase or construct ($500 to $1,000) and the choice of lamps
available for use in the MGRR is limited because of the fixed dimensions of the
center well.

In summary, the MGRR and optical bench systems are both useful for
measuring photochemical kinetics and quantum yields. Depending on the laboratory,
the chemicals under investigation, and the number of measurements to be made,
one system may be preferred over another.

Light Sources; A number of light sources with different intensities and
wavelength distributions are available (Calvert and Pitts, 1966; deMayo and
Shizuka, 1976; Murov, 1973). The use of an optical bench or MGRR will often
narrow the choice of a lamp with regards to the use of a point source or a tube
type lamp, since the former can be focused to give a collimated beam while the
latter cannot. The main criterion for selecting a light source is that the
lamp provides light at a constant and high intensity in a narrow wavelength
region during the photolysis experiment. The output of the lamp should also
be high enough to allow for attenuation of light by the isolation filter system
and yet provide a high enough flux to perform the experiment within a reasonable
time. DeMayo and Shizuka (1976) have suggested that, in general, for an ex-
periment to be conducted in a reasonable time of 15 minutes to 10 hours, the
intensity of the filtered light should be greater than 10x" photons cm~a sec-1.
The lamp most commonly used in MGRRs is a 400-watt, medium-pressure Hg lamp.
The characteristics and application of other lamps are presented in detail by
Calvert and Pitts (1966), Murov (1973), and deMayo and Shizuka (1977). The
last paper also discusses the use of lasers as light sources; if available,
lasers are a convenient source of intense monochromatic light.

Light Filter Systems; Monochromatic or narrow wavelength light is es-
sential for accurate measurements of photochemical quantum yields. Although a
set of emission lines or a broad spectrum of light might be used to calculate
a quantum yield, the absolute intensities at each wavelength would have to be
known or calibrated continuously. The use of light in a narrow wavelength
region is then more convenient, once the light source and filter system are set
up in the MGRR or optical bench.

A narrow wavelength region is conveniently isolated with a combination
of solution and glass filters; some of these combinations have been summarized
by deMayo and Shizuka (1977), Murov (1973), and Calvert and Pitts (1966) . As
described earlier, these filter systems must be protected against excessive
heat from the lamp. Although moderately expensive (> $50), glass interference
filters very efficiently isolate narrow wavelengths of light. Glass filters
that function by absorbing unwanted wavelengths of light are relatively cheap,
quite stable and are recommended.

Filter solutions containing chemicals that absorb light in specific wave-
length regions are also useful when glass filters are not available or are in-
applicable to certain wavelength regions. However, since these solutions degrade

83
-------
on prolonged photolysis, they must be carefully monitored. Even when tap water
is passed through the immersion well to cool the lamp, the buildup of solid
material or algae in the well may reduce the light intensity. Repeated
actinometry is the only method for detecting changes in output of the filtered
light source.

Two filter systems commonly used for isolating the 313 nm and 366 nm
bands from a 450-watt medium-pressure Hg lamp are described below:

• 313 nm filter system: Corning CS 7-54 glass filters with a 0.001 M
potassium chromate solution in 3% aqueous sodium carbonate are
circulated in an immersion well. This system transmits primarily the
313.2 and 312.6 nm Hg lines, which represent greater than 95% of the
light incident on the reaction solutions (a small Hg line at 302.2 nm
is also present).
• 366 nm filter system: Corning glass CS 0-52 and CS 7-60 glass filters
are used. This pair of glass filters transmits only the 365.1, 365.6,
366.4 nm lines of the Hg lamp, with no other lines observed (less than
1% of light outside the 366 nm band).

When these filter systems were used in a MGRR with 10 cm between the light
source and reaction solutions contained in 10 mm-O.D. borosilicate glass tubes,
the light flux entering the solutions at 313 nm and 366 nm was about 5 x 10~6
einstein cm"2 sec"1 (Smith et al., 1977).

Reaction Cells and Solutions: Cells of large volume are appropriate for
use with optical benches, and small cells are used with MGRRs. For quantum
yield measurements relevant to environmental photochemistry, cells constructed
of borosilicate glass are suitable because they transmit only light above 290
nm. To duplicate as closely as possible the optical chacteristics of the photo-
chemical apparatus, actinometers and reaction mixtures should be photolyzed in
identical reaction cells.

When actinometer solutions with optical densities greater than 2 are
used, the cells should be examined after photolysis to determine whether solids
have deposited on the walls of the cell as a result of a photoreaction at the
cell-solution interface. Use of a more dilute solution of actinometer will
remedy the problem. No problems of this kind have been encountered using fer-
rioxalate or nitrobenzaldehyde actinometers.

As mentioned earlier, the pathlength £ of a 1-cm-square cell is easily
defined, but for a long path rectangular cell, and especially for a cylindrical
cell where the light falls on rounded surfaces, the pathlength is less easily
defined because of refraction and reflection in the cell. Zepp (1978) described
an experimental method using an isolated wavelength band to determine the ef-
fective pathlength of any cell. Equation (3.59) is used in the pathlength
calculation
Ratec = *IoXr(l - 10~e£c) (3.59)
89
-------
When tiC > 2 (as in actinometry), equation (3.60) applies
Rate = <(>I .r (3.60)
max OA
where Ratemax is the maximum rate of disappearance for the chemical in the
system (i.e., the light entering the cell is the rate-limiting factor). Divi-
sion of equation (3.59) by equation (3.60) gives
RateC -
• - 1 - 10 - X (3.61)
Rate
max
-log(l - X) = e£C (3.62)

Zepp (1978) measured the effective cell pathlength I using the
benzophenone-sensitized isomerization of cis-l,3-pentadiene. Described below
are the steps followed in using equation (3.62) with the potassium ferrioxalate
(FO) actinometer system at wavelength interval X:

(1) Prepare FO solutions with OD > 2 with known concentration C^.
(2) Prepare, by sequential dilutions of the solution above, FO solutions
with optical densities 1 to 0.05 with known concentrations Ci, C2,
C 3, C i., and C 3.
(3) Photolyze the six solutions for identical times in a MGRR and analyze
for ferrous ion by standard procedures. Reaction times should be for
less than 10% reaction of FO.
(4) Determine the ratios Ad/AC,,,, AC2/ACm, etc., where ACi, AC2, etc.,
are the amounts of ferrous ion formed in each respective photolysis.
The ratios are designated Xt, X2, etc.
(5) Plot the quantity [-log(l - Xx)] versus e^Ci, [-log(l - X2)] versus
e\Ca, etc., for each set of data points; e\ is the absorption coef-
ficient for FO at A.
(6) Calculate the slope of the plot, which is equal to the effective cell
pathlength I. A more accurate and precise value of i may be obtained
by a fit of the data by linear regression analysis.
*
We have found that a cylindrical borosilicate reaction tube with an I.D. of
11.0 mm and an O.D. of 13.0 mm has an effective pathlength of 11.2 mm. A re-
action tube made from borosilicate glass stock of I.D. 9.7 mm and O.D. 12 mm
had an effective pathlength of 10.0 mm.
The tubes are Corning Glass disposable culture tubes, 13 x 100 mm and are
especially convenient because they have screw caps for easy sealing.
90
-------
Other workers have pointed out that when actinometry is carried out in
cylindrical cells the light flux measured (and therefore any quantum yields)
will be solvent dependent because of the refractive indices of the solvent.
Thus the quantum yields for photoisomerization of 1,3-pentadiene in benzene
were 0.64 and 0.55 when ferrioxalate (in water) and benzophenone-benzhydrol (in
benzene), respectively, were the actinometers used (Vesley, 1971). The reason
for the difference was attributed to the difference in refractive indices of
water and benzene. Benzene has a refractive index (n20° = 1.501) similar to
glass and allows all incident light to pass into solution, whereas water (n^O
= 1.332) refracts and reflects some of the light at the inner cell walls. The
aqueous ferrioxalate actinometer therefore underestimated the light that actually
entered the solution in the cell when benzene was the solvent and thus over-
estimated the true quantum yield for pentadiene isomerization by 15%.

Since the quantum yields of interest in these protocols are for aqueous
solutions, actinometry should be performed in aqueous solutions whenever possible.
In cases where aqueous actinometers are not practical, an actinometer solvent
such as acetonitrile (n20° = 1.344) may be suitable.

3.7.6 Actinometers and Actinometry

Actinometers are chemicals that photolyze in solution over a wide spectral
range with well-known quantum yields that change little with wavelength and
produce products that are easily measured. Two examples are potassium fer-
rioxalate in water
and o-nitrobenzaldehyde in acetonitrile
Neither reaction is affected by oxygen and only slightly by temperature; there-
fore, these reactions can be used to measure reliably the light flux entering
a reaction cell.

Typically, a solution of actinometers of known optical density and path
length is exposed to the light source for a known period of time and then
analyzed for product. Since most actinometers have high quantum yields, even
low photon fluxes will make 1% to 2% changes in short times and require exclusion
of stray light during preparation and analysis. The incident photon flux is
calculated using equations (3.43), (3.45), or (3.47) and solving for Io^r, using
the known value of . Precisions of ± 10% are usual in this determination.
Although the common practice has been to use highly absorbing solutions of

91
-------
actinometers to ensure that all light is absorbed and zero-order kinetics is
obeyed (equation 3.4 7), there is no reason that more dilute solutions cannot
be used, provided the correct kinetic equation is used to determine I Ar.
O A

Because of the low quantum yields in environmental photochemistry, it
is frequently necessary to use protracted exposure times of chemicals to achieve
significant reaction. Actinometry must then be carried out at frequent inter-
vals to ensure that the light flux has not changed. In practice, this usually
means that actinometry is performed once at the beginning of the experiment and
once at or near the end.

Excellent descriptions and instructions on the use of some known high-
optical-density actinometers are available (Demas, 1976; deMayo and Shizuka,
1976; Calvert and Pitts, 1965; Murov, 1973). Of the actinometers cited by these
authors, the actinometers in aqueous solution are the most useful for environ-
mental studies because of the solvent-refractive index problem discussed above
(Section 3.7.5). All the aqueous actinometers are metallo-organic redox reac-
tions. Only o-nitrobenzaldehyde in acetonitrile solvent also appears to be
useful for environmental photochemical studies.

As pointed out by Zepp (1978) and Demas (1977), dilute solution
actinometers have several practical advantages over high-optical-density
actinometers but none of the dilute solution methods can be considered well
enough established for routine use at this time.

Few chemicals are available for use as reference standard chemicals for
sunlight photolyses. Most common laboratory actinometers react far too rapidly
in sunlight to be of practical use as sunlight actinometers. While it is
provisionally acceptable to use chemicals that have been shown to give good
correlation between measured and calculated sunlight photolysis rates (Zepp and
Cline, 1977; Zepp, 1978; Smith et al., 1977), more data on the chemistry occur-
ring in such systems would provide more reliability for general use. Certainly
more sunlight experiments are necessary to verify half-lives calculated as a
function of the time of year and latitude.

3.7.7 Light Sources to Simulate Sunlight

Several systems described in the literature (Roller, 1965) simulate sun-
light in a qualitative manner. These light sources are either lamps with no
output below 300 nm or coupled with filters (most commonly borosilicate glass)
to block light below 300 nm. Except for the xenon lamp, none of the laboratory
sources closely approximates the intensity and distribution of sunlight over
the entire solar spectrum in a manner suitable for general application to
estimating environmental photolysis rates. Xenon lamps require expensive
auxiliary equipment; moreover, while all lamps show some decay in light output
with time, xenon lamps are particularly prone to decay. Lamps with a broad
spectrum output above 300 nm have an additional drawback in quantitative ap-
plications in that they must be continuously calibrated for comparison with
sunlight, and no inexpensive and simple procedure is available at this time.
Since the photon flux is the important property of light related to reaction
rate, a simple measurement of the energy output of a lamp over a broad region
is not an acceptable way of relating the output of a laboratory lamp to sunlight
(see Section 3.7.5).
92
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3.7.8 Sunlight Intensity Variations

A major variable in the sunlight photolysis rates of chemicals in the
aquatic environment is the intensity and wavelength distribution of sunlight
itself, which varies with the time of day, season, and latitude. The intensity
and distribution of light energy in the atmosphere has been discussed by Leighton
(1961), Koller (1965), Bener (1972), and Peterson (1976). These authors treat
sunlight observed at the earth's surface and in the troposphere as composed of
two components. One component is the direct light from the sun, which has an
intensity that is dependent on the angle of the sun in the sky. The other
component is sky light, of uniform intensity, which results from light scattering
in the sky. Zepp and Cline (1977) have used the data of Bener (1972) and Leighton
(1961) in their computer program to calculate photolysis rate constants in aquatic
systems.
Although cloud cover, air pollution, ambient particulate, and other
transient conditions reduce the incident sunlight intensity and can cause sig-
nificant fluctuations in solar flux, the effect of such transient or localized
conditions cannot be reliably included in estimations of sunlight intensity.
The need for a general and uniform set of data for sunlight photolysis rate
constants requires that clear-sky light intensity data be used; however, the
user of such data should be aware of error limits of the rate constants obtained
with the data (see Error Analysis, Section 3.6.8).

Strong support for using the clear-sky intensity data has been provided
by the good agreement obtained between photolysis rate constants measured in
sunlight experiments and those calculated using quantum yields and absorbance
spectra for several pesticides (Zepp, 1978) and for polynuclear aromatic hydro-
carbons and heterocycles (Smith et al., 1978). The agreement found for rates
of photolysis of several of these chemicals (Smith et al.) is shown graphically
in Figure 3.3. Zepp and Cline's program calculates rate constants as a function
of the time of day or averaged over a full day, with good agreement found again
as shown in Figure 3.3 for midday or day-averaged photolysis half-lives.

The program of Zepp and Cline can also calculate photolysis rate constants
and half-lives as a function of dates and latitude. Calculated half-lives for
two compounds are shown in Tables 3.7 and 3.8 and show the effect of changes
in latitude and season on the rates at which chemicals photolyze in sunlight.

Benzo[a]pyrene shows a 2.2-fold change in rate at 40° latitude between
winter and summer, whereas methyl parathion shows a 3.8-fold change in rate for
the same latitude and seasons. Methyl parathion is more dependent on the low
wavelengths of sunlight for photolysis than benzo[a]pyrene and therefore shows
a greater difference between winter and summer than benzopyrene because of the
greater variation in shorter wavelength light flux between the two seasons.

A problem that occasionally arises in some photolysis experiments is how
a chemical that has "no extinction coefficient" (or at least none detectable)
in the solar spectral region may be found to photolyze when exposed to sunlight
(Rosen, 1972). Some reasons suggested for this behavior have been: a small
amount of sunlight below 290 nm that penetrates the earth's atmosphere (Barker,
93
-------
(BENZOTHIOPHENE —
r
METHYL PARATHION
CARBAZOLE
. DIBENZOtc.g]CARBAZOLE

BENZ [a] ANTHRACENE
BENZOIflQUINOLINE

I I I I I I
//
hours
6 8' ' 21 23' 35 37
dayi
MEASURED HALF-LIFE
SA-4396-76
FIGURE 3.3 COMPARISON OF MEASURED AND CALCULATED HALF-LIVES FOR DIRECT
PHOTOLYSIS
94
-------
TABLE 3.7. BENZO [a] PYRENE PHOTOLYSIS HALF-LIVES (hours)
(Calculated for Midday)
Season Date

Latitude
0
10
20
30
40
50
60
70
Spring
0.52
0.47
0.52
0.54
0.58
0.68
0.85
1.22
Summer
0.53
0.52
0.50
0.52
0.54
0.59
0.68
0.85
Fall
0.51
0.53
0.58
0.68
0.85
1.21
2.09
4.72
Winter
0.53
0.58
0.68
0.85
1.2
2.1
4.8

TABLE 3.8.
METHYL
PARATHION PHOTOLYSIS HALF-LIVES
(Calculated for 24-Hour

Season Date
Calendar Day)

(days)

Latitude
0
10
20
30
40
50
60
70
Spring
9.2
5.6
9.1
9.6
10.7
12.7
16.0
21.8
Summer
9.60
8.84
8.48
8.45
8.68
9.24
10.2
11.4
Fall
9.00
9.73
11.1
13.6
18.1
27.7
51.4
144.
Winter
9.5
11.0
13.8
19.1
30.7
61.6
190
—

95
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1968), changes in the absorption spectrum of the chemical as a result of surface
interactions, or adventitious reactions with oxidants or photosensitizers.
While such processes are possible, direct photolysis of a chemical also may oc-
cur if the reaction quantum yield (c) is high enough to compensate for low ab-
sorption coefficients (equation 3.55). For example, assuming that a
chemical has constant absorption coefficients e\ equal to 0.1 M"1 cm~l in the
wavelength region 296 to 320 nm and = 1, the calculated half-life is 120 days
in summer at 40° latitude. If the wavelength region extends to 360 nm with
EX constant at 0.1, the calculated half-life is 12.0 days in summer. Thus,
the ability to predict, or even to rationalize environmental photolysis rates
for some chemicals may depend on the state of instrumentation for measuring ab-
sorption coefficients accurately below 0.1 M"1 cm"1.

3.8 REFERENCES

Andre, J. C., M. Niclause, J. Joussot-Dubien, and X. Deglise. 1977. Photo-
degradation of Pyridine in Aqueous Solution. J. Chem. Educ. 54(6): 387-8.

Barker, R. E. Jr. 1968. The Availability of Solar Radiation below 290 nm and
Its Importance in Photomodification of Polymers. Photochem. Photobiol.
7: 275-295.

Barltrop, J. A., and J. D. Coyle. 1975. Excited States in Organic Chemistry.
John Wiley & Sons, Inc., New York.

Bener, P. 1972. "Approximate Values of Intensity of Natural Ultraviolet Radi-
ation for Different Amounts of Atmospheric Ozone." U.S. Army Report
DAJA37-68-C-1017, Davos Platz, Switzerland.

Calvert, J. G., and J. N. Pitts. 1966. Photochemistry. John Wiley & Sons,
Inc., New York.

Crosby, D. G. 1972. The Photodecomposition of Pesticides in Water, in "Fates
of Organic Pesticides in the Aquatic Environment." Adv. Chem. Series III,
Am. Chem. Soc., Washington, D.C.

Crosby, D. G., K. W. Moilanen, M. Nakagawa, and A. S. Wong. 1972. Photonucleo-
philic Reactions of Pesticides. "Environmental Toxicology of Pesticides,"
F. Matsumra, G. M. Boush and T. Misato, Eds. Academic Press, New York.

Demas, J. N. 1976. The Measurement of Laser Intensities by Chemical
Actinometry. "Creation and Detection of the Excited State, Vol. 4. W. R.
Ware, Ed., Marcel Dekker, Inc., New York.

de Mayo, P., and H. Shizuka. 1976. Measurement of Reaction Quantum Yields.
"Creation and Detection of the Excited State," Vol. 4, W. R. Ware, Ed.
Marcel Dekker, Inc., New York.

Hutchinson, G. E. 1957. A Treatise on Limnology. Vol. I. Geography, Physics,
and Chemistry. John Wiley & Sons, Inc., New York.

96
-------
Kirk, J.T.O. 1977. Attenuation of Light in Natural Waters. Aust. J. Mar.
Freshwater Res. 28:497-508.

Koller, L. P. 1965. Ultraviolet Radiation, 2nd Ed. John Wiley & Sons, Inc.
New York.

Leighton, P. A. 1961. Photochemistry of Air Pollution. Academic Press, New
York.

Mill, T., D. G. Hendry, and H. Richardson. 1977. Chemical Transformation of
Pollutants in Water. Proc., 2nd Intl. Symp. Aquatic Pollutants, Amsterdam,
September 1977. Pergamon Press, in press.

Moses, F. G., R.S.H. Liu, and B. M. Monroe. 1969. The "Merry-go-round" Quantum
Yield Apparatus. Mol. Photochem. 1(2):245-249.

Murov, S. L. 1973. Handbook of Photochemistry. Marcel Dekker, Inc., New York.

Peterson, 1976. Calculated Actinic Fluxes (290-700 nm) for Air Pollution Pho-
tochemistry Applications. EPA 600"4-76-025.

Rosen, J. D. 1972. The Photochemistry of Several Pesticides. "Environmental
Toxicology of Pesticides," F. Matsumura, G. M. Boush, and T. Misato, Eds.
Academic Press, New York.

Ross, R. D., and D. G. Crosby. 1975. The Photooxidation of Aldrin in Water.
Chemosphere 4(5):277-282.

Smith, J. H., W. R. Mabey, N. Bohonos, B. R. Holt, S. S. Lee, T.-W. Chou, D. C.
Bomberger, and T. Mill. 1977. Environmental Pathways of Selected Chemicals
in Freshwater Systems. Part I. Background and Experimental Procedures.
EPA-600/7-77-113.

Smith, J. H., W. R. Mabey, N. Bohonos, B. R. Holt, S. S. Lee, T.-W. Chou, D. C.
Bomberger, and T. Mill. 1978. Environmental Pathways of Selected Chemicals
in Freshwater Systems. Part II. Laboratory Studies. EPA-600/7-78-074.

Turro, N. J. 1965. Molecular Photochemistry. W. A. Benjamin, Inc., New York.

Vesley, G. F. 1971. Complications in Measuring Quantum Yields Using Cylindrical
Sample Cells. Mol. Photochem. 3(2):193-200.

Zepp, R. G. 1978. Quantum Yields for Reaction of Pollutants in Dilute Aqueous
Solution. J. Amer. Chem. Soc. 12(3):327-329.

Zepp, R. G., and D. M. Cline. 1977. Rate of Direct Photolysis in Aquatic En-
vironment. Environ. Sci. Technol. 11(4) :359-366.

Zepp, R. G., N. L. Wolfe, G. L. Baughman, and R. C. Hollis. 1977. Singlet
Oxygen in Natural Waters. Nature 276(5610)-.421-422.
97
-------
Appendix 3. A

CALCULATION OF L. VALUES
A

In a water body exposed to the sun, the intensity of light passing into
the water body is (I ,) is composed of light directly from the sun (I,,) and
the light from the sky (Is,)- Leighton (1961) discussed the calculation and
contribution of I . and I . to the total light intensity at a point on the
earth's surface as a function of the zenith angle z (Figure 3. A.I). Zepp and
Cline (1977) extended the discussion to the I,, and I . components that enter
the water body, and the reader is referred to this paper for a more complete
discussion of the subject.

Zepp and Cline showed that the pathlength, £ , , of direct radiation in
a water body is

SL, - D sec 0 (3. A.I)
d

where D is the depth, 0 is the angle of light refraction from vertical in the
water body (Figure 3. A.I), defined by sin z - n sin 9 where n is the index of
refraction of water and z is the angle of the sun from vertical. Assuming
that the sky is uniformly bright and neglecting reflection from water, the
pathlength I of sky radiation in water is

£ - 1.20 D (3.A.2)
s

if the index of refraction of water is taken as 1.34. Allowing for the indi-
vidual intensity and pathlength terms for the direct and sky radiation, the
term for I .1 in a water body becomes

I .£ - I ,1.200 + I..D sec 0 (3. A. 3)
OA SA dA

The general equation for photolysis in water (see page 30)

x (3.A.4)
dt "

may be considerably simplified by two assumptions. First, when the chemical
absorbs only a small fraction of the light compared with the water body,
e, C H « o. SL, then
A A
. dC , 4Ioi. 11 i _
dt D
. "A

ba -ox--10'"*"'
A 98
-[£1 (3.A.5)
-------
sin 6

(0<48°)
2 = Angle of incidence (solar zenith angle in case of direct sunlight)
6 = Angle of refraction
n = Refractive index of water
SA-4396-77

FIGURE 3.A.1 REFLECTION AND REFRACTION OF A LIGHT BEAM PASSING
FROM ATMOSPHERE INTO A WATER BODY
(From Zepp and Cline, 1977)
99
-------
Second, when a I < 0.02, as is the case near the surface of water,

k = 2.3 e.I ,S,/D
p A OA

Substitution in (3. A. 6) for I £ from equation (3. A. 3) gives?
O A
kp =
2.3
(3.A.6)
(3.A.7)
Thus k becomes independent of depth near the surface.
Since the protocol is to be applied to environmental photolysis rates
where the primary concern is for chemicals with half-lives of days or months
rather than hours, the total light intensity (in brackets in equation 3. A. 7)
should be an averaged light intensity for an entire day. This light intensity
term is called L, and was obtained as described below.
A

Zepp and Cline (1977) have written a computer program that calculates
the first-order sunlight photolysis rate constants k for 39 specific wave-
length intervals from 296.3 to 825 nm and then sums these rate constants to
obtain the environmental rate constant k . The computation is based on
equation (3. A. 5) in which I is substituted by equation (3.. A. 3)
OA
- 10~Vs)
- 10~v'd)]
(3-A-8)
and requires input data of $ and e. . Data for cu , depth and other parameters
can also be included for calculating photolysis rate constants and half-lives
under a number of environmental conditions. The I x and I ^ values themselves
are based on the data of Bener (1972) and Leightonstl961) and are calculated
as a function of season, time of day, and latitude.

The output of the program provides the instantaneous rate constants at
specific times of the day for a given latitude and season date. The term
midseason date as used by Zepp and Cline does not refer to a day midway in the
season, but rather a day during the season when the angle of declination of
the sun is at the specific values used in the computer program; in the text,
we have referred to these days as "season dates" to avoid misinterpretation
of the word "midseason." See Section 3.6.4 for further information on the
season dates for the four seasons. The program further calculates a photolysis
rate constant k „, which is averaged over a 24-hour calendar day (with k in
units of day~l)?E pE

To obtain L^ date data for use in equation (3. A. 8), we calculated the day
averaged, season photolysis k_x values, using the computer program with EX
equal to unity and the absorption coefficients a^ for pure water. The kp^
values with $ and eA = 1 are designated L^. The units for L\ are einsteins 10" 3
cm~a day"1. Multiplication of L^ by an actual e^ (in M-1 cm"1) then gives the
first-order rate constant k . x (in day"1) since einsteins liter"1 is equivalent
to M. aX
100
-------
Since the L^ values were calculated using the program of Zepp and Cline
the difference between the Z values in their paper and the L^ values presented
here should be clearly defined. Most importantly Z values pertain to mid-
season, midday light intensity and are used to calculate midday, midseason
photolysis rate constants. L. data are used to calculate day-averaged, 24-
hour Calendar) day photolysis rate constants. Also, units of L. and Z^ are
different.
It is instructive to compare the assumptions underlying the L, and Z^
values. To obtain Z, values, Zepp and Cline used equation (3.A.7) as the start-
ing point and defined

ZX ' (1'2 rsX + ZdX Sec0) <3'A-9>

in units of photons cm~2 sec"1. They define the instantaneous photolysis
constant in sunlight at midday, midseason in terms of Z. as
A
i i
k'PE = -T* £-ZXeX (3.A.10)

which differs from equation (3.A.8) by the conversion factor J (photons/einsteins)
and by the units of cm~2 sec"1 instead of liter"1 day"1.
101
-------
Appendix 3.B

INTEGRATION OF EQUATION (3.40)
Equation (3.40)
dC
-rr = I ,1
dt oA
is readily integrated. For convenience in integration, substitution is first

made of terms a * <|>I ^r and b = 2.3&E, to give
Integration of equation (3.B.I) then gives
(3.B.I)
_ Ct

t r C^r f bO

d" fs^l -/T7
dC
bC
(3.B.2)
at
1 ,_ ~ bC.
- In (1 - e )
(3.B.3)
o o

where Co and Cj- are chemical concentrations at times t0 and t, respectively.
Then
! t ,
1 le c- 1
or - - •
When t = 0, equation (3.B) then gives
- bat - ln(ebCt- 1) - ln(ebCo- 1)
(3.B.5)
102
-------
CHAPTER 4. OXIDATION IN WATER

T. Mill

4.1 INTRODUCTION 104
4.2 OBJECTIVE 104
4.3 SUMMARY 105
4.4 CONCLUSIONS AND RECOMMENDATIONS 106
4.5 SCREENING TEST 107
4.5.1 Screening Test for Peroxy Radical Oxidation of CH Bonds .... 107
4.5.2 Screening Test for Peroxy Radical Oxidation of ArOH, ArNHR or
RSH 110
4.5.3 Screening Test for Oxidation by Singlet Oxygen 110
4.5.4 Scope and Limitations of Screening Tests Ill
4.5.5 Error Analysis 112
4.6 DETAILED TESTS 112
4.7 BACKGROUND 113
4.7.1 General Considerations 113
4.7.2 Oxidants in Aquatic Systems 113
4.7.3 Oxidation Chemistry and Kinetics 114
General Considerations 114
Radical Oxidants R02», R02, and H0» 115
Singlet Oxygen (I0a) 118
Measurement of kp for R02» Oxidations 120
Measurement of RQX for I0a Oxidations 124
B Values 126
Solvent Effects on Oxidation Reactions 127
Radical Oxidants 127
Singlet Oxygen 127
Temperature Effects in Oxidation 128
4.7.4 Review of Environmental Oxidation Studies 129
General 129
Radical Oxidants 131
Singlet Oxygen 132
4.7.5 Design of Laboratory Test Methods 133
R02» Oxidation Test 133
^3 Oxidation Test 135
4.8 REFERENCES 136
103
-------
4. OXIDATION IN WATER
4.1 INTRODUCTION

Chemical oxidation is often observed in aquatic environments as a conse-
quence of photochemical processes which generated free radicals by bond
homolysis of electronically excited species or singlet oxygen by energy trans-
fer from an electronic triplet state to triplet oxygen. Two general types of
oxidation reactions can be distinguished for evaluating chemical oxidation
processes in an aquatic environment:

(1) Reaction of an excited state of a molecule with oxygen, in which the
excited state is produced by direct photolysis or by interaction
with a photosensitizer; this process is termed photooxidation
(2) Reaction of the ground state of the chemical with oxidants in solu-
tion, in which the oxidants are formed by reactions of dissolved or
suspended natural materials in solution; these reactions are termed
thermal oxidation, autoxidation or simply oxidation. The ultimate
driving force for oxidant formation may, however, often be photo-
chemical reactions of the natural materials.

This distinction between photooxidation and thermal oxidation is important
if laboratory test procedures are to be developed that will accurately predict
the rates of these processes in a variety of aquatic environments. In most
cases the properties of a chemical and of an aquatic environment that must be
characterized are quite different for these two kinds of processes. Scheme 1
illustrates the two processes and the rate laws that govern them. In photoox-
idation the relevant molecular and environmental properties are the absorption
coefficient in the solar region, quantum yield, and solar irradiance. In
thermal oxidation the relevant properties are rate constants for oxidant-mole-
cule reactions, oxidant concentrations, and temperature.

This report is concerned only with thermal oxidation (hereafter termed
simply oxidation). Test methods are proposed for evaluating the rate constants
for oxidation based on theoretical and experimental methods used in oxidation
chemistry. Literature and current research on oxidation processes have been
reviewed, and the most reliable methods for predicting rates of oxidation in
aquatic systems are discussed.

4.2 OBJECTIVE

The objectives of this research are to develop simple reliable test pro-
cedures for measuring rate constants for oxidation of most types of chemicals
dissolved in water at 25°C and for using these data to predict the rates of
oxidation in aquatic systems.
104
-------
Scheme 1

PHOTOOXIDATION AND THERMAL OXIDATION
Photooxidation
AY + hv
AY
AY + 0,
(several steps)
or
(several steps)
Thermal Oxidation
AY + OX
Products (several steps)
R
ox
(OX is any oxidant)
4.3 SUMMARY

This report recommends that two screening tests be used to evaluate the
rate constants for oxidation of selected chemicals by alkylperoxy radicals
(R02») and by singlet molecular oxygen (102), both of which are found in natural
water exposed to sunlight. Two screening tests were developed to provide ap-
proximate values of these rate constants. No detailed tests are recommended
at this time owing to a lack of information on kinetic processes and on standard
chemicals needed for relative rate measurements.

Background information on kinetics rate laws for oxidation processes has
been developed in order to use rate constants for oxidation, estimated from
screening tests, for calculating the persistence of chemicals in natural aquatic
systems. The concentrations and reactivities of oxy free radicals and singlet
oxygen are such that only R0a» and 102 are likely to be important oxidants in
natural waters and only selected classes of chemicals are going to be reactive
enough toward these oxidants to justify use of screening tests for oxidation.

105
-------
These reactive chemicals include: phenols, aromatic amines, thiols, hydroxyl-
amines, and hydrazines, all of which are reactive toward R02»; eneamines,
vinyl ethers, internal olefins, furans, dienes, polycyclic aromatics, and
sulfides, all of which are reactive toward 102.

The chemistry and kinetics of R02» reactions have been well worked out
in non-aqueous solvents. Peroxy radicals mostly transfer H-atoms or add to
double bonds. The rates of H-atom transfer are usually slow from CH bonds,
kR02 < 100 M-1 s-1, and usually rapid from ArOH, ArNH and RSH bonds, k > 10fc
M~l s~l. Singlet oxygen undergoes five distinctive types of reactions: 1,2-
and 1,4-cycloaddition, ene reaction, sulfide oxidation and electron transfer;
these reactions vary in rate over five orders of magnitude.

Solvent and temperature effects for both oxidants are expected to be small
enough to minimize the need for close temperature control and allow use of
mixed water-organic solvents at least for 102 reactions.

4.4 CONCLUSIONS AND RECOMMENDATIONS

Selected classes of organic chemicals exhibit sufficiently high reactivity
toward R02» or 102 to warrant belief that these oxidants could play important
roles in aquatic loss processes for some chemicals. Therefore screening tests
for preselected chemicals are needed and test methods are proposed. Preselection
of molecular structures reactive enough to justify oxidation screening tests
is based on the assumption that any chemical that exhibits a half-life for
oxidation in an aquatic environment in excess of 80 days need not be tested
further. Very unreactive chemicals may exhibit longer half-lives toward all
transformation processes, in which case this 80-day limitation will not hold.
The test method proposed for oxidation of ArOH or ArNH bonds by R02» gives
only a lower limit to the rate constant.

Additional experimental and theoretical work will be necessary on the
kinetic processes involving R02» oxidations of -NH, -OH or -SH before satis-
factory tests for these reactions can be developed. No satisfactory standard
chemicals for relative reactivity measurements are now available for either
R02« or 102 oxidations.

We recommend that some additional work be done to improve the screening
level tests and provide the basis for detailed tests if they are needed.

Specifically, wo recommend that the following studies be carried out:

• Survey computer lists of currently manufactured chemicals to determine
the fraction of chemicals that have reactive phenolic or anine functions
to better evaluate the relative importance of oxidation among
transformation processes.
• Conduct both experimental and modeling studies to evaluate kinetic
parameters for oxidation of ArNH or ArOH bonds in water to better
design test methods.
106
-------
4.5 SCREENING TEST

The purpose of screening tests is to provide approximate values of rate
constants and or half-lives for reaction of a chemical with peroxy radical and
singlet oxygen. Half-lives may then be used in comparing the importance of
oxidation with other loss processes.

Since only a relatively small proportion of all chemicals will have re-
active functionalities it is important that the investigator evaluate carefully
the probable reactivity before deciding to screen or not screen. The range
of reactivity for which screening is needed, as shown in Schemes 2A and 2B, is
based on a half-life of 80 days in the environment; chemicals with rate constants
that will lead to half-lives greater than 80 days in aquatic systems should
not ordinarily be screened. Exceptions to this rule will arise only if all
other aquatic processes are found to have half-lives greater than 80 days, in
which case the investigator must reconsider the question of screening for
oxidation.

4.5.1 Screening Test for Peroxy Radical Oxidation of CH Bonds

Materials needed for this procedure are:

(1) Solution A: a solution of the chemical in pure water at a known
concentration below one-half of its solubility limit and at or
below 1 x 10-* M.
(2) Solution B: a solution of 2 M t-butyl hydroperoxide (t-Bu02H) in
pure water.
(3) Solution C: a solution of MAB in water at (3.00 + 0.5) x 10~A M.
(4) A constant temperature bath large enough to hold three 50-ml tubes
and regulated to 50 ± 1°C.

The test is carried out as follows: equal volumes of the solutions A-C are
mixed in several 10 to 50-ml volumetric flasks or tubes at room temperature,
avoiding direct sunlight. Another of volume solution A is mixed with equal
volumes of solution B and pure water as control 1. All reaction tubes are
sealed without grease.^ One or two reaction mixtures are covered with metal
foil to exclude light entirely and are set aside in a cool place as control 2.
The other reaction tubes and control 1 are immersed in the bath at 50°C and
the time is noted. After 10 hours (time noted exactly), the tubes are removed,
immediately cooled, and stored in the refrigerator with control 2 until they
are analyzed. Controls 1 and 2 are analyzed in duplicate first to obtain the
To be used only for very reactive CH bonds.
MAB is our abbreviation for the azo initiator azobis(2,2'-carboxymethyl pro-
+pane). @
A screw cap flask having an inert plastic valve (Minnert , Pierce Chemical)
fitted into the cap is a useful means of sealing flasks containing volatile
chemicals dissolved in water. The valve can be opened as the temperature is
raised to allow for expansion of liquid, closed at the elevated constant
temperature, and then reopened later for sampling.

107
-------

N
O
pf{ £
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t j *_j
w ™
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(4-1 cd
c -H
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c
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co VM o
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(
M
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?

x! t
= i
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jfi

"^™ **"

i -i.i

zS
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tj

n
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i-l
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n
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tt
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ai
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o o
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1
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103
-------
o
- a
0
t-i -H
O -U
<4-l Cfl
C -H
0) X

— CJ BC O H VJ O CJ ^
CJ £S ^4 ^ ^ PC CJ P> C
II M
-------
concentration of chemical at zero time. These control concentration values
should be nearly the same; if not, additional experiments may be necessary to
find the source of the discrepancy, especially if control 1 has a smaller con-
centration than 2 (in this case t-Bu02H has probably reacted directly with the
chemical). The heated solutions are then analyzed in the same way to measure
the concentration of the chemical at 10 hours.

The half-life of the chemical in an aquatic environment at 25°C is
calculated using the following formula (Section 4.7.3)*

todays) = 4500/£n(CQ/Ct) (4.1)

where Co and Ct are concentrations of chemical at time zero and t (days). If
equation (4.1) gives a half-life for the chemical of more than 80 days, oxida-
tion by R0a« is not likely to be an important process for its loss in aquatic
systems, and no additional tests are necessary until other screening tests are
complete.

4.5.2 Screening Test for Oxidation of ArOH. ArN(H)R or RSH by R02«

The materials needed for this procedure are solutions A and C and a
constant temperature bath. The test is carried out as follows: equal volumes
of solutions A and C are mixed as described above for the oxidation of CH bonds.
Control solutions are prepared from solution A and an equal volume of pure
water or water and acetonitrile. Several controls and several reaction
mixtures are heated at 50 ± 1°C for 20 hours. Solutions are analyzed for ArOH
(ArN(R)H or RSH) as described above.

The half-life in the environment at 25°C is calculated using the fol-
lowing formula: if Ct/C0 = 0.75, then k > 10" M~x s"1 and in the environment
< 19 hr

"OX
Conversely if Ct/Co £ 0.75, then k < 10" M~x s-1 and in the environment
tj^ * 19 hr

No detailed test procedure is recommended at this time.

4.5.3 Screening Test for Oxidation by Singlet Oxygen

Materials needed for this procedure are:

• Solution A of chemical in pure water or in 90:10 water: acetonitrile
at a concentration of 1 x 10~" M.
• Solution B of standard chemical in the same solvent as for the test
chemical also at 1 x 10-" M.
• Solution C of rose bengal sensitizer at 2 x 10~" M in the same solvent
as solutions A and B.
• A merry-go-round photolysis unit or visible light source and mounting
for reactions cells.

This equation is based on equation 4.34- The derivation is available on
request. llu
-------
The test procedure is carried out as follows: equal 25 ml volumes of
solutions A and B are mixed and one ml of solution C is added and mixed. A
control solution is prepared by mixing equal volumes of solutions A and B only.
One sample of the control solution is set aside in the dark. Enough of the
reaction mixture and the control solution are placed in the photolysis reactor
to allow four samples of each to be withdrawn for analyses over a period of
100 hr while being photolyzed. The first withdrawal should occur at 1 hr and
if more than 15% of the chemical and reactant have disappeared from the reac-
tion mixture and none from the control, the photolysis should be terminated.
If more than 15% of only one component has reacted in 1 hour, then photolysis
should continue until the more than 15% of the other component (reference or
chemical) has reacted. Time should be noted exactly at each sample withdrawal.
Conversions of more than 50% of either component should be avoided.

Treatment of the data obtained is straightforward: the half-life for
oxidation of the chemical by singlet oxygen in the environment is evaluated
from the following formula:

ln(C /C ) t
" °
t (hr) = 1.9 x 10" x , * -r x -±- (A. 2)
h
where (Co/Ct)s or C is the ratio of concentrations of standard or chemical at
times 0 and t; tQ and tg are the times at which the concentrations of chemical
and standard were taken and k§x is the second order rate constant for re-
action of singlet oxygen and standard in units of M~l s"1. Obviously if both
components were analyzed at the same time the ratio tc/tg is one.
More accurate screening tests for phenols, aromatic amines, and thiols,
hydroxylamines and hydrazines are needed but are not available at this time
owing to complexities in the kinetic schemes for these reactions.

No detailed tests for oxidation are proposed because the most
reactive and numerous classes of reactive chemicals are the phenols, amines,
and hydroxylamines for which no adequate screening test is available.

A detailed test for I0a reactions with many chemicals could be needed
in some cases but more and better standard chemicals needed to be identified
and tested first.

4.5.4 Scope and Limitations of Screening Tests

Screening tests for oxidation by R02» and 102 are designed to provide
the investigator approximate half-lives for chemicals in oxidation reactions
to be used in comparison with half-lives for other processes. These tests are
intended to be used only for chemicals which fall into one or more structural
classes that are known to have relatively large rate constants for oxidation
by R02» or 102. To assist the investigator in selecting those chemicals that
111
-------
might be candidates for one or more oxidation screening tests we have proposed
the simplified classification scheme based on structure reactivity relations
discussed in Section 4.7 and shown in Schemes 2A and 2B.

A. 5. 5 Error Analysis

Estimation methods for error analysis of the test protocol are based
on certain assumptions concerning the accuracy of specific measurements and
the relationship between variables. The screening tests proposed here require
only two measurements of concentration at times 0 and t. Because of the
limited amount of data the error is large.

The error analysis is based on the basic kinetic rate laws cited in
Section 4.7.3 and on the equations in Chapter 2 (Hydrolysis).

kOX = l» 0. The preferred measure of error
in experiments of this kind is the standard error, a,* used here in the form
a2 or the variance. The variance of k_ from n measurements is given by
a* = ^_ nZ[lnC]2 - [ElnC]8 a
CT n-2 nit3 - (St)2 ~ UOX)

This equation shows that a varies with -p- and i> — jj- and directly with o(C).
If we assume that in a typical screening experiment two analyses for chemicals
are performed at time » 0 and time * 5 hr with a standard percent error of 3%
about the mean of 1.00 x 10" 3 M, the standard percent error (a/k) x 100 in the
calculated rate constant k_Y is 20%.
UA.

4.6 DETAILED TESTS

No detailed tests are proposed at this time.
The standard error may be expressed as the standard deviation, (n ± a), the
error ratio, a/k) x 100.

112
-------
4.7 BACKGROUND

4.7.1 General Considerations

Oxidation is the chemical process whereby reactive electron deficient
species called oxidants remove electrons from other more electron-rich mole-
cules.* Examples of oxidants that may be found in the environment are peroxy
radical (R02»), hydroxy radical (§0;), singlet oxygen ^Oa), ozone (03), and
photoexcited triplet diradicals (R-0). Oxygen (302) is itself rarely involved
directly in reactions with stable molecules but does act as the ultimate
electron sink in most environmental oxidation reactions.

This review focuses attention on reactions of the energetic oxidants
found in aquatic systems, namely R02«, H0», and 102. We exclude from con-
sideration here those oxidations that involve electronic excited species
(singlet or triplet states) of the chemical itself (photooxidations); appropri-
ate test methods for predictive fate assessment of photooxidations are included
under the test protocol for photolysis (Section 3).

Predicting the rate of oxidation of a specific chemical in an aquatic
system requires three kinds of information and data:

(1) The identities and concentrations of the oxidants in the aquatic
compartment.
(2) The rate constant for oxidation by each oxidant at a specific site
in a molecule.
(3) The kinetic rate law for each process.

The following sections discuss the oxidants in aquatic systems, kinetics
of oxidation reactions, structure-reactivity relationships for organic mole-
cules, and oxidation chemistry in aquatic systems. Finally the data needs for
laboratory testing and predictive modeling are summarized, the kinetic basis
for the proposed test procedures are formulated, and a kinetic analysis for
the test methods is developed.

4.7.2 Oxidants in Aquatic Systems

For convenience in discussion we will distinguish transient oxidants
such as radicals, singlet oxygen, and triplet diradicals with lifetimes of a
few milliseconds from stable oxidants such as peroxides, peracids, and ozone.
Our present knowledge of the transient oxidants present in natural waters is
fragmentary and in some cases very qualitative. The most recent studies de-
signed to identify and quantitate these species are summarized in Section 4.7.4.
Both H0» and R02« radicals and 102 have been detected by photolyzing natural
waters to give products characteristic of reactions involving these oxidants
(Mill et al., 1977 and Zepp et al., 1977 ) . These oxidants must have their
origin in the organic humic material present in natural waters, but the details
of their photolytic generation are unknown.
Electron removal or transfer is often effected by simultaneous transfer of an
electron and proton as H», namely: X« + RH —» XH + R».

113
-------
The reactivities of important oxidants are summarized in the next
section. It is worth noting that although the reactivities of R02», 102, and
HO range over twelve orders of magnitude, their concentrations in aquatic
systems also exhibit wide variation. As a result all of these oxidants can
play important roles in some oxidation processes. Further research may show
that alkoxy radicals (RO) and diradicals also contribute to some oxidation
processes, but their contributions are now incorporated as part of the calcu-
lated concentration of R0a», which, although much less reactive, undergoes
similar reactions. Still other transient oxidants_peculiar to aquatic systems
may include superoxide anion ('Oa), ferrate ion (HOFe"+), and polyaromatic
radical cations
The presence of these species in water, however, is entirely speculative.

Stable oxidants have been detected in natural waters, but they have not
been identified (see Section 4.7.4). Very likely several peroxides including
hydrogen peroxide (H20a,) alkyl hydroperoxides (ROOH) and peracids [RC(O)OOH)
are formed by oxidation of natural organic structures, but speciation of these
peroxides has not been accomplished and their actual importance in environ-
mental oxidation is questionable. Rate constants for their reactions with re-
active organic structures generally are smaller by two to twelve orders of
magnitude than for reactions with R0a», H0» or 10a [Corci and Edwards (1970)
and Swern (1970)].

4.7.3 Oxidation Chemistry and Kinetics

General Considerations

The simplest form of the oxidation rate law is

Rox = kox[C][OX] (4.3)

where kgjj is the specific second order rate constant for oxidation at a speci-
fic temperature and [C] and [OX] are molar concentrations of chemical and oxi-
dant respectively; k0x is usually given in units of M"1 s"1. The total rate
of oxidation of a chemical is the sum of the rates for reaction of each kind
of oxidant with C:
ROX(T) '
-------
^ -RO H + «C-
y n |
RO • + H-C -- >-RO H + «C- (n = 1 or 2)
n
R = alkyl or H; n = 1 or 2

(2) Addition to double bonds

H0» or R02» + \,=C R02C-C« or HOC-C«
R = alkyl or H

(3) HO addition to aromatics

HO +
^^
HC

(4) R02» transfer of 0-atoms to certain nucleophilic species
115
-------
R02» + PR
R0
OPR
The fate of carbon radicals formed by H-atom transfer is to add oxygen to form
new R02» and then either chain transfer with other molecules or terminate by
reactions with other radicals
-€
fast
= R'02«
R'02» + R02»
stable products + 02
(4.8)
(4.9)
Some carbon radicals including cyclohexadienyl radical react by 1,2 or 1,4-
elimination to give olefins or substituted aromatic rings and H02»
(4.10)
+ 0,
(4.11)
The rate law for radical oxidation in aquatic systems is readily
formulated as the sum of two bimolecular expressions

R»,, >
(4.12)
Although many different kinds of alkylperoxy radicals could be present in a
natural system, we can make a simplifying assumption that the structure of R
in R02« (primary, secondary, or tertiary) has little effect on its reactivity
(a reasonable assumption within a factor of ten) ; we can then use a lumped rate
constant kROa and use [R02»] to represent the total concentration of these
radicals [equation (4.8)]. A large number of rate constants kROz and kno are
known for organic chemicals (Howard, 1972; Hendry, 1974; and Denisov, 1971).
Concentrations of R02« and H0» in aquatic systems have been estimated from
studies of Mill et al. (1977). With these values and equation (4.12) we can
estimate half-lives for different chemicals in reactions with these oxidants
at environmentally realistic concentrations. Tables 4.1 through 4.3 summarize
these values and include data for RO radical at 10" ^ M.
Two important conclusions emerge from inspection of the data in these
tables. First, the range of reactivity of H0» toward most organic structures
is much smaller, (a factor of 100 at most) than for R02» even though the abso-
lute reactivity of H0« is 5 to 10 orders of magnitude greater than for R0a».
116
-------
TABLE 4.1. RATES OF OXIDATION BY R02» RADICAL
Class
Olefin
Benzyl
Aldehyde
Alcohol
Phenol
Aromatic amine
Hydroquinone
Hydroxylamlne
Hydroperoxide
Polycyclic aromatic
aFor 10-' M R02»
TABLE 4.2.
k
P
M-1 s-1
0.09
1
0.1
0.01
1 x 10"
1 x 104
1 x 10s
1 x 10s
1 x 10s
1 x 103

RATES OF OXIDATION BY R0« RADICAL
Half-Life, t,a
(days)
9 x 10"
8 x 103
8 x 10"
8 x 10s
0.8
0.8
12 min
120 min
120 nin
8

Class
Alkane
Olefin
Benzyl
Alcohol
Aromatic amine
Phenol
k. x 10~s
A
M-1 s-1
0.3
24
10
1
3000
1000
Half-Life, t^a
73 year
334 days
801 days
22 year
64 hour
192 hour
aFor 10-x" M RO-

117
-------
TABLE 4.3. RATES OF OXIDATION BY H0» RADICAL
Class
Alcohols
Ethers
Ketones
Aromatics
Oleflns
Dienes
Hydroquinones
^o x 10""
M-1 s-1
1
2
0.9 - 2.0
1-5
0.5 - 2
10
12
Half-life
tj^ (days)3
800
400
400 -

900
800-160
400 -
80
67
1600

10-17 M H0»
Second, because the concentration of H0» estimated in aquatic systems is low,
H0« is of negligible importance as an oxidant for most types of organic structures,
whereas R0a« can be important for certain classes of common but reactive organic
structures.

The reactivity and selectivity of R0» (or triplet diradical R-0) falls
somewhere in between those of R02* and H0«; the possible importance of RO as
an environmental oxidant remains uncertain until some evidence can be found for
its presence or absence in aquatic systems.

Singlet Oxygen (X02)
Singlet oxygen (^a), is an electronically excited form of oxygen which
has 22 kcal/mol more energy than its triplet ground state form,* is very electro-
philic, and exhibits a wide variety of reactions with organic structures not
observed with triplet oxygen. These reaction, though diverse, can be categorized
as five types (Foote, 1976).

(1) Ene-reaction with many internal olefins to give allylic hydro-
peroxides
W-CH + L0a
(4.13)
*A higher energy form (^g, 37 kcal) is not important in photooxidation chemistry
(Kearns, 1970). 118
-------
(2) Cyclo addition to dienes (2 + 4)
f V+102 *- -( >- (4.14)
\>-o'
(3) Cycloaddition to electron rich olefins (2 -I- 2)

. „ X
(4.15)

'0—O

(4) Oxidation of sulfur in sulfides, disulfides, and mercaptans

2R2S + ^2 * 2R2SO (4.16)

(5) Electron transfer from phenols and other electron donors

ArOH + 102 >- ArO + H02» (4.17)

Rate constants for these processes generally range from lO^-lO7 M"1 s"1. Table
4.4 summarizes rate constants for reactions of several types of organic structures
with 102 and lists half-lives based on the recent estimate of Zepp et al. (1977)
for the concentration of 102 in aquatic systems.

Singlet oxygen, like R02«, exhibits a very wide range of reactivity
toward organic structures. Table 4.4 shows'that, at the concentrations reported
in aquatic systems (^ 10"12 M), its reactions with certain classes of organic
structures can be important loss processes. For this reason screening tests tor
oxidation by 102 are recommended for selected classes of chemicals.
119
-------
TABLE 4.4. RATES OF OXIDATION BY SINGLET OXYGEN

Structure i 2_! t^a

Unsubstituted olef in 3 x 103 7.3 day

Cyclic olefins 2 x 10s 40 day

Substituted olefin 1 x 10* 8.0 day

Dialkyl sulfide 7 x 106 27 hr

Diene 1 x 107 19 hr

Imidazole 4 x 107 4.8 hr

Furan 1.4 x 108 1.0 hr

Trialkyleneamine 3 x 10° 14 min

3For 10" 12 M *02; see section 4.7.4.
Measurement of k.,,. for R0a» Oxidations
IxLJg

The kinetics of oxidation involving H-atom transfer from CH bonds is

described by the following scheme where RH is any CH bond:

ki
Initiation Initiator —+- 2X« (R±) (4.18)

X- + RH *- XH + R- (4.19)

p. + Q2 *-R02» (4.8)

R02« + RH *~R02H + R» (k«0 ) (4.20)
Propagation

by R°2* 2R02. —>-2RO.+ 02 (ak.) (4.21)
x

Propagation R0» + RH »- ROH + R» ^o^ (4.22)

by R0«

Termination 2R02« —=*-Products [(l-a)k -k) (4.23)
A W

120
-------
Reactions (4.8) through (4.18) may be used to derive several important
relationships. Oxygen consumption is expressed as

- IF = R0z = kR02[RH][R02«] + kRQ[RH][RO.] (4.24)
/R. Vs R.

Ro2=(ik;l V[RH]+^ (4

where R-^ is ;he rate of radical formation (R^ = 2k^[Initiator] and the R^/a
term take^ into account oxidation by RO radicals and initiators. RJ can be
controlled by using an added free radical source.

If RO cleaves to form new carbon radicals, termination becomes more
complex, involving two different R02» in three possible termination reactions.
However, if enough R02H is added to the reaction to scavenge all RO

RO + R02H »- ROH + R02» (4.26)

the rate law for oxidation simplifies to
<4'27)
This equation can be used to evaluate k^Q from oxygen uptake if k^ and R-^ arc
known. Usually, however, both k^Q and kt for a new chemical are unknown and
some other method must be sought to measure k^Q . The simplest method is to
add 0.2- 1.0 M t-Bu02H to the solution of the chemical so that all R02» are
efficiently converted to t-Bu02«

R02» + t-Bu02H - +- R02H + t-Bu02» (4.28)

Now all propagation and termination reactions occur by way of t-BuOz», for
which the value of 2k is known with considerable accuracy at 30°-100°C
floward and Ingold, 19§8)

X» + RH - *-XH + R« (4.29)

R. + Q2 - >- R02« (^-8)

R02« 4- t-Bu02H - >- ROjH + t-BuOa» (4.30)

t-Bu02« + RH - >- t-Bu02H + R» (4.31)

2-t-Bu02« — *- 2- t-BuO + 02 (4.32)

t-BuO» + t-Bu02H — *- t-BuOH + t-Bu02« (4.33)

121
-------
2kt(t-Bu02)}
kp(t-Bu02)™
-(tB D 1 is t^e sPec:i-fic rate constant for H-atom transfer from RH to t-Bu02«;
s valui'will be similar to values for other kRO . This method for evaluating
has been used extensively (Howard, 1972) and is the method of choice in
cases where there is no direct reaction between t-Bu02H and the chemical.

The method can be further simplified by using a standard chemical (SH)
for which kt_Buoa has been carefully measured by the above method or by an
absolute method. In this case at low conversions of standard SH and unknown
RH where their concentrations change very little (k
„ ..
t-DUU2
= k__ )
KO2
kROa(SH)[SH:i

V(RH)CRH]
av
(4.36)
av
Since both A[SH] and A[RH] are very small, their values are inaccurately de-
termined by measuring their concentrations at times o and t; they are very ac
curately determined by measuring [SOOH] and [ROOH] at time t.
A[SH] [SOPH] _ kR03(SH)[CH]

"
av
..
Furthermore, the difficult direct analyses for SOOH and ROOH may be avoided by
reducing the mixture with NaBHA (in water) or (C6H5)3P (in organic solvent) to
the mixture of corresponding alcohols and analyzing for their ratio.
The expression for the unknown value of k
is then
(4-38)
If more than one type of CH bond in RH is oxidized, which is usually the case,
then the ratio of isomeric ROH gives values for kr>0 for each different CH bond.
This method is applicable to a broad group of chemicals that: oxidize via CH-
atom transfer or addition to a double bond. This group includes most alkanes,
olefins, ethers, alkyl halides, and similar structures. However, table 4.1
shows that oxidations of CH bonds are generally very slow under environmental
conditions: even the most reactive of dienes, cyclohexadiene with kp ^ 300 M"1
s~l, has a half-life of 641 hours (26 days) in reactions with 10~* M R0a«,
the concentration reported in some natural waters. Most types of oxidations
of CH bonds are far slower (Hendry et al., 1974).
122
-------
The most reactive chemicals in oxidation with t-R02» are those in which
H-atom transfer occurs from 0, N, or S (see Table 4.1) and where no R02» chain
is possible; termination reactions between R02» and, for example, ArO» are
very rapid

R02« + ArOH —*- R02H + ArO» (4.39)
R=
R02« +
02R
Many phenols, aromatic amines, and thiols are effective inhibitors for this
reasons.

Oxidations of these chemicals are often complex and involve competitive
terminations between R02» and ArO (or ArNH). Moreover the back reaction of
ArO + R02H is usually rapid.

Step 1: R02» + ArOH *- R02H + ArO« (ki) (4.41)

Step 2: ArO* + R02H *~ ArOH + R02» (k2) (4.42)

Step 3: 2ArO» —^coupling products (k3) (4.43)

Step 4: ArO« + R02« —* R02ArO (kO (4.44)

Step 5: 2R02« *- R202 + 02 (2kfc) (4.45)

Rate constants for the steps in this sequence are known for many phenols and
some amines and thiols. Typically kj. or k2 is 10\ and k_i or k_2 is 103 M-1
S"1; steps 3 or 4 have rate constants of 107 M-1 s"1 (Mahoney and DaRooge,
1975) much faster than step 5 for which 2kfc % 103 M"1 s"1 (Howard et al., 1972).

Kinetics of inhibition, which basically involve a competition for R02«
between a phenolic or amine inhibitor and a hydrocarbon, (RH), can be complex
owing to varying combinations of the reactions in steps 1 through 5 and

Step 6: R02« + RH *- R02H + R02» (4.46)

But in the simplest case where only steps 1, 4, and 6 are important, the rate
law takes the form

_ ^ = _ dJJH], m R^ m Rik(.[RH]/nki[AroH] (4.47)

where n is the number of R02« that react with each ArOH (usually 2). Equation
(4.47) can be used to evaluate kx by measuring oxygen uptake or loss of RH as
a function of the ratio [RA]/[ArOH]. However, equation (4.47) can be used only
if the system is shown by kinetic analysis to follow this simple relationship,
hardly a routine procedure suitable for standard test methods.
123
-------
The use of added hydroperoxide to simplify the kinetics of oxidations
at CH bonds is not applicable to oxidation of OH or NH bonds; because of the
rapid reaction of ArO or ArNH with t-Bu02H (Step 2) and the possible direct
reaction of some phenols and amines with hydroperoxide (Hiatt, 1970).

An approximate estimate of ki may be obtained by measuring the loss of
ArOH in the presence of R02«, where the ratio [AH]/[R02»] < 1. Under these
conditions, the bulk of R02» will terminate by self-reactions and the kinetic
expression
d[ArOH]/dt
(R /2k
i [ArOH]
(4.48)
applies. To achieve the low ratio [ArOH]/ [R02»] needed for application of this
equation, a large concentration of initiator and low concentration of ArOH are
needed, a requirement that imposes unreasonable limitations on the test proce-
dure. Therefore, the recommended screening test procedure is carried out under
conditions that provide only a lower limit for kj. for these reactive chemicals.
Preliminary computer modeling of the reaction of R02* and a phenol in-
dicates that at 50°C if kj is larger than 1 x 10* M~x s-1, the rate of loss
of phenol will nearly equal one-half the rate of production of R02». Under
this condition all R02» are scavenged by the phenol and the rate of loss of
phenol is zero order.
Initiator

R02» + ArOH

R02» + ArO*

d[ArOH]/dt
2R02« R

R02H + ArO-

R02ArO

kx [R02«] [ArOH]
2kd[MAB]
(4.49)

(4.41)

(4.44)

(4.50)
[R02»] = R±/2k1[ArOH]
d[ArOH]/dt = R±/2
Measurement of k^ for X0a Oxidations
•'" " " ' ' " " " ' ' " ' ' " " ' '
(4.51)

(4.52)
Kinetic schemes for 102 oxidations can be written in the general form
(Foote, 1968),
Sen
Sen + 02
(4.53)
+ C
COa
(4.54)
+ S - +• S + 03 or S02 (k.)
O

124
(4.55)
-------
(kd) (4.56)

Where Sen is a triplet sensitizer (usually a dye), C is the chemical of
interest; S is a chemical that competes at a known rate with the test
chemical, C, for '02, and kd is the rate of the radiationless transition from
singlet to ground state. Of interest here is the value of kQjj where kg and
k
-------
The value of kg is 2 x 108 M~1 s l and from the measured ratio of rate constants
kQX is 4 x 106 M-1 s~l for ATU.

Foote and Denny (1968) used a similar inhibition kinetics analysis to
evaluate the quenching rate constant for carotene in MeOH:C6H6
In this case C was 2-methyl-2-pentene. A plot of [CC^]"1 versus [C]~l with
varying amounts of S gives a series of straight lines from which they evaluated
first k at [C] = 0 and then kox/ks. As a further check, they plotted [COa]"1
versus [S] at constant [C] to evaluate the same ratio k0x/kg.

Simple competitive techniques also have been used for estimating re-
lative reactivity toward 102> Bartlett et al. (1970) evaluated the relative
rate constants for a series of vinyl ethers in acetone. Gollnick et al. (1970)
measured reactivities for a series of olefins and Matsura et al. (1973) measured
relative reactivities for cyclic olefins in methanol. Relative reactivities
are expressed as the ratio of two first-order processes

kOX(A)
"w«> ( >

where A and B refer to two different chemicals. This method has great ad-
vantages of simplicity over inhibition kinetic methods, but does require more
careful analyses for loss of chemical and selection of a standard that has a
reactivity similar to that of the test chemical. Some trial and error measure-
ments may be necessary with many chemicals, although the general rule that
similar structures will have similar reactivities is a useful guide for selec-
tion of reference chemicals. The use of a standard chemical will also help
detect test chemicals, such as azide ion, diazabicyclooctane, and carotene,
that are not only unreactive toward 102 but also rapidly quench the oxidant by
a physical process.

g Values
The ratio k^/kgx (or k^/kg) is called fi, the value of which equals the
concentration of chemical needed to trap half the 102. p values in water range
from > 8 M for unreactive olefins to ^ 1 x 10~3 for reactive furans and poly-
cyclic aromatics. The value of k^, but not kgx> is markedly dependent on
solvent: in organic solvents k
-------
Solvent Effects on Oxidation Reactions

Although the screening tests for evaluating reactivities of chemicals
in oxidations are used in water or water with acetonitrile because of the
obvious relevance for environmental assessment, it is useful to consider what
effect solvent properties have on reactivity because many rate constants and
products of oxidations have been measured in organic solvents and few have
actually been measured in water. Values of koy in nonaqueous systems may be
useful for screening purposes.

Radical Oxidants. The bulk of evidence points to only small solvent
effects on reactions of R02* with CH bonds (Howard, 1972) as expected for re-
actions that have little true ionic character in either the ground or transi-
tion states. However, direct reaction of R02» or t-Bu02« with many organic
solvents may be competitive with reaction with the test chemical if it is
present in much smaller concentration. Reactions of R02» with heteroatom-H
bonds such as with phenols or amines might be expected to exhibit solvent ef-
fects in water associated with competitive hydrogen bonding of the chemical
to water and to R02*. Kinetic evidence indicates that H-atom transfer from
phenols to R02» proceeds via an intermediate complex, possibly involving a
quasi H-bond (Howard and Furimski, 1973)

R0a« + HOAr T"*~ R02.. HOAr (4.65)

R02.. HOAr - *- R02H + »OAr (4.66)

Competition with the water-bonded form of phenol

ArOH...OH2 T"*' ArOH + H20 (Kx) (4.67)
would reduce the effective concentration of ArOH available to R0a» and lower
the value of the observed second-order rate constant.

Rate = k , KjArOHOHa] (4.68)
obs

Few data are available to indicate the extent of this possible effect, but
preliminary data on p-cresol oxidation by R02* in water (Mill and Baraze, 1978)
indicate that it is less than a factor of ten.

Singlet Oxygen. Solvent effects on rates of reactions of singlet oxygen
(102) have been investigated in detail (Merkel and Kearns, 1972; Foote et al.,
1972; Young et al., 1971). Absolute rate measurements of Merkel and Kearns
(1972) show clearly that solvent affects mostly the value of kjj, the unimolecular
rate constant for radiationless decay to ground-state triplet oxygen. In water
k(j is larger than in any other solvent and the lifetime (1/k^) , is the shortest
(2usec) . In CS2 and CC1<,, k^ is much smaller and 1/k^ is 200-700 ysec. These
investigators also showed that deuteration of water or methanol increased the
lifetime of 102 almost tenfold; deuteration of acetone, however, had little
effect on lifetime. Evidently, the transition involves coupling of electronic
to vibrational levels in H-0 bonds. This observation is the basis for the use
of D20 or CD3OD to confirm the role of 102, rather than some other oxidant, in
a photooxygenation process (see, for example, Zepp et al., 1977).

127
-------
Solvent appears to have little effect on the rate of reaction of 102
with some classes of chemicals. The rate of reaction of diphenylisobenzofuran
was unchanged in several solvents (excluding water) where dimerization may
have accelerated its reactivity (Merkel and Kearns, 1972). However, Young et
al. (1971) noted that 102 oxidation of some furans showed significant solvent
effects (x32), whereas reactions with olefins showed only small effects (< x2).

Products of 102 reactions with some olefins show striking solvent ef-
fects on the partition between the ene and 2+2 addition (Bartlett and Schaap,
1970)
polar solvent (4.69)
(CH3CN)
nonpolar solvent (4.70)
(C6H6)

In water we would expect reactions of this kind would proceed mostly (> 90%)
by the 2+2 route, but we know of no specific examples. The effect of solvent
properties mainly on product composition and less on rate points to the
possibility of doing rate studies in mixed solvents with water, but the
necessity of doing product studies in water alone or water containing only a
small amount of acetonitrile.

Temperature Effects in Oxidation

The review of H-atom transfers by R02» from CH bonds (Hendry et al.,
1974) indicates that activation energies for these processes? range from 9 to
18 kcal/mol. Activation energies for oxidation of only the most reactive CH
bonds (kp > 100 M"1 s~x) are close to 10 kcal/mol, corresponding to a factor
of 3.7 in rate between 25° and 50°C. H-atom transfers from OH or NH bonds to
R02« in organic solvents have much smaller activation energies, close to 1
kcal/mol (Howard and Furimsky, 1973) , corresponding to only a 10% change in rate
between 25° and 50°C. In effect, these latter oxidations are temperature-
independent in the temperature range of environmental concern. Special solvent
effects in water might increase these activation energies by the heat of re-
action of hydrogen bonding of phenols or amines to water.

Singlet oxygen reactions have less well-characterized temperature de-
pendences. However, cwo lines of evidence indicate that the activation ener-
gies must be quite low: (1) reactions are often carried out at -25° to -70°C
and proceed quite rapidly; and (2) if the activation entropies have normal bi-
molecular values (*> 10* M"1 s"1), (Benson, 1976) then activation energies must

128
-------
be less than 2 kcal/mol for the most reactive chemicals (10s M"1 s l) cor-
responding to less than a 30% change in rate between 25° and 50°C. For less
reactive chemicals (k ^ 105 M"1 s"1), activation energies are still less than
6 kcal/mol, a factor of 2.2 over the same temperature range. The generally
small activation energies for oxidation by R02» and 102 simplify the require-
ments for temperature control in test methods and for the need to correct
measured values back to 25°C except for the case of R02» oxidations of CH bonds.

4.7.4 Review of Environmental Oxidation Studies

General

Photooxidation under environmental conditions occurs with a wide variety
of chemicals as evidenced by the need for oxygen and/or by isolation of oxida-
tion products under sterile conditions. In only a few cases, however, have
these processes been shown to involve oxidation by thermal oxidants such as
free radicals rather than by direct photolysis. A good illustration of the
distinction between photooxidation involving excited state chemistry and oxi-
dation involving thermal oxidants is found by comparing the reports of Crosby
and Tang (1969) and Crosby and Wong (1973) on the direct photolyses of naph-
thalene acetic and chlorophenoxy acetic acid salts with the reports of Crosby
and coworkers on photooxidations of aldrin, carbamates and Mill et al. (1977)
on the oxidation of cumene, which occur in natural waters but not in pure water.

Direct photolysis of phenoxyacetic or naphthalene acetic acid salts
above 300 nm gives mixtures of products that probably form from radical inter-
mediates generated by electron transfer from the acid salt excited states
*
ArCH2C02 -^ ArCH2C02 (4.71)

*
Ha + 02 —»- ArCH2C02» + »02 (4.72)

ArCH2C02» —* ArCH2« + C0a (4.73)
ArCH2« + 02 seyeraS (ArCHaOH) —*• Ar. + CH20 (4.74)
steps

Ar = napthyl or chlorophenoxyl

The photochemical conversion of aldrin (1) to dieldrin (2) (Ross and
Crosby, 1975)
is not observed in pure water (aldrin does not absorb light in the solar re-
gion) ; however, photolysis of solutions of aldrin in pure water containing

129
-------
acetone or in natural water from rice paddys leads to rapid loss of aldrin and
formation of varying amounts of dieldrin. Experiments using singlet oxygen
showed that it was not the effective oxidant. Peracids were found to effect
the oxidation of 1 to 2, but the concentration required to achieve the rates
observed are far too high to make peracid the likely oxidant. We believe that
either R02» or RC(0)02« is more likely to be the oxidant in this system.
R02« or RC(0)02» + ^^ ^\ *• X—--} + R0» or RC(0)O

(4.76)

Ethylene thiorea is also reported to undergo oxidation in natural water, but
not in pure water, to give ethylene urea and glycine sulfate, again suggesting
that radical oxidants or singlet oxygen are involved.

More recent studies by Crosby and coworkers have shown that oxidation
can account for partial losses of several important agricultural chemicals and
that stable oxidants are formed in natural waters. Molinate (3) appears to
oxidize by two mechanisms (Soderquist and Crosby, 1976)
fJC(0)SEt -
G(0)$Etl —+- products (4.77)
Cr
V rfc(c
\^-
;c(o)SEt
(4.78)
A free radical oxidation seems likely to account at least for oxidation in the
ring while oxidation at sulfur may be radical or singlet oxygen in origin.

Another thiolcarbamate, benzthiocarb (4) , oxidizes on photolyses in
natural water to products also found when 4 was oxidized with H0» radical
(Crosby and Draper, 1978). They noted that other rice pesticides also oxidized
readily under these conditions and inferred that H0» radical may be an important
oxidant in natural waters

4-ClPhCHaSC(0)NEt2 ^ Cl,HOPhCH2SC(0)NEt:2 (4.79)

4 + ClPhCH2S(0)C(0)NEt2

Draper and Crosby (1976) reported that sunlight irradiation of several
kinds of natural waters leads to measurable concentrations of oxidants capable
of oxidizing leucocrystal violet to the colored form. In terms of Ha02
equivalents, samples of irradiated water formed 1 to 24 uM oxidant on exposure

130
-------
for 200 minutes; the average value was close to 2 yM with a sewage stream
having the high value and seawater the low value.

The foregoing reactions are cited as examples of photolytic processes
that have the earmarks of chemical oxidations but for which no incisive
evidence has been adduced as to the oxidants(s) involved. The following sec-
tions summarize recent work that attempts to identify the oxidants formed in
natural water on irradiation with sunlight or light in the solar region.

Radical Oxidants

Mill et al. (1977) investigated the role of free radicals in environ-
mental processes by first measuring the kinetics and products of radical oxi-
dation of selected molecules toward R02- and R0» in pure water and then
measuring rates and products in natural waters exposed to sunlight. Cumene
(isopropylbenzene, CuH) was used as the principal probe for free radicals
because it reacts with R02- and HO- but is not reactive toward 102 and does
not photolyze in sunlight in pure water. However, photolysis of cumene in
natural waters leads to formation of several products characteristic of free
radical oxidation by R02- and HO-, including cumene hydroperoxide, acetophenone,
cumyl alcohol, and isopropylphenols. These findings suggest that photolysis
of the natural organics in water produces the free radical oxidants.

The processes observed with cumene are summarized in the following
scheme:

natural organic —^*-HO- + R02» (4.80)

R02- + CuH *-R02H + Cu- (4.81)

Cu- + 02 *- Cu02- (4-82)

Cu02. several stepS) ^^ + CuQR + phCQMe (4_83)

HO- + CuH *- HOPhCHMe2 (4.84)

HOPb*CHMe2 + 02 *- HOPhCHMe2 + H02« (4.85)

Separate experiments in pure, sterile water with several free radical initiators
in the dark, showed that cumene reacts with R02» to give only side chain oxi-
dation products (hydroperoxide, alcohol, and ketone) while HO- reacts mostly
by addition to the ring to give phenols. Thus the ratio of side-chain products
(SP) to ring products (R) is a measure of the relative abundance of R02» and
HO- oxidants. The ratio of products from side-chain and ring oxidation can
vary widely from one water source to another as well as within one source at
different times.

Concentrations of radical oxidants in these natural waters can be cal-
culated from the rates of production of ring and side-chain products and a
knowledge of the rate constants for reaction of cumene with R02» and HO-.
131
-------
d[CuH]/dt = (kj^tHO] + kRQ [R02»])[CuH] = k[CuH] (4.86)

[RP] = kHO[HO][CuH]o(l - e~kt)k-1 (4.87)

[SCP] = kR()2[R02.][CuH]o(l - e'^k-1 (4.88)

Table 4.5 summarizes results of calculations using equations (4.87) and (4.88).
These values for [R02»] are corroborated by studies of the rate of oxidation
of pyridine to its N-oxide in natural water. The N-oxide is formed from re-
action with R02« but not with HO, although the latter oxidant does oxidize
the carbon ring to give hydroxypyridines. Values of [R02»] and [H0»] tabulated
in Table 4.5 are for near surface conditions in water; in eutrophic waters at
depths of several meters or more, light penetration will be small and the
average concentration of radicals will be reduced accordingly.
TABLE 4.5. CONCENTRATIONS OF OXIDANTS IN NATURAL WATERS

Water [R02»]^»b x 10* M [H0»]b»c x 1017 M
Aucilla River
Boronda Lake
Coyote Creek
2.8
9.5
9.1
1.8
0.15
1.6
bi«~a'] = k[S]/[CuH]0kR02(l - e~ )
Near surface values (see text).
C[HO»] = k[R]/[CuO] kjj0(l - e~kt).
This investigation by Mill et al. (1977) is the only quantitative study
of radical oxidations in waters at low concentrations. The results leave open
the question of whether some oxidation is due to triplet diradicals as well as
R02» and the possibility that some H0» radicals are generated by photolysis of the
cumene hydroperoxide product.

Singlet Oxygen

Zepp and coworkers (1977) have investigated the formation of singlet
oxygen in a variety of natural waters using the selective and reactive probe
132
-------
dimethylfuran (DMFN), which gives cis-diacetyltchylene via 1,4-addition of 102
(Foote et al., 1967).
(4.89)
Although this same product might conceivably form by a free radical oxidation,
the specific accelerating effect of D20 and inhibiting effect of diazobicyclo-
octane (DABCO) on the rate strongly point to participation by 102 in the rate-
controlling step. Quantum yields for product formation varied by a factor of
5 (from 0.02 to 0.1) for a factor of 23 in optical absorbance in the water
samples used. A kinetic analysis of these reactions was made by following the
loss of DMFN with time and using the usual relation

d(DMFN)/dt =knv[102][DMFN] (4.90)
to evaluate kg^^C^], whi°h i-n turn, can be related to the half-life of the
reaction by

l
Vox

for DMFN is 4 x 10s M~x s~l (Merkel and Kearns, 1972). Values of [102]
varied from (< 0.1-22) x 10"13 M for an average value of 1 x 10~12 M.

As the authors point out and is shown also in Table 4.4, this concentra-
tion of singlet oxygen can be important for oxidation of a variety of organic
chemicals, including amino acids, mercaptans, sulfides, and polycyclic
aromatics. Half-lives for most of these chemicals are in the range of 1 to
10 hours in reactions with this concentration of 102.

4.7.5 Design of Laboratory Test Methods

R02» Oxidation Test

Section 4.7.3 shows how it is possible to evaluate kRO for reaction of
R02» and CH bonds if a free radical initiator is used to provide a known rate
of production of R02« (R^) and t-Bu02H is added to convert all R02« and R0» to
t-Bu02». kj^Q can be evaluated by the loss of chemical directly or relative
to that of a standard chemical having a known kRQ . A. suitable free radical
source for use in either system is azobis(2-carbomethoxy-propane) , MAB, a well-
characterized azo initiator (Mortimer et al., 1964) slightly soluble in water
(1 x 10-3 M) as well as in organic solvents. Water alone with 1 M t-Bu02H is
the first choice as solvent, but because many chemicals have low solubility or
volatilize rapidly from water and because solvent effects in radical oxidations
are small, addition of acetonitrile up to 10% by volume is acceptable and pos-
sibly preferable wherever solubility or volatilization is a problem.
133
-------
Equation (4.23) describes a relative rate measurement in which the
measured variables are alcohols [SOH] and [ROH] derived from standard and un-
known chemicals, SH and RH. Assuming that conventional analyses (gc or Ic)
will allow reliable estimates of products at 5 x 10~6 M, and that 10% conver-
sions of starting chemicals do not invalidate use of equation (4.23) then the
initial concentrations of SH and RH can be ^ 5 x 10~3 M or higher.

Standard chemicals for relative measurements must meet specific chemical
and physical requirements: oxidation must occur readily only at one type of
CH bond; the compound must be soluble at pH 7 to the extent of ^ 10~A M, must
be relatively nonvolatile, and must give an alcohol product that can be analyzed
easily. No ideal standard has been tested but some possibilities include 4-
isopropylpyridine, benzylpyridine and acetylpyridine. Rate constants (kgx^
for these chemicals have not been measured but they probably lie in the range
of 0.5 to 10 M"1 s"1.

Another experimental approach to measuring k^Q involves application
of equation (4.34) where direct loss of the chemical is measured in an aqueous
solution containing a known concentration of MAB and sufficient t-Bu02H to
scavenge all R02» and R0» radicals. If the MAB concentration is chosen as 1
x lO"1* M, the initial steady state concentration of t-Bu02« will be

/Rit /76xlO-ll\l5
[RO>'} =\2k7J = (3.1x10' ) * 1'5 X 10'7 M (4'92)

Therefore the initial rate of oxidation of 5 x 10~5 M chemical having k^ of
100 M"1 s-1 is °2

d[C]/dt = kR02[C][t-Bu02«] (4.93)

= 100x (5 x 10~3) x (1.5 x 10-7)

= 7.5 x 10-10 M s-1

During each initial hour the loss would be 2.7 x 10~6 M; in ten hours the loss
would be close to 2.7 x 10~5 M or 5%. In the environment, where [R02»] ^ 10~*
M, this same chemical would have a half-life of 80 days at 50°C but about 300
days at 25°C. Therefore, a chemical reacting at only this rate may be regarded
as essentially unreactive in oxidation.

We can readily calculate that, if a chemical oxidizes only at CH bonds
with a half-life in the environment of less than 3 months (80 days), ICQX at
50° is > 300 M"1 s-1. This chemical will, in turn, oxidize in the MAB/t-Bu02H
solution at 2.5 times the rate of the example cited above and will half oxidize
in 4.5 hours; 25% loss will occur in about 2.1 hours.

Oxidation rate constants for chemicals that react with R02» at OH, NH,
or SH bonds must be evaluated differently from those that oxidize at CH bonds
because of their rapid reactions (kox > 103 M"1 s"1). Added t-Bu02H is not
used. At this time the simple test procedure can give only a lower limit to

134
-------
based on a loss rate for the chemical equal to half the production rate
s-1

~s
of R02», if k > 10" M-1 s
For example, if a phenol is present initially at 5 x 10~s M, 25% will
be oxidized in 27 hr at 50° with 1 x ICT* M MAB if kox > lO" M"1 s~l. This
calculation assumes that one phenol is oxidized for every two R02» produced
(zero order rate law) and
—
[R0a-]t = 0.4[MAB]Q(1 - e ~ ) (4.94)

where [R02»] is the total concentration of R02* produced in t hours.

^2 Oxidation Test
Rate constants for reaction of 102 are readily measured by using a
reference chemical together with the test chemical and a sensitizer such as
rose bengal (RB) , which efficiently generates 102. Rose bengal is soluble in
water and in some cosolvents and absorbs light at 555 nm (rose red) , well be-
yond the absorption spectra of most chemicals apart from other dyes. A solu-
tion at 10~s M RB absorbs over 90% of the light at 555 nm.

The very low concentrations of chemicals used in this test often are
necessitated by solubility limits, but also are preferred because of closer
relevance to environmental conditions and because low concentrations minimize
secondary reactions of products and starting chemicals. Pure water is preferred
as solvent but at least for rate studies there appears to be little harm in
using up to 10% acetonitrile. Using the reference chemical and test chemical
in the same solution eliminates variables associated with the lamp and dye but
they may be used separately in a merry-go-round apparatus.

No special light source is needed for irradiation, but if the chemical
is sensitive to near uv and visible light (photolysis protocol) , a cut-off
filter removing all light below 450 nm is necessary. Ordinary incandescent
lamps or sunlamps are quite satisfactory for this test as is a merry-go-round
photolysis unit.

Light intensities and therefore reaction times will vary with the source,
its filter system, and the distance from the reaction system. A standard
merry-go-round, which uses a 400-watt mercury lamp (filtered to pass only light
around 546 nm) ,' delivers about 4 x 10~8 einsteins s"1 per 2 ml of reaction
solution or about 2 x 10~s einsteins H~l s"1. If enough rose bengal is used
to absorb 90% of the light (about 10~5 M) at 555 nm U^x) and the quantum yield
for 102 formation is 0.8, we can readily calculate that the rate of X02 forma-
tion is 1.4 x 10~3 Ms"1. Since the rate of loss of X02 in dilute aqueous
solution of chemicals is governed only by the first-order process where k
-------
time period. A variety of chemicals may be useful as reference chemicals for
relative reactivity measurements toward 102. Among the criteria for selecting
suitable reference chemicals are reactivity, solubility in water, lack of
direct photochemical reaction, and preferably nonperoxidic products, i.e., no
reaction by the ene mechanism or rapid reaction of ene products with water.
Some chemicals that may meet these criteria are allylthiourea, dihydropyran,
aliphatic eneamines and vinyl ethers and some furans. Rate constants for
reactions of these chemicals or classes are shown in Table 4.4.

The principal problem in selecting a standard or reference chemical is
choosing one that is not greatly different in reactivity from the test chemical
in order to evaluate with some accuracy the relation.

ln(C /C)/ln(S /S) - kr/k_ (4.95)
O O \j o

where C and S refer to the test and standard chemicals, respectively. If the
two chemicals differ in their reactivity by a factor of 10, loss of half of
the more reactive chemical will be accompanied by loss of only 6% of the less
reactive chemical, an unsuitably small change. Since chemicals having similar
structural units will often have similar reactivities, selection of a reference
chemical as close as possible in structure to the test chemical will help
minimize differences in reactivity and minimize the number of analyses.

4.8 REFERENCES

Bartlett, P. D., G. D. Mendenhall, and A. Schaap. 1970. Competitive Modes of
Reaction of Singlet Oyxgen. Ann. N.Y. Acad. Sci. 171: 79-88.

Bartlett, P. D., and P. A. Schaap. 1970. Sterospecific Formation of 1,2-
Dioxetanes From cis- and transdiethoxyethylenes by Singlet Oxygen. J.
Amer. Chem. Soc. 92: 3223-3225.

Curci, R., and J. 0. Edwards. Peroxide Reaction Mechanisms - Polarity in
Organic Peroxides, D. Swern, ed., Vol. IV, Wiley-Interscience, New York,
pp 199-257.

Crosby, D. G., and C.-S. Tang. 1969. Photodecomposition of 1-Naphthalene-
Acetic Acid. J. Agr. Food chem. 17: 1291-1293.

Crosby, D. G., and A. S. Wong. 1973. Photodecomposition of p-Chlorophenoxy
Acetic Acid. J. Food Chem. 21: 1049-1052.

Denisov, E. T. 1974. Liquid-Phase Reaction Rate Constants. IFI/Plenum, New
York (translated by R. K. Johnson).

Draper, W. M., and D. G. Crosby. 1978. Oxidation of Benthiocarb by Peroxide
and Sunlight. Abstr. 175th Meet. Amer. Chem. Soc., Anaheim, Ca., March
12-17: Pest 52.
136
-------
Draper, W. M., D. G. Crosby, and J. B. Bowers, 1976. Measurement of Photo-
Chemical Oxidants in Agricultural Field Water. Abstr. 172nd Meet. Amer.
Chem. Soc., San Francisco, Ca., August 29-Sept. 9.

Foote, C. S. 1968. Mechanisms of Photosensitized Oxidation. Science, 162:
963-970.

Foote, Christopher S. 1976. Photosensitized Oxidation and Singlet Oxygen:
Consequences in Biological Systems, in Free Radicals in Biology. Volume
II. W. A. Pryor, ed., Academic Press, Chapter 3, pp 85-124.

Foote, C. S., and R. W. Denny. 1968. Chemistry of Singlet Oxygen. Quenching
by B-Carotene. J. Amer. Chem. Soc. 90:6233-6235.

Foote, C. S., and H. Kane. 1967. Singlet Oxygen Oxidation of Dimethylfuran.
Unpublished work cited Foote, 1968.

Foote, C. S., E. R. Peterson, and K.-W. Lee. 1972. Chemistry of Singlet
Oxygen XVI. Long Lifetime of Singlet Oxygen in Carbon Disulfide. J.
Amer. Chem. Soc. 94: 1032-1033.

Gollnick, K., T. Franken, G. Schade, and G. Dorhofer. 1970. Photosensitized
Oxygenation as a Function of the Triplet Energy of Sensitizers. Ann. N.Y.
Acad. Sci. 171: 89-107.

Hendry, D. G., T. Mill, L. Piszkiewicz, J. A. Howard, and H. K. Eigenmann.
1974. A Critical Review of H-Atom Transfer in the Liquid Phase. J. Phys.
and Chem. Ref. Data 3:937-978.

Howard, J. A. 1972. Absolute Rate Constants for Reactions of Oxyl Radicals.
Adv. Free Radical Chem. 4: 49-174.

Howard, J. A., and E. Furimsky. 1973. Arrhenius Parameters for Reaction of tert-
Butylperoxy Radicals with Some Hindered Phenols and Aromatic Amines. Can.
J. Chem. 51: 3788-3745.

Howard, J. A., and K. U. Ingold. 1968. Absolute Rate Constants for Hydro-
carbon Oxidation. XI. The Reactions of Tertiary Peroxy Radicals. Can.
J. Chem. 46: 2655-2660.

Ingold, K. U. 1969. Peroxy Radicals. Acct. Chem. Res. 1: 1-45.

Kraljic, A., and B. Kramer. 1978. Photooxidation of Allylthiourea. Photochem.
Photobiology 27: 9-15.

Mahoney, L. R., and M. A. DaRooge. 1975. The Kinetic Behavior and Thermo-
chemical Properties of Phenoxy Radicals. J. Amer. Chem. Soc. 97: 4722-
4731.
137
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Matsuura, T., A. Horinaka, and R. Nakashima. 1973. Photoinduced Reactions.
LXXII. Reactivity of Singlet Oxygen Toward Cyclic Olefins. Chera. Letters,
887-890.

Mayo, F. R. 1968. Free-Radical Autoxidations of Hydrocarbons. Accts. Chem.
Res. 1: 193-216.

Merkel, P. B., and D. R. Kearns. 1972. Radiationless Decay of 102 in Solution;
An Experimental and Theoretical Study of Electronic to Vibrational Energy
Transfer. J. Amer. Chem. Soc. 93: 7244-7253.

Mill, T., and A. Baraze. 1978. Free Radical Oxidation of p-Cresol in Dilute
Aqueous Solution. Manuscript in preparation.

Mill, T., D. G. Hendry, and H. Richardson. 1978. Chemical Transformation of
Pollutants in Water, in Aquatic Pollutants - Transformations and Biological
Effects, ed. 0. Hutzinger, I. H. Van Llelyveld, and B.C.J. Zoeteman,
Pergamon Press, Oxford, in press.

Mortimer, G. A. 1964. A New High-Temperature Free Radical Source. J. Org.
Chem. 30: 1632-1633.

Ross, R. , and D. G. Crosby. 1975. The Photooxidation of Aldrin in Water.
Chemosphere 5: 277-282.

Ross, R. D., and D. G. Crosby. 1973. Photolysis of Ethylenethiourea. J.
Food Chem. 21: 335-337.

Soderquist, C. J., J. B. Bower, and D. G. Crosby. 1976. Photodecomposition
of Molinate. Abstr. 172nd Meeting of Amer. Chem. Soc,., San Francisco,
Ca., August 29-Sept. 3.

Swern, D. 1971. Organic Peroxides as Oxidizing Agents. Epoxides, in Organic
Peroxides, D. Swern, ed., Vol. II, Wiley-Interscience., New "York, pp 355-
533.
Walling, C. 1957. Free Radicals in Solution, John Wiley and Sons, New York.

Young, R. F., K. Wehrly, and R. L. Martin. 1971. Solvent Effects in Dye-
Sensitized Photooxidation Reactions. J. Amer. Chem. Soc. 93: 5774-5779.

Zepp, R. G. , N. L. Wolfe, G. L. Baughman, and R. C. Hollis. 1978. Singlet
Oxygen in Natural Water. Nature 267: 421-423.
138
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CHAPTER 5. ATMOSPHERIC CHEMISTRY

D. G. Hendry
5.1 INTRODUCTION 140
5.2 OBJECTIVE 141
5.3 SUMMARY ' 141
5.4 CONCLUSIONS AND RECOMMENDATIONS 143
5.5 SCREENING TESTS 143
5.5.1 Photochemical Reaction: Absorption Spectrum 143
5.5.2 Screening Test for Reaction with OH 149
5.5.3 Screening Test for Reaction with Ozone 153
5.6 DETAILED TESTS 154
5.6.1 Determination of Quantum Yield for Photolysis Measurements . . . 155
Error Analysis for kp' 156
Error Analysis for $ 157
Error Analysis for k 158
5.6.2 Determination of Hydroxyl Radical Rate Constant Measurements . . 158
Error Analysis for Rate Constant Ratio k^/kStr 162
5.6.3 Determination of Ozone Reaction Rate Constant Measurement .... 163
Error Analysis for kg and 03 165
5.7 BACKGROUND 165
5.7.1 General Considerations 165
5.7.2 Photochemical Transformations 166
Rates of Reactions 166
Computation of Photochemical Reaction Rates 170
5.7.3 Atmospheric Oxidation 171
General 181
Atmospheric Concentration Units 181
Hydroxyl Radical Reactions and Rates 181
Ozone Reactions and Rates 185
5.7.4 Environmental Studies 1&5
Problems of Direct Measurement of Atmospheric Lifetimes 185
Determination of OH Concentrations in Polluted Air 1&7
Estimation of Average Tropospheric OH Concentration 188
Direct Measurement of OH Concentrations 189
Computational Estimates of Tropospheric OH Concentrations .... 190
Summary of OH Concentrations Data 190
Determination of Ozone Concentrations 191
5.7.5 Design of Laboratory Test Methods 191
Photochemical Reaction 191
Reaction with OH 197
Reaction with Ozone 198
5.8 REFERENCES 199
APPENDIX 5.2 STATISTICAL ANALYSIS FOR K£ /k^, 205
Url Url
139
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5. ATMOSPHERIC CHEMISTRY
5.1 INTRODUCTION

Chemical processes compete with physical processes in determining the fate
of chemicals entering the atmosphere. The more reactive compounds (lifetimes
of ^ 1 day) will react rapidly within the boundary layer of the atmosphere
immediately adjacent to the earth's surface where the emissions generally occur.
Less reactive compounds will be distributed by diffusion and turbulent mixing
into the remainder of the troposphere and in some cases will be reasonably well
mixed in the entire troposphere before appreciably reacting. Finally, those
compounds that are stable to the oxidative and photic environment of the tropo-
sphere, and are not removed by physical process such as rainout, will gradually
diffuse into the stratosphere where additional loss mechanisms exist—the most
important of which is photolysis in the 150-300 nm region of the solar spectrum.
To understand the effects of industrial chemicals on the environment, it is
important to anticipate what processes are critical for each chemical and in
what regions of the atmosphere they will occur.

The important chemical processes in the atmosphere are all the, result of
the absorption of sunlight in the atmosphere. In some cases the chemical
compounds can absorb sunlight directly and thereby undergo reaction. Other
compounds only react with reactive species, such as ozone and hydroxyl radicals
formed as the consequence of absorption of solar energy by other species and
the subsequent complex chemistry that follows. The three basic atmospheric
reactions that account for reaction of organic compounds are

(1) Direct photolysis
(2) Reaction with hydroxyl (OH) radical
(3) Reaction with ozone (03).

These processes, as well as methods to determine their importance for specific
compounds, will be discussed in detail in this chapter. However, they compete
with a number of physical processes, including:

(1) Dilution
(2) Dry deposition
(3) Sorption to particulate
(4) Rainout and washout
(5) Diffusion to stratosphere.
Dilution generally accounts for a very rapid reduction of concentration of
emissions, but it does not result in any loss of mass from the atmosphere.
Dilution affects all compounds equally, whereas the other physical processes
are compound-specific. Dry deposition is important for compounds that have an
affinity for reaction or sorption on surfaces such as soils, water bodies,

140
-------
plants and man-made structures. Once a compound is sorbed to a particulate,
its fate is determined by factors that affect the particulate, including rain-
out, washout, conglomeration, and fallout; desorption is also a possibility
because dilution reduces the concentration of free compound around the particu-
late. Rainout and washout affects compounds with high water solubility,
depositing them in water bodies and on land. In either case, the pollutant
may be revolatilized depending on the atmospheric conditions and the affinity
of the compound for solution in water or sorption to soil.

Atmospheric sources and fates of both natural and man-made chemicals are
summarized in Figure 5.1. Heterogeneous chemistry associated with the chemicals
sorbed to the particulate phase is not included. We currently have no data on
how important such processes can be but we expect them to be limited to a small
group of compounds of low volatility that strongly sorb to the particulate phase.

This protocol is concerned solely with the chemistry of compounds in the
vapor phase. The reactions considered include direct photochemical reaction and
reactions with OH radical and with ozone. The protocol does not consider
physical processes, but these processes are expected to be important for only
a small number of compounds.

5.2 OBJECTIVE

The main objective of this chapter is to develop two-tier test procedures
to determine the rate constants of atmospheric chemical processes that control
the lifetime of chemical compounds in the atmosphere, including direct photolysis
and reactions with ozone and hydroxy radical.

5.3 SUMMARY

A two-tier series of tests has been outlined to evaluate the lifetime of
compounds in the atmosphere as determined by photolysis and reactions with hy-
droxyl radical (OH) and ozone (03).

The first tier of tests screens these three pathways and estimates the
approximate importance of each. An upper limit for the rate of photolysis is
obtained by assuming that reaction occurs with a quantum efficiency of unity
and by equating the rate of reaction with the rate of absorption of light.
The latter rate is determined by combining ultraviolet-visible absorption spectral
data with the solar spectral intensities. A hand method of integrating absorp-
tion and solar intensity data for various times of the year is provided.

Estimates of the rate constants for reaction with hydroxy radical and
ozone are based on analogy to other structures. From these rate constants and
estimates of the environmental concentrations of OH and ozone, estimates of the
lifetime are made.

Once the relative importance of the three basic processes is determined,
the rate constants for those processes that clearly dominate are measured in
detailed tests. These detailed tests constitute the second tier of tests.

141
-------

Emission
Manufa
Applica
Disposa

Chemistry with
Y\v, OH, and 03
i
s From:'

Diffusion to
Stratosphere

cturina ^ Homogeneous
tion
1 ... ,,
Rai
Was

Gas Phase
Or
1 Depos
nout-
hout
*

» F
V t \
ition I Pal
Vapor-
ization
i i

•articulate
Phase
out
Rainout-
Washout
I
Land and Water
SA-4396-79R
FIGURE 5.1 FATE OF GASEOUS EMISSIONS
142
-------
The rate constant for reaction with OH is determined by measuring the rate
of loss of the chemical relative to the loss of a standard compound with known
OH rate constants in the presence of OH generated from nitrous acid photolysis.
If the reaction with ozone appears to be important, the rate constant will be
determined by following the disappearance of ozone in the presence of the
compound.

For the photochemical reaction, the quantum yield at one wavelength is
measured, generally in the solar spectrum, and is combined with the rate of
absorption of light determined in the first tier to obtain the rate of photolysis.
5.4 CONCLUSIONS AND RECOMMENDATIONS

The rates of reaction of most chemicals in the atmosphere can be readily
determined using relatively simple laboratory measurements. The important
chemical processes in the atmosphere that can be evaluated using techniques
outlined in this report are photolysis by direct absorption of solar radiation,
and oxidation by reactions with both hydroxyl radical and ozone.

Further research is needed to determine the effect of particulate absorp-
tion on environmental lifetimes. If this process deactivates compounds toward
further chemical reactions, then environmental lifetimes can be increased, but
if additional reaction pathways exist for absorbed materials, then the environ-
mental lifetimes will be decreased.
5.5 SCREENING TESTS

The purpose of the screening tests is to set upper limits or approximate
values for the half-lives for photochemical reaction and reaction with ozone
and OH.

5.5.1 Photochemical Reaction; Absorption Spectrum

This screening test involves measuring the vapor phase uv spectrum in
air over the solar spectrum. A maximum rate of photolysis is calculated by
assuming a quantum yield of unity over all wavelengths where absorption occurs
in the solar spectrum.

The following are required for this procedure:

(1) A uv spectrophotometer capable of scanning the region 290 to 800 nm.
(2) A uv gas cell, with quartz windows and suitable gas handling system
for measuring the pressure of vapor in cells.

Figure 5.2 shows a suitable gas handling system for charging the uv cell.
Mercury should not be used in the apparatus in either the pumping or pressure
measuring systems. Stopcocks should be high vacuum 0-ring stopcocks; if ground
glass stopcocks are used, a lubricant should be used that does not absorb the
compound being studied.
143
-------
Vacuum Pump
and Trap

/ \/} Pressure
\/V/ Gauge

SA-4396-80

FIGURE 5.2 GAS HANDLING SYSTEM FOR CHARGING UV CELL
144
-------
The following procedure is recommended for use with the apparatus shown
in Figure 5.2. The uv cell is attached to the apparatus by the vacuum-tight
joint (10 mm o-ring) and evacuated to less than 10~5 torr, if possible, but to
at least one-hundredth of the pressure of the compound to be introduced into
the cell. Several milliliters of liquid compound are then placed in the sample
reservoir and degassed by repeated freezing, pumping, and thawing for three
cycles . Then the compound is allowed to warm to room temperature and a sample
is allowed to expand into the uv cell and manometer. The pressure is read and
the stopcocks to the cell and reservoir are closed. The vapor in the connecting
tube is pumped out. Then air, dried over molecular sieves, is allowed to fill
the connecting tubing first and then allowed to slowly enter the uv cell until
atmospheric pressure is obtained. Then the stopcock on the cell is closed and
the cell is warmed to 75°C for one hour to enhance mixing. Then the uv cell
is allowed to cool, disconnected from the apparatus, and placed in the uv
spectrophotometer . The uv-visible spectrum is then measured relative to a
matched cell filled with air according to manufacturers' directions using
minimum slit openings. This procedure is to be repeated at two other pressures
of compound. The pressures should differ by at least a factor of two and pre-
ferably five to ten, providing the absorption is sufficiently strong at the
lower pressure to provide an absorbance one-tenth of the more sensitive scale.
However, this limit depends on instrument stability, which is partly a function
of the slit opening.

The data are then tabulated, and the cross sections or absorption coef-
ficients can be determined from Beer-Lambert Law (equation 5.1) in the form
a = (£C)-lln (5.1)

where a is the cross section in cm2 molec"1, Si is the pathlength in cm, C is
the concentration in molec cm~3, and Io and I are the intensities of incident
and final light in photons cm2. From the consistency of the data at three
pressures plus estimates of possible deviations, it will be possible to deter-
mine if there is deviation from Beer-Lambert Law. In cases where there is a
consistent variation between the cross sections, determined at different
pressures, the low pressure values are preferred, providing that the precision
of the measurements is ± 25%.

The cross sections are combined at each wavelength range with the solar
intensities from Tables 5.1, 5.2, and 5.3 to obtain the average seasonal photolysis
rate constants at 10°, 30°, and 50°N latitude. This is done using the procedure
in Section 5.7.2, assuming unit quantum efficiency. Because of the latter as-
sumption, the calculated rate constant is an upper limit (k )

k = Ea,J. ' (5.2)
p A A

The half-life, which will be a lower limit, is

todays) = In2/k (5.2a)
1 p

145
-------
TABLE 5.1. J, ' VALlffiS AT 10° N LATITUDE3
Wavelength
Range, nm
285-295
295-305
305-315
315-325

325-335
335-345

345-355
355-365
365-375
375-385
385-395
395-405

405-415
415-425

425-435
435-445
445-455
455-465
465-475
475-485
485-495
495-515
515-535
535-555
555-575
575-595

595-635
635-675

675-715
715-755
755-795
Solstice
Summer
0
6.39 17
9.701 18
Winter
Equinox
0 0
3.31 17 6.38 17
6.679 18 9.522 18
Season Average
Spring/Summer Fall/Winter
0
6.63 17
9.815 18
2.451 19 < 1.852 19 2.386 19 2.457 19
I
4.474 19 3.518 19
4.945 19 3.957 19
1
5.666 19 ' 4.605 19
5.85 19 ; 4.758 19
7.301 19 5.976 19
7.157 19 5.891 19
7.329 19 6.065 19
1.004 20 8.341 19
I
1
1.275 20 1.063 20
1.331 20 1.114 20

1.349 20 1.133 20
1.491 20 ; 1.256 20
1.718 20 ' 1.449 20
1.857 20 ! 1.568 20
1.914 20 1.619 20
1 . 941 20
1.945 20
3.970 20
1.645 20
1.652 20
3.370 20
4.013 20 ' 3.41 20
3.995 20 3.398 20
4.053 20
4.197 20
3.446 20
3.573 20
i
8.529 20
7.235 20
8.976 20 i 7.658 20
|
9.077 20
8.744 20
8.460 20
7.778 20
7.514 20
7.287 20
4.341 19
4.789 19

4.468 19
0
4.6 17
7.91 18
2.685 19

3.877 19
4.828 19 4.321 19

5.479 19 i 5.638 19

4.735 19
5.656 19 5.820 19 4.925 19
7.655 19 7.226 19 6.357 19
6.913 19 7.125 19 6.343 19
7.075 19 i 7.278 19
9.687 19 9.966 19

1.23 20 1.265 20
1.283 20 ' 1.320 20

1.30 20 1.338 20
1.436 20 1.478 20
1.655 20 ; 1.702 20
1.789 20 1.840 20
1.843 20 1.896 20
1.869 20 1.922 20
1.873 20
3.823 20
3.863 20
3.846 20
3.902 20
4.040 20

8.211 20
8.637 20

8.732 20
8.410 20
8.135 20
1.926 20
3.932 20
3.974 20
3.956 20
4.014 20
3.659 20

8.446 20
8.884 20

8.961 20
8.650 20
8.367 20
6.663 19
8.927 19
!
1
1.135 20
1.187 20

1.205 20
1.339 20
1.538 20
1.664 20
1.716 20 |
1.742 20
1.747 20
3.565 20
3.605 20
3.591 20
3.692 20
3.774 20

7.652 20
8.077 20

8.186 20
7.897 20
7.648 20
Second number in column is the power of ten by which the first number is
multiplied.
Units are in photons cm day"' as discussed in text.
146
-------
TABLE 5.2. J ' VALUES AT 30°N LATITUDE'
a,b
Wavelength
Range , nm
285-295
295-305
305-315
315-325
325-335
335-345
345-355
355-365
365-375
375-385
385-395
395-405
405-415
415-425
425-435
435-445
445-455
455-465
465-475
475-485
485-495
495-515
515-535
535-555
555-575
575-595
595-635
635-675
675-715
715-755
755-795
Solstice
Summer
1.0 16
7.40 17
1.09 19
2.74 19
4.98 19
5.49 19
6.28 19
6.49 19
8.09 19
7.93 19
8.12 19
1.11 20
1.41 20
1.47 20
1.49 20
1.65 20
1.90 20
2.05 20
2.12 20
2.15 20
2.15 20
4.39 20
4.44 20
4.42 20
4.48 20
4.64 20
9.44 20
9.92 20
1.00 21
9.67 20
9 . 35 20
Winter
0
6.80 16
2.83 18
1.00 19
2.11 19
2.48 19
3.11 19
3.10 19
3.95 19
3.95 19
4.12 19
5.72 19
7.36 19
7.80 19
7.99 19
8.93 19
1.04 20
1.13 20
1.17 20
1.19 20
1.20 20
2.45 20
2.49 20
2.49 20
2.52 20
2.62 20
5.39 20
5.72 20
5.85 20
5.70 20
5.57 20
Equinox
0
3.98 17
7.49 18
2.03 19
3.82 19
4.28 19
4.96 19
5.13 19
6.43 19
6.33 19
6.51 19
8.94 19
1.14 20
1.19 20
1.21 20
1.34 20
1.55 20
1.67 20
1.73 20
1.75 20
1 . 76 20
3.59 20
3.63 20
3.62 20
3.67 20
3.80 20
7.70 20
8.15 20
8.27 20
7.98 20
7.74 20
Season Average
Spring/Summer
1.18 15
6.24 17
9.77 18
2.50 19
4.58 19
5.07 19
5.82 19
6.01 19
7.51 19
7.36 19
7.55 19
1.03 20
1.31 20
1.37 20
1.39 20
1.54 20
1.77 20
1.92 20
1.98 20
2.01 20
2.01 20
4.10 20
4.15 20 '
4.13 20
4.19 20
4.34 20
8.81 20
9.28 20
9.39 20
9.05 20
8.76 20
Fall/Winter
0
1.78 17
4.60 18
1.41 19
2.79 19
3.20 19
3.68 19
3.92 19
4.96 19
4.92 19
5.09 19
7.04 19
8.64 19
9.37 19
9.67 19
1.08 20
1.25 20
1.35 20
1.40 20
1.42 20
1.43 20
2.92 20
2.96 20
2.95 20
2.99 20
3.11 20
6.34 20
6.72 20
6.84 20
6.64 20
6.46 20
Second number in column is the power of ten by which the first number is
multiplied.

Units are in photons ctn" 2 day"1 as discussed in text.
147
-------
TABLE 5.3. J, ' VALUES AT 50°N LATITUDE3'1'
Wavelength
Range, nm
285-295
295-305
305-315
315-325
325-335
335-345
345-355
355-365
365-375
375-385
385-395
395-405
405-415
415-425
425-435
435-445
445-455
455-465
465-475
475-485
485-495
495-515
515-535
535-555
555-575
575-595
595-635
635-675
675-715
715-755
755-795
Solstice
Summer
0
5.7 17
1.005 19
2.680 19
5.0 19
5.577 19
6.446 19
6.659 19
8.341 19
8.204 19
8.427 19
1.157 20
1.472 20
1.540 20
1.564 20
1.732 20
1.996 20
2.159 20
2.227 20
2.261 20
2.268 20
4.629 20
4.682 20
4.664 20
4.732 20
4.903 20
9.935 20
1.048 21
1.061 21
1.023 21
9.902 20
Winter
0
6.0 14
2.981 17
1.857 18
5.429 18
7.118 18
8.513 18
9.536 18
1.248 19
1.279 19
1.070 19
1.951 19
2.569 19
2.792 19
2.915 19
3.326 19
3.91 19
4 . 30 19
4.533 19
4.685 19
4.769 19
9.789 19
1.001 20
1.002 20
1.014 20
1.063 20
2.227 20
2.463 20
2.610 20
2.644 20
2.648 20
Equinox
0
1.12 17
3.945 18
1.317 19
2.714 19
3.163 19
3.86 19
3.923 19
4.985 19
4.967 19
5.165 19
7.161 19
9.194 19
9.715 19
9.938 19
1.109 20
1.283 20
1.392 20
1.443 20
1.471 20
1.483 20
3.026 20
3.069 20
3.062 20
3.104 20
3.228 20
6.631 20
7.015 20
7.165 20
6.977 20
6.809 20
Season Average
Spring/Summer
0
3.763 17
7.724 18
2.173 19
4.162 19
4.700 19
5.495 19
5.670 19
7.130 19
7.038 19
7.255 19
9.987 19
1.274 20
1.337 20
1.361 20
1.510 20
1.743 20
1.886 20
1.948 20
1.981 20
1.983 20
4.060 20
4.109 20
4.095 20
4.153 20
4.308 20
8.749 20
9.253 20
9.40 20
9.089 20
8.821 20
Fall/Winter
0
2.55 16
1.398 18
5.699 18
1.314 19
1.597 19
1.984 19
2.057 19
2.648 19
2.646 19
2.816 19
3.949 19
5.132 19
5.478 19
5.652 19
6.366 19
7.413 19
8.087 19
8.444 19
8.659 19
8.758 19
1.791 20
1.823 20
1.822 20
1.845 20
1.926 20
3.983 20
3.428 20
4.431 20
4.370 20
4.311 20
aSecond number in column is the power of ten by which the firsl: number is
multiplied.
bUnits are in photons cm" J day"1 as discussed in text.
148
-------
5.5.2 Screening Test for Reaction of OH

For the purposes of screening the importance of reaction with OH, the
method of rate constant estimation outlined in Section 5.7.3 is applied. The
rate constant is expressed by the equation

i 3 *
kOH = 1f1niaHl|JHikHi + .^"Ej^j + £^eaAtkA£ (5'3)

The first summation accounts for reaction of all reactive hydrogen atoms
within the molecule. The term k^. is the reactivity of the hydrogen atoms from
Table 5.4, taking into account the position and degree of substitution on the
adjacent atom by alkyl, vinyl, phenyl, C(0)-, 0-, S-, and N- groups. The terms
otfli and BH-^ account for the effect of groups in the o-position and 0-position
on the carbon-hydrogen bond and are also defined in Table 5.4. These terms
are applied for each a and 0 substituent; thus,

-- and pHi = NHI'^"'

The term n.^ accounts for the repetition of the i carbon-hydrogen bond.

The second summation accounts for the reactivity of all carbon-carbon
double bonds in the molecule. The term kg is the intrinsic reactivity of each
double bond, taking into account the degree of substitution, whereas org accounts
for the effect of any halogen substituted directly to the double bond. These
terms are defined in Table 5.5. as accounts for the repetition of each unique
double bond.

The third summation accounts for addition of OH to aromatic rings in the
molecule, k^ is the intrinsic reactivity of the ring, taking into account the
degree of alkyl substitution, a^ accounts for halogen substituents in the ring.
Both k. and a. are defined in Table 5.6.
A A
The sum of the three terms determines kQH (in cm3 molec"1) for the
compound. Examples of this calculation are given in Figure 5.3.

The half-life for reaction with OH is

t°H = ln2/kOR[OH] (5.4)

Assuming an average ground level concentration over the year of OH = 10s
molec/cm3 (1.7 x 10" 8 ppm) based on the discussion in Section 5.7.4, the
half-life is

OH
t^ (seconds) = 6.93 x IQ-'/k..., (5.4a)
149
-------
TABLE 5.4. ABSTRACTION RATE CONSTANTS (kR) FOR REACTION OF OH WITH GENERALIZED
GROUPS AND VALUES OF INDUCTION FACTORS (c^ AND Pfl)
Group

C CX —H
(Cg)aCX-H
(CS)3C-H
CD-H
C_CX2-H
D
(Cg)(CD)CX-H
(Cs)a(CD)C-H

-?-H
S-H
CD0-H
10 12 k-^ (per hydrogen)

0.065 ± 0.013
0.55 ± 0.07
2.9 ± 0.58
0.01 ± 0.002
0.3 ± 0.1

2.5 ± 1.0
4.0 ± 1.5

17 ± 4 x
2.6 ± 1.3
1.7 ± 0.8 ,

\
H
Cl, Br
F
OH
} 0-alkyl
O
ofi-
c-
<
s-

all cases

«H

1.0
2.4 ± 0.6
1.0
2.0 ± 0.05
6.0 ± 2.0

1.0
1.3 ± 0.2
100 ± 50
200 ± 100

1.0

1.0
0.4 ± 0.1
0.3 ± 0.1
1.0
1.0

1.0
1.0
1.0
1.0

1.0

aCR - Saturated carbon, -0, -C-0, or-S; CD - unsaturated carbon as in vinyl or
pRenyl groups; X - H, F, Cl, or Br.
Rate constant expressed as cm3 molec'1 s"1.
150
-------
TABLE 5.5. ADDITION RATE CONSTANTS (kg) FOR REACTION OF OH WITH CARBON-CARBON
BOND, AND VALUES OF INDUCTION FACTORS (a )
Subscituent
none (echene)
1-alkyl
1,1-dialkyl
1,2-dialkyl
cis
trans
trialkyl
tetraalkyl
vinyl or phenyl
OMe
10'Jka (per double bond)
7.9
27 ± 5
50 ± 10

60 ± 12
.70 ± 14
80 ± 16
150 ± 30
80 ± 20
33
Substituent a£

F - 0.5 ± 0.3
Cl.Br - 0.7 ± 0.3

*Rate constant expressed as cm3 molec"1 s"
TABLE 5.6. ADDITION RATE CONSTANTS (kA) FOR REACTION OF OH WITH AROMATIC RINGS,
AND VALUES OF INDUCTION FACTORS (a )
Substituent
H
alkyl
dialkyl
1,2,3-trialkyl
1,2,4-trialkyl
1,3,5-trialkyl
methoxy
OH plus alkyl
P.
-CH
1012ka
1.4
5.0 ± 2
12 ± 4
10 ± 5
25 ± 5
49 ± 5
17 ± 5
34 ± 10
< 1.0
Substituent
H
Cl.F.Br

"A
1.0
< 1.0

Kate constant expressed as cm1 molec*1 s~
151
-------
1,2-Dichloroethane:
ClCHaCHjCl
HaCClCCl:

1,1-Dichloroethane:

HCClaC:

H3CCC12:
4(0.065 ± .013)(2.4 ± 0.6)(0.4 ± 0.1) = 0.25(0.11-0.47)

Measured value (Table 5.14) =0.22

C12CHCH3

(0.065 ± .013X2.4 ± 0.6)2 = 0.37(0.17 - 0.70)

3(0.065 ± .013X0.4 ± O.I)2 = 0.03(0.015 - 0.06)

Z - 0.40(0.17 - 0.72)

Measured value (Table 5.14) - 0..26

HOCHa XC(0)OCH3
3-Chloro-4-hydroxy-cis-butenoic methyl ester:
cis-C=C:

-CH2-:

CH3-:

OC-H:
(60 ± 12) (0.7 ± .3) = 42 (15 - 72)

2(2.5 ± 1)(2.0 ± 0.5) = 10 (4.4 - 17.6)

3(0.55 ± 0.07) = 1.6 (1.4 - 1.9)

(0.01 ± 0.002) - 0.01 (0.008 - 0.012)
Z - 54 (21 - 91)
CHaCH3
3-Chloroethylbenzene

ring:

-CHa-:

CH3-:

ring-H:
o
(5 ± 2)(< 1)

2(2.5 ± 1)

3(0.065 ± 0.013)

4(0.01 ± 0.002)

Z
< 5(< 3-7)

5(3 - 7)

0.2(0.16 - 0.23)

0.04(0.03 - 0.05)

5-10(3 - 14)
FIGURE 5.3 ESTIMATION OF k (10ia cm3 molec"1 s ') USING EQUATION
AND DATA IN TABLES 5.4 TO 5.6
152
-------
t1°H(days) = 8.0 x 10-12/kQH (5.4b)

Because [OH] does vary considerably during the day, very reactive com-
pounds (tPH < 0.5 days) will show a range of tu values depending on the time
of release2. However considering that release occurs continually throughout the
day, equations (5.4a) and (5.4b) still give the average half-life. The ex-
pression will apply best for compounds having t^ value of 1 to 10 days. For
more reactive compounds emitted during the day in polluted areas, the ti^ values
estimated from equations (5.4a) and (5.4b) will be too large by a factor of
3-10. For compounds of low reactivity where mixing into the entire troposphere
occurs, calculated tPH values [equations (5.4a) and (5.4b)] will be a factor
of 2-3 too small because of the smaller [OH] at higher elevations (see Section
5.7.4).

5.5.3 Screening Test for Reaction with Ozone

To screen for the importance of reaction with ozone, the structure of
the compound is analyzed for the reactive groups identified in Table 5.7.
Thus, the method involves determining if the compound has a carbon-carbon
double bond; if it does have such a bond, the degree of substitution is deter-
mined. Then, from data in Table 5.7, the rate constant for that specific type
of group is determined. If the compound contains an aromatic ring, the degree
of substitution is determined and the estimated rate constant is determined
from Table 5.7. If the molecule contains more than one reactivity group, the
molecular reactivity is the sum of the rate constant for each group.

The half-life for reaction with 03 is

t°3 = In2/k[03] (5.5)
* vJ 3

Since the average tropospheric ozone concentration is 1 x 1012 molec cm"3 (1.7
x 10~" M or 0.041 ppm), the half-life may be expressed as follows:

t°3(seconds) = 6.9 x 10~l3/k0 (5.5a)

t°3(days) = 8.0 x 10-l8/kQ3 (5.5b)

where k is in molar units of cm3 mole s
One3must keep in mind that ground level ozone concentrations do fluctuate
and the true tj, values will also. In urban atmosphere and downwind from urban
centers, the values of daytime ozone concentrations can be 2-5 times larger
than used in equations (5.5a) and (5.5b). Therefore the actual ti^ values for
reactive compounds (tu < 0.5 day) under these conditions will be shorter than
estimated by equations (5.5a) and (5.5b) by a similar factor.
153
-------
TABLE 5.7. RATE CONSTANTS FOR REACTION OF OZONE WITH GENERALIZED STRUCTURES'
Structure
Ethenes
alkyl
1,1-dialkyl
1,2-dialkyl
cis-
trans-
trialkyl
tetraalkyl
Cycloalkenes
C3
c«
Alkadienes
1QIB *o3>
c3 molec" l s~ l
1.9
12
14

160
260
500
1500

800
170

1,3-butadiene | 8.4
Benzene
alkyl
dialkyl
trialkyl
tetraalkyl
hexaalkyl
hydroxy
0.00005
0.003 - 0.0006
0.001 - 0.002
0.006 - 0.008
0.02
0.4
1-2
t^, days
4.2
0.7
0.6

0.06
0.03
0.01
0.006

0.01
0.05

1.0
2 x 10s
2 x 10"
7 x 103
2 x 103
400
20
3-7
*Data from Table 5.14.
5.6 DETAILED TESTS
The purpose of the detailed procedures is to determine the rate constants
of the chemical processes that control the lifetime of chemicals in the at-
mosphere. In general, the rate constants need be determined only for processes
shown to be of potential importance in the screening tests. Thus if the value
of either t^H or t£|3 is less than 0.01 times t£, then only kQH and/or kQ
must be determined. If t£ is less than 0.01 tfiH or tfia, then
-------
5.6.1 Determination of Quantum Yield for Photolysis

The following equipment is required for measuring the quantum yield
for photolysis:

(1) An optical train with the appropriately isolated wavelength of uv
or visible light as discussed in Section 5.7.5.
(2) A uv reaction cell, with borosilicate windows if radiation is
> 300 nm, or Vycor if radiation is > 220 run, and a gas handling
system such as in Figure 5.2 to handle and measure the pressure of
vapor in the cell. No mercury vapor should be allowed in the
system because even traces can serve to sensitize photochemical
reactions.
(3) An actinometer that photolyzes at the wavelength at which the
quantum yield is being measured.

Three sets of experiments are necessary to determine the desired
quantum yield. First, tests must be made for a constant rate of photolysis
of the actinometer by charging the system with the actinometer, using the tech-
nique described in Section 5.5.1 (keeping the absorbance below 0.02). Once
the lamp has stabilized, the actinometer must be photolyzed in the optical
train until the reaction proceeds to about 10%. Then the process is repeated
twice more for two and four times longer. The log of the observed concentra-
tion is then plotted versus time. The slope of the regression line (k'a) is
a^Io^. ^ t*ie Plot °f the initial and three final concentrations gives no
evidence of curvature, the reproducibility of the actinometer and light source
have been demonstrated. If the rate of reaction increases with time, then
possibly the light source has not been allowed to stabilize sufficiently. If
the long run indicates a significantly smaller rate than the shorter runs,
then the conversion of the actinometer may be too large (absorbance greater
than 0.02) or products are affecting the reaction. Based on these experiments,
an optimum time for measuring the light flux can be determined.

In the second set of experiments, the reaction cell is loaded with a
pressure of compound not greater than 50% of the room temperature vapor pres-
sure, while keeping the absorbance below 0.02. Then the compound is photolyzed
to about 10% conversion. Then two additional runs are made for two and four
times longer, always allowing the lamp to stabilize before beginning the re-
action. The log of the concentration is plotted at each time, including the
initial time, and the regression slope (kl^ is determined. If the plot shows
a noticeable curvature suggesting a slower rate at the later stages, then one
of the products may be quenching the reaction; if the curvature suggests a
faster rate, then a product may be sensitizing the reaction. In either case,
the initial slope would give the most reliable value of k'.

If no measurable decomposition can be observed during a reaction time
of one week, then the third set of experiments may be omitted and an estimate
of a maximum value of the quantum yield can be made from equation (5.9), as-
suming a loss of an amount equal to twice the standard deviation of the
analytical procedure over the maximum reaction time.

155
-------
From the above experiments, the optimum conditions may be selected for
measuring the light flux and photolyzing the compound under study. A third
series of experiments should then be carried out consisting of an actinometer
run, a sample run, and a second actinometer run using these optimum conditions.
From each experiment, an apparent first-order rate constant k' is defined.
The average of the two actinometer runs (k'a) is used to determine the light
flux for the sample photolysis and thus correct for lamp aging during the ex-
periment. The quantum yield (4>c) can then be calculated from kpa, the sample
constant kpc, cross sections of compound (ac) and actinometer (aa) , and the
actinometer quantum yield (<£ ), using the following equation:
pa c

The process should then be repeated twice, and the average of the three values
and the standard deviation should be determined.

The quantum yield may now be combined with the absorbance data using
the hand integration data in Section 5.7 to calculate the atmospheric photoly-
sis rate constants at various times of the year and latitudes

k = d> Za, J! .
p a A A

If the values of kp have been determined for all the desired times of year and
latitude, then k is determined by

k - k (5.7)
P P

for each case. The half-life is then

t, (seconds) = In2/k (5.7a)
*5 p
t, (days) = 8.0 x lCTs/k (5.7b)
Error Analysis for k'
The estimate of the experimental rate constant kp is related to the
measured variables, concentration and time, by the following regression equation.

L-I - nZtlnC - EtHElnC] <* t
kp ~
where C is concentration of chemical measured at time t. This version of the
regression equation does not require that ln(C/C ) = 0 at t = 0; that is, the
line is not forced through the origin and any significant departure from the
origin indicates bias in values of C at t > 0.
156
-------
The intercept, C the concentration at t = 0, is obtained from the equa
tion °
ln(CQ) = zinC - k^(zt) (5.9)

The preferred measure of error in experiments of this kind is the standard
error, a.* The standard error in k' from n measurements where n > 2 is' given
by p
°'- r-^h^^i' M^l - (k')2l (5.10)
Equation (5.13) shows that a varies approximately with y- and directly with
a(C).

Error Analysis for 4>

The equation used to calculate the reaction quantum yield for photolysis
of a chemical is
pa Ac

The standard error may be expressed
4>
c
(a,
(5'12)
Thus, if the standard errors for kpc, k'a, a , a&, and g are 0.10, 0.10, 0.05,
0.05, and 0.1, then

l<
- = [(0.10)2 + (0.10)2 + (0.05)2 + (0.05)2+ (O.l)2]^
C

= 0.19
The standard error may be expressed as the standard deviation, k ± a; the er-
ror ratio, a/k; or percent error (a/k) x 100.
157
-------
Error Analysis for k_
p

The sunlight photolysis rate constant k is calculated from
(5.13)
The standard error ratio for k is then

(k ) T*~ (Za J')2
p I. A A
where for each interval X,
aa(aj') o2(o.) a2(J')

A * _ * I A

a " 2 7
The second term in equation (5.14) can be substituted by the terms in equation

(5.15) where, if we assume the standard error ratio in o, is ± 0.04 and in J,

± 0.10, then

(q A a = [(0.04)2 + (0.10)2] = 0.0116
and
') = 0.0116(cyTx)2
Substitution of error ratios for and a,L, in equation (5.14) then gives
,,
A A
ffl
rV J
v^

Multiplication of the last term by 2/<|>2 and substitution of k 2 for 2(Ea J')2
. P A A
gives *

a(k )

-£*- - 0.108jl + " " > S 0.108

P ( P

5.6.2 Determination of Hydroxyl Radical Rate Constant

Measurements
158
-------
Materials needed to determine the hydroxyl radical rate constant in-
clude :

(1) Sealed Teflon-film bag of approximately 100-liter volume with
fitting to fill and withdraw gas samples.
(2) Pure air source.
(3) Nitrous acid generator consisting of a 500-cc round-bottomed flask
with connections to allow the contents to be swept with air. The
nitrous acid is generated by adding dropwise a specific amount of
an accurately prepared solution of about 5 x 10~2N NaN02 solution
to approximately-150 cc of 5% sulfuric acid under a stream of pure
air, which carries the MONO into the reaction bag. (1.0 cc of 5
x 10~2N NaN02 produces 12.5 ppm MONO in a 100-liter reaction bag
if the MONO is completely transferred and none is lost to secondary
reactions.)
(4) Appropriate reference compound listed in Table 5.8.

The following procedure is recommended for determining the hydroxyl
radical rate constant. The reaction bag is first tested for contamination by
filling it with dry air and exposing it to sunlight for one hour. Then air
samples are withdrawn and analyzed, using the same analytical conditions to
be used to analyze the reaction mixtures. If any substances that wi]J. inter-
fere with the analyses are found, then the bag should be cleaned by flushing
with pure air for an extended period of time with heating up to 80°C if
necessary. If this procedure is not effective, then the bag should be replaced
with a bag demonstrated to be uncontaminated with interfering substances.

The uncontaminated bag is filled approximately three-quarters with clean
air and then injected with 4-y£ liquid consisting of each of the compounds to
be tested and the reference compound, which is selected to have a reactivity
similar to the test compound. The contents of the bag are then mixed by al-
ternately pushing in the sides and ends of the bag several times. At the point
of injection, the surface must be inspected to ensure complete volatilization
of the reactants. After the bag is allowed to stand for 10-15 minutes, a gas
sample is withdrawn and analyzed to serve as an initial reference point. One
hour later, a second sample is withdrawn and analyzed. These two analyses
should give the same concentrations of each material within the precision of
the analytical procedure. If not, additional mixing time is probably needed
to complete mixing. Samples should be taken periodically until the analyses
are stable. If the analyses show one or both reactants to decrease with time
then adsorption on the surface of the bag is occurring ; in this case the ex-
periment should be repeated with lower concentrations of substrate.

Once the concentrations of compound and reference are shown to be stable
in the reaction bag, approximately 5 x 10~2 mmole HONO is generated in the
HONO generator while it is swept with pure air to carry the HONO into the re-
action bag. Exposure to light is kept to a minimum. The bag is again kneaded
to effect complete mixing. After 10 minutes, three samples are withdrawn and
analyzed to serve as t0 points. The bag is then placed outside in the direct
sunlight. Under weather conditions that limit the amount of sunlight, the bag
may be irradiated by placing it immediately adjacent and parallel to a bank

159
-------
Table 5.8
REFERENCE COMPOUNDS FOR DETERMINING THE
REACTIVITY OF COMPOUNDS TOWARD OH
IN THE ATMOSPHERE
Standard
Compounds
Methane
1,1,1-Trichloro-
ethaneb
rt
Chloroform
(Trichloromethane]
Ethane3
d
Benzene
Toluened
Ethylbenzene6
m-Xylene
2-Methylbutene
1.298
KrtTT 3 .. •" 1 — 1
OH, cm molec s
9.5 x 10~1S
15.0 x 10~ls
1.0 x 10~13

2.9 x 10~13
1.2 x 10~12
6.4 x 10~12
7.9 x 10~12
20.6 x 10~12
80 x 10~12
-Methane
KOH/KOH
1.0
1.6
10.5

30.5
130
670
1000
2920
10,000
Howard and Evenson, 1976.
Howard and Evenson, 1976 (b).
p
Howard and Evenson, 1976 (a).
cTerry, Atkinson, and Pitts, 1927.
6Ravishankara et al. (1978).
Atkinson, ^1976 or later.
160
-------
of four to eight standard fluorescent lights. Samples are withdrawn every
one-half hour for 4 hours in triplicate and analyzed. In direct sunlight most
of the change should have occurred in the first 2 hours; however, in cases where
fluorescent lights are used, the conversions are less readily predicted and
considerably more time may be required to complete the conversion.

It is important that the conversion of both compound and reference is
sufficient. The analyses will fall into four different categories:

(1) If less than 10% change is observed in the compound (assuming a
standard deviation for the chemical analysis of 5.0%) and the
reference decreases more than 30%, then the experiment should be
repeated using a less reactive reference [also see category '3^1.
(2) If no change is observed in the standard but the compound decreases
(> 30%), then the experiment should be repeated using a more re-
active reference.
(3) If neither compound or reference decreases more than 30%, then the
experiment should be repeated using 2 to 4 times the amount of
HONO.
(4) If both compound and reference decrease more than 30%, then it
should be possible to calculate the relative reactivity of compound
versus reference as indicated below.

The preferred method of determining the ratio of rate constants for the
reaction of compound and standard toward OH radical (k£u /k§ ) is to apply the
C 1 1 J • >"'" ""
following expression:
log(Co/Ct) = (kH/l)log(So/St) (5.16)

The ratio of rate constants is the slope when log(C0/Ct) is plotted versus
log(So/St) and can be determined by standard regression methods. If only ini-
tial and final points are available, then the ratio of rate constants may be
determined directly from the expression

lo8(Co/Ct)/lo8(So/St) -1&/1& (5.16«)

The values from each run should be averaged to give the best estimate of
fcC /kS and standard deviation. In cases where k§jj/k§H > 3 or < 0.3, data
should oe carefully analyzed to ensure that the substrate changing the least
is changing significantly. (This is especially true if the standard deviation
of the individual chemical analyses is greater than 0.05.)

S C
Since k „ is available in Table 5.8, k-T, may be estimated as follows:
Utl Un
To verify kgg, it is important to repeat the above process with a second
standard. This standard should be selected from Table 5.8 to best match k(jg

161
-------
as estimated above. For example, if the data indicate k^ is 5 x

then ethylbenzene should be used in the verification.
The environmental half-life is
ln2/kQH[OH] (5.18)
assuming [OH] = 10s molec cc-1 (Section 5.7.4) ,

OH
ti (seconds) = 6.9 x IQ-'/k... (5.18a)
-5 uti

OH
todays) = 8.0 x 10-12/kQH (5.18b)

C S
Error Analysis for Rate Constant Ratio k^TT/k^TT
Un— OH

C S
The estimate of the rate constant ratio k/ko i-n t^16 case of three or
more data points is related to the measured concentrations of compound C and

reference S by the following regression equation:
X

r _ nZln(C /C.)ln(S /S.) - Zln(C /C. )Zln(S /C. )
kc /iS __ o t o t _ Q t __ o _ t_ fc.

OH/KOH nZ[ln(So/St)]2 - [Zln(So/St) ] 2 ^

The best estimate of the standard error is given by

fnZ[ln(C /C )]2 - [Eln(C /C )]2 1
O t O L " 2 "
I'"OH' n-2 nZ[ln(S /S J ]T -
LOt u u J

The value of ln(C /C ) at ln(S /S ) = 0 may be estimated from the equa-

tion °
The standard error of ln(C /C ) is

a[ln(C/C)] = l [nZ[ln(C/C)]2 - [Zln(C/C) J2]*5 (5.22)
ot i£ot

Since initially ln(Co/Ct) is zero, large deviation of the estimated

value from zero indicates error in the experimental or statistical procedures.

In cases where only the initial and final concentrations of C and S are

measured, the value of k§jj/k§g is approximated by equation (5.16a). A detailed

derivation is given in Appendix 5-A, which indicates this formula has a snail

bias provided ln(So/St) > ^ 7as. The standard error ratio fork^k^ estimated

by this method is expressed as

162
-------
c s
OH/kOH _ 2a2(lnC) 2a2 (InS)
0 (k/k) 2 2
,C ,,S ~ ln(C /C.) ln(S /S J
kOH/kOH L ° t • ° t

If a(lnC) = a(lnS) = 0.05 and Co/Ct = So/St = 2, then the standard error equals
0.12. However if the conversion of C and S are only 10%, then the standard
error is 0.31. Thus, this expression can be very useful for estimating the
uncertainty of a result based on the conversion and experimental error in the
concentration measurements, and it may be used to select optimum conversions
for determining k£u /k§ by both methods.
Un Url

5.6.3 Determination of Ozone Reaction Rate Constant
Measurement

The following equipment is needed to determine the rate constant for
reaction of ozone:

(1) Commercial ozone monitor or comparable assembled system. If such
instrumentation is not available, a suitable wet method for deter-
mining ozone may be used, such as suggested in the Federal Register
(Vol. 43. 26962, June 22, 1978) or by Flamm (1977).
(2) Ozone generator for producing up to 1.0 ppm 03 in a pure air gas
stream.
(3) Two 100-liter Teflon bags. One bag, for containing the reaction,
is fitted with a suitable manifold to add the ozone-air mixture
and the compound-air mixture, and to withdraw samples for analysis.
The volume of the reaction bag is determined to within 5% using a
wet test meter. The second bag is used to prepare a mixture of
the compound to be studied and is connected to the first by a 10-mm
stopcock.

The following procedure is recommended. First, the bag is filled with
pure air containing about 1 ppm of 03 to determine the stability of ozone in
the reaction bag. The bag is allowed to stand for one hour in the absence of
direct illumination and the ozone is monitored. A plot of the log of the ozone
concentration as a function of time is then made. The slope gives the back-
ground ozone disappearance rate constant (1O
where C0 and Ct are the concentrations of ozone initially and at time t (in
seconds). If kg is > 0.01 min"1, the bag may be contaminated, in which case
the bag should be allowed to stand overnight with ^ 1 ppm 03. This treatment
should be repeated until the background rate reaches the indicated limit.

Then the reaction bag is filled three-quarters with 1 ppm 03 in pure
air and the ozone concentration is monitored. In the second bag, which should
be connected to the first bag with a freshly cleaned 10-mm stopcock, the
compound-air mixture is prepared by injecting a sufficient amount of liquid
compound to give 20 ppm in 50 liters. (This will give^ 7 ppm of compound in
the 150-liter reaction bag.) The syringe should be weighed before and after
163
-------
injection to obtain an accurate measure of the amount injected. The bag is
mixed by alternately pushing in the sides and ends for several minutes, and
is then inspected to ensure no liquid is visible at the place of injection.
Once the compound is totally vaporized, the stopcock is opened and the mixture
is forced totally (> 95%) into the reaction bag. It may be necessary to vent
some of the ozone mixture before adding the hydrocarbon to ensure sufficient
space in the reaction bag. Once the hydrocarbon mixture is added, pure air
should be added to bring the bag up to volume. There will be a reduction in
the ozone reading reflecting the dilution that has occurred.
The rate constant for oxidation by ozone, kn , is defined by the rela-
tion
03
ln(C 1C) = (kB + kn [RH])t (5.25)
O t a U3

where Co and C^ are ozone concentrations at times zero and t, and kg is the
background loss rate constant determined initially. By applying the regression
analysis procedure indicated in equation (5.26) below, we obtain the term kg
+ kn [RH]. The rate constant k_. is then evaluated using the relation
U3 (J3

(slope-kR) x Molec. Wt. x Vol.

k03 Weight x 6.023 x 1020(5'26)

where Weight is the weight of the compound in grams, Molec. Wt. is the molecular
weight of the compound, and Vol. is the volume in liters of the reaction bag.

The measurement of kg should be repeated several times so as to improve
the conditions, increase the accuracy of measurement, and test the dependence
on [RH], which should be varied by a factor of 3 at least. If less than 50%
of the ozone disappears during the experiment, then additional experiments
should be made at higher [RH]. If the total ozone disappears in less than an
hour, then the [RH] should be decreased. However, it is important to keep the
ratio of [RH]/[03] > 10 if at all possible; therefore, if [RH] is reduced, the
initial [03] should also be reduced accordingly. The following data should
be reported: (1) 5 to 7 values of kg , (2) initial concentrations of 03 and
[RH], (3) reactor temperature during each measurement, (4) the average of the
krt values and the standard deviation.
03
The half-life is estimated from the expression

^ - ln2/kQ [03] (5.27)

Assuming an environmental [03] of 1.0 x 10ia molec/cc (= 0.04 ppm) (see Section
5.7.4)t this expression reduces to

tj^ (seconds) = 6.9 x 10-l3/kQg (5.27a)

t, (days) = 8.0 x lQ-l8/k (5.27b)
164
-------
Error Analysis for k and 03
1 " ' Ij ~ " ~* "

The estimates of the rate constants kg and kg + kg [RH] are related to
the measured variables, concentration and time, by the following regression
equations

] in the absence of RH (5.28)
in the P^sence of RH (5.29)
where C is concentration of chemical measured at time t. This version of the
regression equation does not require that ln(C/Co) = 0 at t = 0; that is, the
line is not forced through the origin and any significant departure from the
origin indicates bias in values of C at t > 0.

The intercept, C , the concentration at t = 0, is obtained from the
equation
ln(CQ) = zinC - kp(t) (5.30)
The preferred measure of error in experiments of this kind is the standard
error, a.
. ,
given by
error, a. The standard error in k,, and k,, + k_ [RH] from n measurements is
O D \J3
2 = 1 [nZ[lnC]a - [ZlnC]2 _ 2]
n - 2[ n£t* - (Et)a (k) J
where k is kg or (kg + kQ3[RH]) depending on the experiment. Equation (5.31)
shows that a varies approximately with 1 and directly with o(C).
•n

5 . 7 BACKGROUND

5.7.1 General Considerations

The detailed atmospheric chemistry by which compounds containing carbon-
and hydrogen are largely converted to COZ and H20 and by which organic nitrogen
and sulfur are converted to nitrates and sulfates is quite complex (Leighton,
1961; Demerjian et al., 1974; Pitts and Finlayson, 1975; Baldwin et al., 1977;
Hendry et al., 1978; Carter et al., 1978). We have spent considerable effort
studying these processes, and our understanding is reasonably good, although
semi-quantitative at best. Currently we are developing chemical mechanisms
that describe the chemistry of individual hydrocarbons; the mechanisms, which
can be readily integrated as a function of time by numerical methods, are then
used to simulate the chemistry occurring in smog chambers for those hydrocarbons.
These simulations are reasonably effective in predicting the smog chamber re-
sults. However, extrapolating these results to a wide variety of chemical
structures under atmospheric conditions introduces uncertainties because in
most cases the concentrations of organic compounds and NO in the atmosphere
are orders of magnitude less than those in the chamber.

165
-------
Our understanding of atmospheric chemistry is sufficient to allow
identification of the critical chemical processes that will affect the life-
time of chemicals in the atmosphere. These processes involve photochemical
transformations and oxidation reactions similar to those discussed in previous
sections concerning water chemistry. For the purposes of the atmospheric
chemistry protocol, these two basic processes are defined as follows.

Photochemical transformations are those reactions wherein the compound
absorbs solar energy directly to form an electronically excited intermediate
that undergoes further reactions by either first-order or second-order pro-
cesses. In all cases the rate determining step is the absorption of solar
energy and follows the relation

Rate of Phototransformation = $1 /h (5.32)
d.

where Ia is the light absorbed (in photons cm"2 s~l), h is the depth (in cm)
over which the light is absorbed, and , quantum yield, is the fraction of
excited species that give reaction.

Oxidation reactions involve interaction of a compound in its electronic
ground stae with a reactive species such as oxygen, ozone, 0 atom, or OH
radical. In this case the rate determining step is the bimolecular reaction
of compound and reactive species

Rate of Oxidation = kQX[OX][C] (5.33)

where k0x is the rate constant for the process, [OX] is the concentration of
reactive species, and [C] is the concentration of chemical.

The clear distinction between phototransformation and oxidation is
important in order to accurately predict the rate of each type of process.
The factors that control photochemical transformation are absorption coeffi-
cients of the compound in the solar region, solar irradiance, and quantum
yield. For oxidation processes the controlling factors are rate constants for
reaction with each reactive species and the concentrations of the reactive
species.

5.7.2 Photochemical Transformation

Rates of Reaction

The rate of photochemical reaction depends on the absorption of solar
energy, which is determined by Beer-Lambert law.

!,/!,- eaACi (5.34)
OA. A

where Io\ (in photons cm~2 sec-1) is the intensity of incident light at a given
wavelength entering a layer of atmosphere, 1^ (also in photons cm"2 sec" ) is
the intensity of transmitted light, ax is the cross section (in cm2) at wavelength
X, C is the concentration of chemical (in molecules cm"3), and I is the path
length of light. The light absorbed by the chemical (I&A) is expressed

166
-------
(5.35)
clA UA A UA

Except for N02 on occasion, the concentrations of light absorbers in
the atmosphere are not sufficient to attenuate the light intensity more than
a few percent; thus, equation (5.33) may be simplified by substituting the
exponential term with the appropriate approximation (ex - 1-x when x < 0.02)

I . = I . - I, = aCJII . (5.36)
aX oX X oX

IOX is a complex function of the direct light from the sun (1^) and the
scatter light (I ); the path length (H) varies for both of these. For the
direct light S

I = h secant z
d

where h is the depth of the atmospheric layer of interest. For the scattered
light, which is assumed to come equally from all portions of the sky, the
average path length is a constant i times the depth

a = ih
s

Leighton has demonstrated that i is approximately 2.

Thus, substituting these and I terms in equation (5.36) gives

I . = oC{I,,hsecant z + I ,ih} (5.37)
aX dX sX

To convert I ^ into volume units, we divide by the atmospheric depth, h.
aA

-~ = a C{I secant z + I ,i} (5.38)
h A dA sA

Leighton defined the term in the parenthesis as the actinic irradiance,
JX

J, = {I., secant z + I .i}
A dA sA

Thus,
a.CJ. (5.39)
h XX

The rate of absorption of light by a compound over the entire solar region
(290-800 nm) is

if ' CZVx

167
-------
The rate of photochemical reaction is

Rate
The apparent first-order rate constant (k ) is thus
P
kp = <(.ZaxJA (5.40)

which is conveniently independent of C and h (concentration and depth of the
atmospheric layer) .

To determine J^ values, it is necessary to know the solar intensity at
the top of the atmosphere, the absorption due to atmospheric ozone and aerosols,
the molecular (Rayleigh) scattering, and the aerosol (Mie) scattering.
Leighton originally estimated 1^ values based on limited information. However,
Peterson (1976, 1977) has recently reanalyzed the problem and has estimated
J^ values using more recent data, and these values have been summarized by
Schere and Demerjian (1977). The differences between Leighton's and Peterson's
value are not large because of fortuitous compensation in the various data
inputs. Leighton assumed the earth to be nonref lective, whereas Peterson
assumed 5 to 15% reflection depending on the wavelength. This difference was
largely balanced by the solar constants used by Leighton, which were about 9%
larger than those now preferred. Currently, the best values of stratospheric
ozone are 35% higher than previous assumptions. This difference is balanced
by assumptions regarding light scattering by aerosols. Because of lack of
data, Leighton assumed that half of the aerosol scattered radiation was directed
backward; Peterson based on the radiative transfer model developed by Dave
(1972), assigns only a small fraction of actual backscattering. Since the
first two and the last two factors each tend to cancel each other, the dif-
ferences in J^ values are not large except at the short wavelengths, where
new values are much smaller than the older values. For compounds that absorb
broadly over the solar spectrum (such as N02, which absorbs more or less
equally from 300-400 nm) , there is very little difference in the calculated
values of kp. However, for compounds that absorb only near 300 nm, the new
data indicate k values that are 50% smaller.
P
One of the most important results of Peterson's analysis is an under-
standing of the effect of elevation on the J\ values. This effect results
from aerosol scattering of light, which causes J^ values to increase with ele-
vation. The effect is more important at shorter wavelengths at small zenith
angles. Table 5.9 summarizes the effect of elevation and s:enith angles on the
photolysis of NOZ, assuming aerosol loading and distribution typical of the
Los Angeles basin.

The N0a photolysis rate at 4 km is about 40% larger than at the surface
at low zenith angles and 160% at large zenith angles. For compounds that
largely absorb largely near 300 nm, the effect will be about twice as large.

The change in J^ with elevation tends to level off above 4 km because
a large fraction of the aerosol is below that elevation. Thus the N02 photolysis
values at 4 km should be good estimates for higher elevations.

168
-------
Table 5.9
EFFECT OF ELEVATION ON RATE CONSTANTS (MIN ) FOR
PHOTOLYSIS OF N02 AS A FUNCTION OF SOLAR ZENITH ANGLE
(PETERSON, 1977)
Level
Surface
0.15 km
0.36 km
0.64 km
0.98 km
1.38 km
1.84 km
2.35 km
2.91 km
3.53 km
4.21 km
0
0.579
0.614
0.645
0.675
0.703
0.729
0.752
0.772
0.790
0.808
0.824
10
0.574
0.609
0.640
0.671
0.700
0.725
0.748
0.769
0.787
0.805
0.821
20
0.560
0.596
0.628
0.659
0.688
0.715
0.737
0.758
0.777
0.795
0.812
30
0.535
0.572
0.605
0.637
0.667
0.694
0.717
0.738
0.758
0.776
0.794
40
0.496
0.534
0.568
0.601
0.631
0.659
0.683
0.704
0.725
0.745
0.764
50
0.438
0.477
0.512
0.545
0.576
0.604
0.628
0.650
0.673
0.694
0.713
60
0.352
0.391
0.426
0.459
0.490
0.517
0.541
0.564
0.586
0.608
0.631
70 78
0.234
0.264
0.295
0.325
0.353
0.378
0.400
0.421
0.443
0.466
0.489
0.114
0.133
0.153
0.174
0.194
0.212
0.229
0.246
0.264
0.283
0.303
86
0.025
0.027
0.030
0.034
0.037
0.040
0.043
0.046
0.050
0.055
0.060
169
-------
When photolysis rates are estimated for compounds that are widely mixed
in the troposphere, the surface photochemical reaction rate estimated from
ground level J values will be low. In these cases, rates should be increased
by about 50% for compounds photolyzing from absorption primarily in the longer
wavelength region. Compounds that photolyze in the ^ 300 nm region will
photolyze faster by about a factor of two. Computational techniques are
available to more accurately calculate the effect of elevation on the photolysis
for any compound; however, they require considerable computational time and
the gain in accuracy over these approximations is probably not significant.

Computation of Photochemical Reaction Rates

To calculate the photochemical reaction rate constants, it is necessary
to integrate equation (5.39) over the solar spectrum.

k = 4>Za,J, (5.41)
p A A

Schere and Demerjian (1977) have published a computer routine to carry out
this integration over 10-mm wavelength intervals. The routine calculates
momentary photochemical rate constants throughout the day for any day of the
year at any latitude and longitude. The JA values of Peterson are used in the
calculations. Because most compounds require more than one day to photolyze,
it is necessary to integrate the output from the Schere and Demerjian routine
to obtain rates on a day basis.

To facilitate the computation of photochemical rate constants, we have
prepared in Tables 5.1 to 5.3 day-averaged light intensity values as a function
of wavelength at latitudes of 10, 30, and 50°N for the summer and winter
solstices and the equinox. In addition, the tables include average rates for
spring-summer and fall-winter light intensity values. The light intensity
values in the tables refer to J^' values and represent that: total available
actinic light flux in a given wavelength region for a specific day and at a
specific latitude. The wavelength ranges in Tables 5.1 to 5.3 are divided
into 31 intervals over the total range 290-800 nm to maintain reliability of
the calculations and yet to allow them to be carried out rapidly.

The data in Tables 5.1 to 5.3 are multiplied by the average absorption
coefficients over the wavelength ranges in the appropriate table with cor-
responding J. ' values and summing
kp

The value of k corresponds to the latitude and time of year of the J, ' values
* P "
used.

To test the reliability of the hand calculation procedure, photolysis
rates for benzaldehyde and biacetyl were calculated using both these methods and
the 10-nm interval computer computation. Both methods gave identical rates

170
-------
within 1%. Table 5.10 summarizes the rates. To demonstrate the hand compu-
tation, Table 5.11 shows calculations of the photolysis rates for benzaldehyde
and biacetyl.

5.7.3 Atmospheric Oxidation

General

Except for some compounds that photolyze rapidly, the most important
reactions of organic compounds in the atmosphere are with OH radical and ozone.
Table 5.12 summarizes approximate daytime concentrations of these species along
with a number of other oxidants also believed to be present in the atmosphere.
Included in the table are rate constants for reaction of these oxidants with
propane, n-butane, and toluene, which are common atmospheric pollutants. The
product of the rate constant and the concentration of oxidant is the apparent
first-order rate constant (k'v) for that process.
UA

Rate = k [OX][C] = k' [C]
UA v/A

Clearly, in the case for propene the reaction with OH is most important, while
the reaction with 03 is second most important. Together, OH and 03 account
for more than 99% of the reaction; ground state oxygen atom (0(3P)) accounts
for only 0.1% of the reaction. For both n-butane and toluene, OH alone accounts
for greater than 99% of the reaction. These conclusions obviously are dependent
on the concentrations that are assigned for each oxidant. However, the con-
centrations of OH and 03 are not expected to vary significantly from the values
in the table (see Section 5.7.5).

In some cases a compound might have unusually high reactivity to one
of the other oxidants, although this should be the exception. One important
case is the oxidation of NO by H00» (or R00«). The reaction

H00« + NO —*- H0« + N02 (5.42)

is the major route by which NO is oxidized in the atmosphere. The reaction
competes favorably with the reaction with ozone. However, to our knowledge,
there are no cases involving organic compounds where reaction with oxidants
other than OH and 03 are important.

Thus, to estimate the lifetime of chemicals in the atmosphere as deter-
mined by oxidation processes, we need to determine only the rate constants for
reactions with OH and 03. The rate constants for reaction of a number of com-
pounds with OH and 03 are summarized in Tables 5.13 and 5.14.

The lifetime(t) for reaction of substrate (S) with an oxidant is defined
as

l/knv[OX] (5.43)
kQX[OX][S]
171
-------
Table 5.10

RATE CONSTANTS FOR PHOTOLYSIS OF BENZALDEHYDE AND BIACETYL
AS A FUNCTION OF LATITUTDE AND DATE3
Compound
Benzaldehyde

Biacetyl

Date
June 22
March 21/
Sept. 23
Dec. 22
Spring/
Summer
Average
Fall/
Winter
Average
June 22
March 21/
Sept. 23
Dec. 22
Spring/
Summer
Average
Fall/
Winter
Average
Rate Constant, days' 1
10°N
7.91
7.67
6.25
7.89
6.76
9.83
9.49
8.14
9.76
8.73
30°N
8.80
6.78
3.84
8.10
4.96
10.9
8.74
5.54
10.1
6.73
50°N
8.86
4.90
1.02
7.41
2.42
11.3
6.95
1.86
9.74
3.80
aComputed by computer routine and data in Tables 5.1 to 5.3;
seasonal averages computed only from tables.
172
-------
Table 5.11
EXAMPLES OF HAND COMPUTATION OF PHOTOCHEMICAL RATE CONSTANTS0

Avg. Cross-
Section (a.)

Photon cmjd~

VJ- o"

EVx'- fl
i
—— Benzaldehyde Day Rates at 30°N on Summer Solstice——
285-295
295-305
305-315
315-325
325-335
335-345
345-355
355-365
365-375

7.10 -20
3.33 -20
3.84 -20
4.30 -20
4.22 -20
3.42 -20
2.76 -20
1.32 -20
7.48 -21

1.0 16
7.4 17
1.09 19
2.74 19
4.98 19
5.49 19
6.28 19
6.49 19
8.09 19

Biacetyl Day Rates at 30°N on
285-295
295-305
305-315
315-325
325-335
335-345
345-355
355-365
365-375
375-385
385-395
395-415
415-435

1.03 -20
4.98 -21
2.04 -21
1.11 -21
9.61 -22
2.19 -21
3.94 -21
6.10 -21
8.68 -21
1.24 -21
1.88 -20
2.37 -20
2.96 -20

1.0 16
7.4 17
1.09 19
2.74 19
4.98 19
5.49 19
6.28 19
6.49 19
8.09 19
7.93 19
8.12 19
1.11 20
1.41 20

7.10 -4
2.46 -2
4.19 -1
1.18
2.10
1.88
1.73
8.57 -1
6.05 -1
k
P
7.10 -4
2.54 -2
4.44 -1
1.62
3.72
5.60
7.33
8.19
8.80
- 8.80 d"1
Summer Solstice — —
1.03 -4
3.69 -3
2.22 -2
3.04 -2
4.79 -2
1.20 -1
2.47 -1
3.96 -1
7.02 -1
9.83 -1
1.53
2.63
4.17
1.03 -4
3.79 -3
2.60 -2
5.64 -2
1.04 -1
2.25 -1
4.72 -1
8.68 -1
1.57
2.55
4.08
6.71
10.88
k - 10.88 d~*
P
Cross-section data from Berger, 1973.
Cross-section data from Calvert and Pitts, 1966.
cSecond number in column is the power of ten by which the first number is
multiplied.
173
-------
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174
-------
Table 5.13

RATE CONSTANTS AND ENVIRONMENTAL HALF-LIVES FOR REACTIONS OF HYDROXYL RADICALS NEAR 300°K3
Compound
Alkanes
Methane
Ethane
Propane
Methyl
Dimethyl
n-Butane
Methyl
2,3-Dimethyl
2,2,3-Triraethyl
2,2,3, 3-Tetramethyl
n-Pentane
2-Methyl
3-Methyl
2,2,4-Trimethyl
n-Hexane
n-Octane
Cycloalkanes
c-Butane
c-Pentane
c-Hexane
Haloalkanes
Methane
Fluoro-
Dif luoro-
Trifluoro-
Tetrafluoro-
Chloro-
Dichloro-
Trichloro-
Tetrachl jro-
Bromo
Ethane
Chloro
1,1-Dichloro
1,2-Dichloro
1,1,1-Trichloro
1,1, 1-Trif luoro-2-chloro
l,l,l-Trifluoro-2,2-dichloro
1,1,1,2-Tetraf luoro-2-chloro
1,2-Dibromo
Alkanone
Butanone
2-Methylpentanone
2 , 6-Dimehtylheptanone
Alkanols
Methanol
Ethanol
Propanol
2-Propanol
Butanol
4-Methyl-2-pentanol
0,N,S Substituted alkanes
Methyl ether
Ethyl ether
n-Propyl ether
10" kOH-
cm3 molec"1 s~l
0.0079
0.29
2.2
2.2
0.81
2.7
3.3
5.1
3.8
1.1
6.5
5.3
7.1
3.8
6.0
8.5
1.2
6.1
7.0
0.016
0.0078
0.0002
< 0.0004
0.04
0.14
0.11
< 0.0004
0.04
0.39
0.26
0.22
0.015
0.010
0.028
0.012
0.25
3.3
14.9
24.9
0.95
3.0
3.8
7.1
6.8
7.1
3.5
9.3
17.3
V daysb
1,000
28
3.6
3.6
9.9
3.0
2.4
1.6
2.1
7.3
1.2
1.5
1.1
2.1
1.3
0.9
6.7
1.3
1.1
500
1,030
40,000
> 20,000
200
57
73
> 20,000
200
20
31
36
530
800
280
670
32
2.4
0.54
0.32
8.4
2.7
2.1
1.1
1.2
1.1
2.3
0.86
0.46
175
-------
Table 5.13

RATE CONSTANTS AND ENVIRONMENTAL HALF-LIVES FOR REACTIONS OF HYDROXYL RADICALS NEAR 300°K(Cont.)
Compound
0,N,S Substituted alkanes
Tetrahydrof uran
1-Propylacetate
2-Butylacetate
Methylamlne
Methyl sulfide
Formaldehyde
Acetaldehyde
Propionaldehyde
Benzaldehyde
Alkenes
Ethene
Propene
Methyl-
1-Butene
2-Methyl
3,3-Dimethyl
2-Butene
cis-
trans-
2-Methyl
2,3-Dimethyl
1-Pentene
cls-2-Pentene
1-Hexene
1-Heptene
Cycloalkenes
c-Cyclohexene
1-Methyl
Haloalkenes
Ethene
Fluoro
1,1-Difluoro
Chloro
Trlchloro
Tetrachloro
Chlorotrlfluoro
Bronio
0-Substituted alkene
Methoxy
Alkadlenes
Propadiene
1,3-Butadlene
2-Methyl
Terpenes
p-Menthane
o-Plnene
6-Plnene
3-Carene
Carvomenthane
B-Phellandrone
d-Limonene
Dlhydronyrcene
Myrcene
cis-Oclmene
10" kOH, cm1 molec"' s~ '
14.6
4.5
5.6
21.9
33.9
15
16
21
13
7.9
24.8
50.6
35.4
58.1
28.2

53.6
69.9
79.7
153
29.9
64.8
31.5
36.5

71.4
96.3

5.6
2.0
6.6
2.0
0.17
7.0
6.8
33.5
4.5
77
78
6.6
25.7
21.6
28.2
41.5
38.2
48.1
59.7
74.7
105
tv days"
0.55
1.8
1.4
0.37
0.24
0.53
0.50
0.38
0.61
1.0
0.5
0.2
0.3
0.2
0.4

0.2
0.2
0.1
0.1
0.4
0.2
0.4
0.3

0.2
0.1

1.4
4.0
1.2
4.0
47
1.1
1.2
0.24
2.6
0.1
0.1
1.2
0.31
0.37
0.28
0.19
0.21
0.17
0.13
0.11
0.076
176
-------
Table 5.13

RATE CONSTANTS AND ENVIRONMENTAL HALF-LIVES FOR REACTIONS OF HYDROXYL RADICALS
NEAR 300 *K (Cone.)
Compound
Alkynes
Ethyne
Methyl
Aralkanes
Benzene
Methyl
1,2-Dlmethyl
1,3-Trimethyl
1,4-Trimethyl
1,2,3-Trlmethyl
1,2,4-Trimethyl
1,3,5-Trimethyl
Ethyl
1,2-Ethylmethyl
1,3-Ethylmethyl
1,4-Ethylmethyl
propyl
2-propyl
1 , 4-methy lpropyl-2-
hexafluoro
propylpentafluoro
Substituted Aralkanes
Me thoxyb enz ene
o-Cresol
10 ia kQH, cm1 molec"1 s~ l
0.16
0.95
1.4
5.9
13
20
10
24.7
33.2
49.3
7:5
13.6
19.4
12.9
6.0
7.8
15.2
0.22
3.0
19.6
34.0
tv daysb
50
8.4
5.7
1.3
0.62
0.40
0.80
0.32
0.24
0.16
1.1
0.59
0.41
0.62
1.3
1.0
0.53
36
2.7
0.41
0.24
Compiled from data and references in Pitts et al., 1977, and Raopson
and Garvin, 1978.
••,
Environmental half-livoo in 24-hour days, assuming an OH concentration
co.ual to 1 x 10* radicals cm" '
177
-------
Table 5.14

RATE CONSTANTS AND ENVIRONMENTAL HALF-LIVES FOR REACTIONS OF OZONE AT 300°K
Compound
Alkanes
Methane
Ethane
Propane
Methyl
n- Butane
Alkenes
Ethene
Propene
Methyl-
1-Butene
2-Butene
cis-
trans-
2-Methyl
2 , 3-Dimethyl
1-Pentene
2-Pentene
cis-
trans-
1-Hexene
1-Heptene
1-Octene
1-Decene
Cyclohexene
Conjugated Alkenes
1,3-Butadiene
Phenylethene
10 18 krt , cm3 molecr l sr l
O3
1.4(-6)
1.2(-6)
6.8(-6)
2.0 (-6)
9. 8 (-6)
1.9
13
15.1
12.3
161
260
493
1510
10.7
456
563
11.1
8.14
8.14
1.08
169
8.4
171.0
Reference
a
b
a
a
a
h
h
h
h
h
h
h
h
h
h
h
h
e
Le
e
h
h
.1
tjj. days
5.73 (6)
6.68 (5)
1.18 (6)
3.95 (5)
8.18 (6)
4.22
.617
1.30
.652
.05
.031
.016
.005
.75
.018
.014
.723
.99
.99
7.43
.047
.95
.05
178
-------
Table 5.14

RATE CONSTANTS AND ENVIRONMENTAL HALF-LIVES FOR REACTIONS OF OZONE AT 300°K
(Continued)
Compound
Halogenated Alkenes
Ethene
Chloro
1,1-Dichloro
1,2-Dichloro
cis
trans
Trichloro
Tetrachloro
Tetrafluoro
Propene
3-Chloro
Hexaf luoro
Terpenes
a-Pinene
Alkynes
Ethyne
Aromatic Hydrocarbons
Benzene
Methyl
1 , 2-Dimethyl
1,3-Dimethyl
1,4-Dimethyl
1,3,4-Trimethyl
1,3,5-Trimethyl
1,2,4,5-Tetramethyl
Pentamethyl
Hexamethyl
10 l8 k. , cm3 iriolec~ l sT *
U3
1.96
3.67 (-2)
6.14 (-2)
3.82 (-1)
5.98 (-3)
1.66 (-3)
134
18.3
21.6
164
7.8 (-2)
4.65 (-5)
2.76 (-4)
1.58 (-3)
1.30 (-3)
1.58 (-3)
4.65 (-3)
6.97 (-3)
1.78 (-2)
8.30 (-2)
0.407
Ethyl 5.65 (-4)
I
Reference
i
i
g
g
i
i
c
i
c
d
j
f
f
f
f
f
f
f
f
f
f
f
t^, days
4.09
2.19 (2)
1.31 (2)
2.10 (1)
1.34 (3)
4.83 (3)
.06
.438
.37
.05
102.8
1.72 (5)
2.91 (4)
5.09 (3)
6.19 (3)
5.09 (3)
1.76 (3)
1.15 (3)
4.51 (2)
96.6
19.71
1.42 (4)
179
-------
Table 5.14

RATE CONSTANTS AND ENVIRONMENTAL HALF-LIVES FOR REACTIONS OF OZONE AT 300°K
(Concluded)
Compound
Aromatic Hydrocarbons
Benzene (cont.)
1,3-Diethyl
1,3,5-Triethyl
Pentaethyl
Hexaethyl
2-Propyl
t-Butyl
10 18 k. , cm3 molec- * f l
U3
1.78 (-3)
5.64 (-3)
1.74 (-2)
5.58 (-3)
5.81 (-4)
1.15 (-4)
Reference
f
f
f
f
f
f
t%> days
4.51 (3)
1.42 (3)
4.61 (2)
1.44 (3)
1.38 (4)
6.97 (4)
Schubert and Pease (1956).
Morrissey and Schubert (1963).
'JHeicklen (1966) .
Ripperton and Jeffries (1972).
^Cadle and Schadt (1952).
Nakagawa, Andrews, and Keefer (1960).
^Blume, Hisatsune, and Heicklen (1976).
.Japar, Wu, and Niki (1974).
^Williamson and Cvetanovic (1968).
j
Cadle and Schadt (1953).
180
-------
where kgx is the bimolecular rate constant and [OX] is the approximate concen-
tration of the reactive species. The time to deplete one-half of the chemical
is referred to as the half-life (ti ) and is defined

t^ = ln2/kQX[OX] = Tln2 (5.44)

Atmospheric Concentration Units

The subject of reaction kinetics is sometimes complicated by the use
of different units to express concentrations and rate constants. In this at-
mospheric protocol we have followed the current practice in gas-phase kinetics
of expressing concentration in units of molecules/cm3 (molec/cm3) . Table 5.15
lists conversion factors for use in converting to other common units of
measurement .

Concentrations are often expressed in molar units (moles/liter). As
shown in Table 5.15, concentration in molec/cc is interconverted to molar units
by a factor of 1.66 x 10s1:

(Cone, in molec/cm3) x 1.66 x 10~2 1 = Cone, in moles/liter

(Cone, in moles /liter) /1. 66 x 10~21 '= Cone, in molec/cm3

Second-order rate constants depend on the concentration units used to
express concentration. Thus, when concentration is expressed in molec/cm3, the
second-order rate constant will be expressed in units of ( molec/cm3 )r 1 s~ x
or cc/molec-s, which in most cases is the preferred convention for gas-phase
rate constants. To convert rate constants expressed in these concentration
units to other units, it is necessary to divide by the corresponding factor
in Table 5.15 because of the inverse nature of the concentration term in the
rate constant units. Thus, to convert a rate constant in cc/molec-s to
liters/mole-s (the convention used in solution chemistry), one divides by
1.66 x 10* *.

To convert to the often used units of ppm"1 min-t, it is necessary to
divide by 4.06 x lO"1** and then multiply by 60 sec/min to change the time unit.

(k in cm.3/mole-os)1.48x 10 15 = k in ppnT1 min"1

Hydroxyl Radical Reactions and Rates

From the data in Table 5.13 it is possible to make a number of
generalizations about OH reactivity that can be useful in estimating the re-
activity of compounds. Most alkanes except methane and ethane react toward
OH with a rate constant of 1 to 10 x 10~12 cm~3 molec s~l. The reaction with
alkanes entails abstraction of hydrogen to form water and an alkyl radical
Substituents can have a number of different effects. Single halogen atoms in
181
-------
Table 5.15

FACTORS FOR INTERCONVERTING ATMOSPHERIC CONCENTRATION UNITS
(To convert units in first column to units in another column, multiply by
number in the column of the desired unit.)
Unit
molec/cm3
atm(25°C)
ppm(25°C)a
moles/ cm
moles/liter
i
Molec/cc
1.0
2.46 x 101*
2.46 x 10 13
6.02 x 1023
6.02 x 1020
atm(25°C)
4.06 x 10~20
1.0
1.0 x 10-6
2.44 x 104
24.4
ppm(25°C)a
4.06 x 10- x*
1.00 x 106
1.0
2.44 x 1010
2.44 x 107
Moles/ cm3
1.66 x 10-2"
4.09 x 10-s
4.09 x 10'11
l.o
1.00 x 10-3
Moles/liter
1.66 x 10-21
4.09 x 10-2
4.09 x 10~8
1.00 x 103
1.0
Assumes total pressure of 1 atm.
132
-------
the a-position activate the carbon-hydrogen bond but in the (3-position they
tend to deactivate the bond. Thus, single halogen atoms do not have a large
effect on the reactivity of any alkane except methane. Multiple halogens in
a molecule generally deactivate the molecule relative to the parent alkane.
Thus 1,1,1-trichloroethane is about 1/20 as reactive as ethane; one-half of
the reduction is due to reduction of the number of available hydrogens and
then each remaining hydrogen is reduced in reactivity by 1/10.

In ketones, alcohols, ethers, and esters, activation is seen relative
to the parent hydrocarbon after correction for the number of hydrogens. Amines
and sulfide appear to show even larger rate enhancement due to activation of
adjacent C-H groups.

The carbon-carbon double bond is much more reactive than the carbon-
hydrogen bond and reacts by addition of OH, which generally causes cleavage
of the double bond (Niki et al., 1978).
--C + OH
HOC
U.
i i
Rate constants for these processes are sensitive to the degree of alkyl sub-
stitution on the double bond and vary from 20-200 x 10~12. Consequently, al-
kenes have a half-life in the environment one-tenth of that for most alkanes.
Halogens tend to reduce alkene reactivity somewhat, whereas methoxy has the
same effect as an alkyl group. Conjugated dienes have reactivities equal to
two double bonds. The reactivities of terpenes are consistent with the
similarly substituted alkenes. Alkynes appear to be less reactive than the
corresponding alkenes.

Aromatic hydrocarbons have reactivities about the same as alkenes as
a result of addition of OH to the ring (Kenley, 1978). For example, 85% of
the time, the reaction of toluene with OH gives
CH3
CH3
OH +
(+ isomers) + H02» (5.46)
Hydrogen abstraction (shown below) occurs only 15% of the time.
OH +
o
o
+ H2o
(5.47)
For screening studies it is desirable to be able to estimate rate
constants for reaction of various kinds of organic structures with OH. A rea-
sonably reliable predictive scheme can be developed on the basis that the rate
constant or total molecular reactivity of a molecule is the sum of rate
183
-------
constants for reactivities of each portion of the molecule, and that little
or no effect is exerted on the reactivity of a specific site by a substituent
more than two atoms away. Thus, the same group in different molecules is
assumed to have the same reactivity. For example, the methyl groups in all
alkanes are assumed to have the same reactivity; however, methyl groups in
compounds like toluene, acetone, and methyl chloride are assumed to have dif-
ferent reactivities because the second atom from the hydrogen, which is ab-
stracted, is different.

The chemistry of OH reactions is largely limited to the three kinds of
reactions discussed above: abstraction of a hydrogen atom, addition to a
carbon-carbon double bond, and addition to an aromatic ring. These reactions
are considered separately in the additivity scheme.

The rate of hydrogen atom abstraction is affected by substitution on
the same and adjacent atoms. The total rate constant for abstraction (kjj) may
be expressed as the summation of the rate constants for each reactive hydrogen
atom
where kg^ is the reactivity of the ith hydrogen atom and depends on the degree
of substitution on the adjacent atom and on whether a vinyl or phenyl group
is attached. The terms otjj and 3g account for the effect of substituents other
than hydrogen; ajj is the constant for the substituent in the ot-position and
BH is the substituent in the B-position. The term n-^ is the number of times
the same type of hydrogen group with the same a and 3 substituents appears in
the molecule.

The rate constant for addition to a carbon-carbon double bond (k ) is
expressed by

j
k = la k (5.49)
E J=1EJ EJ

where kg. is the reactivity of the jth carbon-carbon double bond and depends
on the degree of substitution by carbon, oxygen, nitrogen, or sulfur but not
halogen. The Qfg. term is unity unless a halogen is immediately attached to
the double bond.

Similarly, the rate constant for addition to aromatic rings (kA> is
expressed by

kA * j>kA* (5'50)
J6~J_

where k^» is the reactivity of the ith aromatic group, which depends on the
degree of alkyl substitution. The a^ is a factor to account for the effect
of halogen atoms substituted in the ring.

184
-------
Thus the total molecular rate constant (k™) can be expressed by the
sum of these three processes

i J &
kOH - ^i^tAi + j^E *£ + ,!"A£kA^ (5'51)

The a and p constants in equation 5.51 have been calculated from the data in
Table 5.13 and are summarized in Tables 5.4 to 5.6. Figure 5.3 gives the re-
activities of four representative compounds. In these examples the uncertainty
in the estimated value of k(^ is about a factor of 2, the range being one-half
the estimate to twice the estimate. Rate constants have been measured for the
first two examples and the data are given in the figure. The values are con-
sistent with estimated limits.

Ozone Reactions and Rates

The only organics that react with ozone sufficiently fast for the re-
action to be environmentally significant are the alkenes and some of the
aromatic hydrocarbons. Table 5.7 summarizes the effect of structure on the
rate constants. The substituent increases the reactivity of the carbon-carbon
double bond, but the effects are small. Most all alkenes appear to have rate
constants in the range of 1.6-22 x 10~18 cm3 molec"1 s"1. These rate constants
are about 10" 7 times larger than those for reaction with OH radical. However,
the ratio of the average atmospheric conentrations of ozone to OH is about 10s
or slightly larger, so that, on the average, reactions of alkenes with ozone
are about one-tenth as fast as the reactions with OH. In some cases,
because of variations of OH and ozone concentrations in the atmosphere, the
ozone reaction may predominate.

The rate constants for reaction of aromatic hydrocarbons with ozone
vary over a wide range, from less than 10" 21 to 10"18 cm"3 molec"1 s"1. Be-
cause ozone concentrations range from 0.3-3 x 10l2 molec cm~3, only under the
most favorable conditions can the half-lives be less than a few days, in which
case the ozone reactions compete favorably with the OH reactions. However,
for most aromatic compounds, ozone reactions are unimportant relative to OH
reactions.

5.7.4 Environmental Studies

Problems of Direct Measurement of Atmospheric Lifetimes

Direct determination of the lifetime of chemicals in the atmosphere is
a large-scale undertaking. When chemicals are released to the atmosphere,
they are quickly dispersed over large distances and volumes. Turbulent mixing
and diffusion cause the chemical to spread in all directions, and winds carry
the emissions downwind. The rate of mixing depends on the size of area over
which the emission occurs. Figure 5.4 shows the correlation of the diameter
of a cloud center core (expressed as one standard deviation or diameter of 2/3
of the mass) with time under ideal conditions. A spherical emission with a
diameter of 1 meter doubles in about 10 seconds and is diluted eightfold.
After a minute the diameter increases tenfold or to 10 meters, and is diluted

185
-------
1 Hour
K^km
1 Day
1 Month 1 Year
Q
§
Q
3
O
o
UJ
103km
100 km
10km
O
(- 100m
UJ
O
oc
<
Q
10m
100cm
dm)
10cm
1 10 102 103 104 105 106 107 10s
Sec Sec Sec Sec Sec Sec Sec Sec Sec
TRAVEL TIME
SOURCE: Hage (1965).
SA-4396-81
FIGURE 5.4 CLOUD GROWTH AS A FUNCTION OF TIME AND CLOUD SIZE

The growth of the lateral dimensions of plumes and clouds emitted from single sources
as a function of residence time in the atmosphere.
The diagonal lines, labeled K, indicate cloud growth, assuming a constant diffusivity,
Ky, in the relationship a2 = KT. The dashed lines enclose all observations of cloud
dimensions.
186
-------
one thousandfold. Finally after a day the cloud will cover about 100 km and
have undergone a dilution of the order of 10** to 106. Thus, any attempt to
follow the decrease of a chemical with an appreciable half-life becomes im-
possible because of the extreme degree of dilution.

Because of these mixing and transport problems, controlled field studies
to measure the environmental lifetime cannot be considered, except possibly
in special cases where chemical lifetimes are very short (less than one hour)
or where there are unique emissions of chemical already present. Instead, it is
necessary to determine the concentrations of the reactive oxidants in the at-
mosphere from field studies. Then using these concentrations and the rate
constant for the reaction of chemical with the oxidant, it is possible to
calculate the environmental rates for the various processes. In the following
sections we review the data on the concentrations of OH and ozone.

Determination of OH Concentrations in Polluted Air

In several studies, automobile emissions have been monitored in suffi-
cient detail to allow observation of decay of specific hydrocarbons as a func-
tion of time. From these data it is possible to estimate the atmospheric OH
concentrations. The most successful such experiment was the Los Angeles Re-
active Pollutant Program (LARPP) supported jointly by the Coordinating Research
Council and the Environmental Protection Agency. Calvert (1976) was the first
to show that in the same air parcel, the more reactive hydrocarbons decreased
faster than the less reactive hydrocarbons. The most satisfactory data were
obtained by following the ratios of 1-butene/acetylene and propene/acetylene.
1-Butene, propene, and acetylene come almost exclusively from automobiles;
acetylene is relatively unreactive and therefore is a good marker for dilution.

In typical examples, during the hours 8:00 AM to 2:00 PM the molar ratio
of propene to acetylene decreased from 0.36 to 0.20. Similarly, the ratio of
1-butene to acetylene decreased from 0.9 to 0.2 during the same time. Making
the valid assumption that acetylene does not react appreciably, we can estimate
the OH radical concentration from these data using the expression
kOR[OH] (5.52)
or
[OH] =
-------
10s molec cm"3). Following the change of alkanes, such as n-butane, gives
much higher values of OH. It is believed that these values are generally
higher because the alkanes have a number of sources, whereas the simple alkenes
have only one source; hence, the ratio of alkane to acetylecie can be sensitive
to mixing of air parcels with varying origins. Because alkanes are much less
reactive than alkenes, small changes in the ratios lead to large uncertainties.
Statistical analysis of the data based used in estimating the [OH] concentra-
tion by Singh et al. (1978), at SRI, indicates that the alkane data base shows
considerably more scatter and the estimates of [OH] have poor correlation co-
efficients and considerably larger uncertainty bounds. Therefore, the OH value
of 0.7 x 106 molecules/cc (0.3 x 10~7 ppm) obtained from the alkene data is
the best estimate of OH in polluted urban atmosphere using this technique.
The evidence for the nonurban atmosphere (downwind from the urban area) places
the OH concentration slightly lower but within the limits of experimental un-
certainty.

The general technique described above assumes that the air parcel that
is being tracked and from which samples are being collected is isolated. Al-
though dilution may occur both the reactive hydrocarbon and standard (acetylene)
will be diluted at the same rate and thus their ratio will not be affected.
Generally, vertical mixing below the inversion layer occurs quickly between
ground level and the base of the inversion layer, but mixing across the inver-
sion layer is slow, so that mixing of air parcels with older air parcels above
the inversion layer and where the reactive hydrocarbon to acetylene ratio is
low is not expected to occur. However, the sample air parcel is subject to
fresh emissions from all sources, including automobiles, that produce the re-
active hydrocarbons and acetylene in the initial ratio. This constant addition
of these hydrocarbons will tend to make the calculated value of OH lower than
its actual value in the cases where fresh emissions enter the air parcel.
This problem clearly is most important in the urban areas, and therefore the
measured OH value should be considered a lower limit in these cases. However,
the effect should not be more than a factor of two. Because emissions in the
nonurban areas should be minimal, OH concentration estimates for such areas
would be expected to approximate reliably the true value. Thus, the small dif-
ference observed between urban and nonurban OH values may only appear so
because of the effect of continued emissions in urban studies. If a correction
for emission could be made, we might find that estimates of the urban OH con-
centrations are a factor of two or three larger than those for nonurban areas.

Estimation of Average Tropospheric OH Concentration. Our modern in-
dustrial civilization produces and emits a number of compounds that have long
lifetimes in the atmosphere and no natural sources. Some of these compounds,
especially the Freons, have no known chemical loss mechanisms in the troposphere,
although others are subject to slow reactions in the troposphere. By comparing
the amount of compound emitted to the atmosphere with what is found, it is
possible to determine loss reaction rates. A compound of considerable interest
in this regard is methylchloroform (1,1,1-trichloroethane). This compound has
been produced for use largely as a nonreactive and nontoxic cleaning solvent,
and essentially all that is produced is eventually lost to the atmosphere.
The tropospheric chemistry is limited only to reaction with OH

CClaCHa + OH >- HOH + CC13CH2» (5.53)

188
-------
Thus since the quantities of methylchloroform produced must match the material
in the atmosphere plus what has reacted with OH and diffused to the stratosphere,
careful measurement of the atmospheric concentrations can lead to an estimate
of the average OH concentrations according to the equation

] (5 <

where kjj is the rate constant for diffusion to the stratosphere. Thus, a value
of OH can be obtained that is averaged over the total day, all elevations, and
all seasons, and it should represent the best value for predicting environmental
lifetimes that are sufficiently long that total mixing in the troposphere occurs.
Singh (1977; 1977a) has shown that the methylchloroform concentration in the
atmosphere is consistent with an atmospheric residence time of about 8 years,
which translates to an average tropospheric OH concentration of about 4.1 x
10s molec/cc. The concentration is slightly larger in the southern
hemisphere than in the northern.

Neely and Plonka (1978) have also analyzed existing methylchloroform
data, and based on monitoring data through 1976, they suggest an average
tropospheric lifetime of 2 to 4 years. However, atmospheric concentrations
projected from their data underpredict more recent monitoring data. Thus a
lifetime in this range appears to be too short. Chang and Penner (1978) have
recently made a detailed analysis of the methylchloroform problem. Using un-
published monitoring data of Rasmussen, they obtained a lifetime of 11.3 years;
random errors of about 10% in the measured atmospheric concentrations could
lead to uncertainties in the lifetime of ± 30%. Use of Singh's recent data
(1978) would not significantly alter this conclusion. Thus our best estimate
of the tropospheric lifetime of methylchloroform is about 11 years, which leads
to an average OH radical concentration of about 3 x 105 molec/cc, consistent
with Singh's original estimate.

Direct Measurement of OH Concentrations. Because of the great importance
in accurately knowing how the concentration of OH varies in the atmosphere,
considerable effort is being made to measure it using direct methods. Several
different techniques have been used.

Perner et al. (1976) have used laser absorption spectroscopy over a
7.8-km path length to measure OH over the city of Julich, Germany. Their
results indicate a general upper limit for mid-day concentration of 4 x 10s
molec/cc, with concentrations as high as 7 x 10s molec/cc being observed oc-
casionally.

Wang et al. (1975) have used laser- induced fluorescence to estimate OH
in Detroit. Concentration estimates ranged from the detection limit (5 x 10s
molec/cc) to 6 x 10 7 molec/cc at mid-day. A disadvantage of this technique
is the uncertainty as to whether or not the laser light used to induce fluores-
cence may also be photolyzing other atmospheric components to produce OH and

189
-------
thereby generating spurious concentrations of OH.

Davis et al. (1976) have used laser-induced fluorescence to attempt to
measure OH at 7 and 11.5 km. At night they observe less than 2 x 10s molec/cc—
the detection limit of their experiment. However, in the early afternoon,
values of 3.5 to 8.1 x 106 molec/cc were observed, with the data possibly
showing some dependence on elevation and latitude. However, these data must
be considered carefully because of the possibility of the same types of inter-
ferences discussed for the Wang et al. experiments.

Further attempts are being made to improve the sensitivity of these
various atmospheric measurements. However, at this time most weight should
be given to the laser absorption spectroscopy technique because it should be
most free from interferences. At present, the best values, based on direct
measurements, place the mid-day OH concentration in urban areas at about 4 x
10s molec/cc, with lower values being likely to occur more frequently than
higher values.

Computational Estimates of Tropospheric OH Concentrations.

Early modeling of the clean troposphere by Levy (1974) indicated ground-
level OH concentrations in the range 1 to 6 x 106 molec/cc, whereas at the
tropopause the values range from 2 to 5 x 10s molec/cc. Thus, an overall
tropospheric average could be set at about 1 x 106 molec/cc. In general, this
value was supported by other attempts to model the troposphere. However,
recent efforts of Cruzen and Fishman (1977) which make use of the most recent
rate constant data, suggest an average northern hemisphere value of 2 to 4 x
10s molec/cc. Correcting for a higher southern hemisphere value gives total
troposphere average of 4 to 8 x 105 molec/cc, about one-half of earlier
estimates. At ground level, the estimates indicate a range of 2 to 4 x 106
molec/cc at noon.

Computer simulation of the polluted atmospheric chemistry, which was
developed to predict ozone, can be used to predict OH concentrations. For
simulation of smog chamber data the values depend on reactant concentrations
but fall in the range 2 to 10 x 10s molec/cc (Hendry et al., 1978). Conditions
that most clearly match the urban atmospheric conditions indicate OH concen-
trations of 2 to 6 x 10s molec/cc.

Summary of OH Concentrations Data. Our best picture of how the OH con-
centration varies in the atmosphere may be summarized as follows.

(1) At ground level at mid-day in the highly polluted troposphere, the
OH concentration ranges from 2 to 8 x 106 molec/cc, whereas in the
clean troposphere the range is 2 to 4 x 10s. In moderately polluted
air the OH concentration may drop to 1 x 10s molec/cc or below.
(2) OH concentration decreases with increasing elevation by at least
a factor of 10 from ground level to the tropopause.
(3) At ground level the annually averaged concentration is 5 to 10 x
10s molec/cc.
(4) The best diurnal, seasonal, and elevation averaged tropospheric
concentration is 4 x 105 molec/cc. In the northern hemisphere the

190
-------
best value is 2 to 3 x 105 molec/cc, and in the southern
hemisphere the value is 4 to 6 x 10s molec/cc.

Determination of Ozone Concentrations

Figure 5.5 represents the annual averaged distribution of ozone in the
troposphere as a function of latitude and elevation based on ozonesonde data
(Fishman and Crutzen, 1978). In general, there is a gradient from higher
elevations to lower due largely to ozone mixing into the troposphere from the
stratosphere. Ground-level concentrations are between 0.5 to .8 x 10 12 molec
cm"3 (20 to 30 ppb). A realistic tropospheric average is 1 x 1012 molec cc~3
(40 ppb) ozone, with the value being somewhat higher in the northern hemisphere
and lower in the southern hemisphere. This difference in value between
hemispheres reflects largely a difference in the rate of photochemical produc-
tion of ozone due to the higher CO concentrations in the northern hemisphere.

In polluted areas, the ground-level concentrations can easily increase
to 4 x 10 l2 molec cm~3 as a result of photochemical reactions of the higher
concentrations of hydrocarbons and nitrogen oxides that are found there
(Lonneman et al. , 1976). Ozone often continues to develop downwind from large
metropolitan areas to give higher than average concentrations (Bufalinl, 1977).
These high values will have localized effects on ozone chemistry but will
generally decrease at night at the surface and have little effect on the average
tropospheric ozone concentration.

5.7.5 Design of Laboratory Test Methods

Photochemical Reaction

Screening. Section 5.7.2 shows how rates of photochemical reaction
may be calculated from the absorption spectrum data, quantum yield, and solar
intensity data according to the equation
kp = *laxJx (5.55)

For developing a screening test for photolysis, we recommend that the absorp-
tion spectra be obtained and that the integration with solar intensity data
be performed assuming unit quantum yields. This assumption is valid for a
number of photochemical processes, as shown in Table 5.16. For those cases
where the quantum yield is smaller than unity, the estimated value k is a
reliable upper limit, signified by k , ^

kp = ZaxJx (5.56)

Having an upper limit for kp is still useful because in most cases the estimate
will be orders of magnitude less than the rate constants for reaction with OH
or 03 because of the weak absorption of most organic chemicals in the solar
spectrum.
191
-------
60
40
20
0
E
I Southern Hemisphere I Northern Hemisphere I
Contours in parts per 109 by volume
SOURCE: Fishman and Crutzen, 1978.
SA-4396-82
FIGURE 5.5 AVERAGE ANNUAL DISTRIBUTION OF OZONE
192
-------
Table 5.16

EXAMPLES OF GAS PHASE PHOTOLYSIS PROCESSES, QUANTUM YIELDS, AND ENVIRONMENTAL HALF-LIVES
Compound
CH,0

CH3CHO
CH3C(0)CH,
ft ^>-CHO
^0
CF3NO
CH3NO,
CH 3ONO
CH3ONO,
CH3Br
CH3I
CH3NjCH3
H,0,
(CHjCHjKPb
Wave-
length, nm
303
313
323
330
303
313
323
330
313
313
313-366
540-780
313
366
313
254
254
366
254
300-340
Primary Products
H« + HCO-
H« + HCO-
H« + HCO-
H« -1- HCO«
H2 + CO
H2 + CO
H2 + CO
Hj + CO
CH3. + CHO
CH3C(0)« + CH3
uncertain
CF3. + NO
uncertain
CH30- + NO
CH30« + NO,
CH3- + Br
CH, + I
2CH3 + N,
2HO-
uncertain
Quantum
Yield
0.760
a
t^, days
\
0.735 II
0.519 M
0.330 1
0.24 ^°-23
0.26 1
II
0.48 1
0.67
•^ 0.5
"< 1.0
0.006
^ 1.0
0.6
0.76
-- 0.5
•v. 1.0
•v- 1.0
1.0
1.0
^ 1.0
|
1.1
1.8
0.55
0.003
2.3
0.014
40
1.5 x 10s
4.4
.13
2.9
0.30
Reference
b

c
d
e.f
d
g,d
h
d
i
d
d
j.d
k
Calculated for June 22 and 30°N from data in table and absorption cross sections
over the range 290-800 nm reported by Calvert and Pitts (1966); calculations assume
that the reported quantum yields, which were obtained in most cases in the absence
,of oxygen, apply in the environment.
Horowitz and Calvert (1978).
^Weaver, Meagher, and Heicklen (1976/77).
Calvert and Pitts (1966).
?Gandini, Parsons, Back (1976).
Gandini, Hackett, Back (1976).
%onda, Mikumi, Takahasi (1972).
^Wiebe, Villa, Hellman, Heicklen (1973).
.Frank and Hanrahan (1978).
^Molina, Schinke, Molina (1977).
Tlarrison and Laxen (1978).
193
-------
In determining the absorption spectrum care should be taken in estimating
absorption coefficients where the absorbance is small, because even a coeffi-
cient of 0.1 cm-M over a broad region of the solar spectrum can be sufficient
to account for a relatively rapid rate of photolysis. In general, the use of
long-path uv cells increases the accuracy of the absorption coefficient,
especially when it is small and the vapor pressure is low. For example, in
a 10-cm cell, approximately 20 torr of compound having cross section of 1 x
10~22 (0.1 M-cm) will give an absorbance of 0.001. However, in a 10-meter
long-path cell, only 20 ym are necessary to obtain the same absorbance. Since
many compounds will have both small cross sections and low vapor pressures,
the long-path cell is essential for obtaining gas phase absorption spectra.
An alternative to using a long-path cell in these cases is to determine the
spectra of the chemical dissolved in solvent that does not absorb in the solar
region. Acetonitrile, cyclohexane, and 1,4-dioxane are examples of solvents
that could be used. In general, solvents such as water, organic acids, and
alcohols should be avoided because of their greater ability to perturb absorp-
tion spectra. The spectra should be obtained over as wide a range of concen-
trations as possible in a 10-cm cell, in at least two solvents. Values of k
or k based on absorption data obtained from liquid phase spectra should
always be labeled as such.

Detailed Tests. For the detailed measurements, the quantum yield is
determined by laboratory measurement at a single wavelength and incorporated
into the photochemical reaction rate calculation equation 5.40. This allows
kp, the upper limit for the photochemical reaction, to be converted to a true
value of k .
P

k = 4>k (5.47)
P P

The quantum yield (4>) for a photochemical reaction is the fraction of
light absorbed by a molecule that results in chemical reaction

, _ moles chemical reaction _ c , ,_o\
einsteins of light absorbed c
a

The value for the moles of chemical reaction is determined by measuring the
decrease in concentration (ACC) during the time the compound is exposed to
light in the photoreactor. The amount of light absorbed (Tc) is calculated
from the expression

ICa = IQ(1 - e°ciCc )tc (5.59)

where I0 is the intensity of the light photons/s in the photolysis cell and
to which the compound is exposed. otc is the cross section (cm2 molec"1) at
the wavelength of the photolytic beam, I is the path length (cm), C|v is the
average concentration (molec cm~3), and t is time (seconds). At value of I0/I
less than 1.02, this expression is approximated by
194
-------
Ic = I a 1C t . (5.59a)
a o c c c

Io is determined by following the decrease under the same conditions of a
standard compound (actinometer) for which both the quantum yield, , and
cross section, a are known. The I may be evaluated from the expression

o S,CaV
I = AC / (1 - ess )t (5.60)
OSS S
or at I /I < 1.02
o
I = AC /d> a £C t (5.60a)
o s s s s s
where the subscript s signifies constants for the standard compound or
actinometer in the calibration experiment.

Combining both equations (5.59) and (5.60) or (5.59a) and (5.60a) gives
the following expression:
(5.61)
)Cc
AC a C t

-cY (5'58)
S C C C

Alternatively, the disappearance of both the compound, C, and actinometer, S,
may be expressed as first-order rate constants, k and k , from the equations

ln[C ] /[C ] = k -t and ln[C ] /[C ] = k -t (5.62)
co cjt pc c so L sjt pa a ^

where k_c = Iocac& and kpa = Iosas&. In this case, the quantum yield,
-------
Arc
Reaction
Vessel
SA-4396-83
FIGURE 5.6 PHOTOCHEMICAL APPARATUS FOR DETERMINING QUANTUM YIELDS
196
-------
minimize light striking the reactor walls. The third lens concentrates the
light beam so that a photocell can monitor the intensity. Although the
monitoring system (P) is not essential, it does provide information regarding
the stability of the lamp that otherwise could be obtained only by additional
standard runs. The light is filtered to isolate the simple emission bond from
the lamp that best matches absorption by the compound under study. The filters
(F) can be either chemical solutions or commercially available glass filters.
The effectiveness of any filtering system over the range 190-800 nm should be
checked with a uv-visible spectrometer before use. Because the chemical solu-
tions are not stable indefinitely, they should be checked frequently to ensure
their stability.

Because the refractive index in glass varies with wavelength, the light
beam cannot be properly aligned visually if the wavelength selected for study
is less than 400 nm. If the focal length at a visible wavelength is known,
it is possible to calculate the focal length at the desired wavelength for the
lenses using the literature refractive indexes for the glass at each wavelength.
An alternate method of tracing invisible ultraviolet light is to use filter
paper impregnated with a fluorescent material such as anthracene.

As a word of caution, it is important the the investigator wear eye
protection to prevent eye exposure to either the direct or reflected radiation
of ultraviolet light. Similarly, skin should be shielded with clothing to
avoid severe sunburn.

Reaction with OH

Screening. In Section 5.7.3 we showed that the rate constant for re-
action with OH can be estimated for a wide variety of compounds using equation
(5.51) and data in Tables 5.1 to 5.3. This estimation method is used to
estimate the OH rate constant at the screening level. In most cases, when
properly applied, this technique is expected to be reliable within a factor
of two.

Detailed Tests. The method of choice for measuring the rate constant
for reaction of a chemical with OH is to generate OH by pulse photolysis of
an OH source such as H20 or HZ02 and then to follow the OH decay either by
resonance fluorescence or laser- induced fluorescence. The kinetic expression
is
= k[OH][C] (5.64)
or
(5-65)

This general technique is discussed fully in the literature (Atkinson et al. ,
1975).
197
-------
The proposed procedure using photolysis of a mixture of the chemical,
reference compound, and HONO (Niki et al.,'1978a; Hoshino et al., 1978) deter-
mines the rate of reaction toward OH relative to a standard compound for which
the absolute rate constant toward OH is known. In general, the precision of
the proposed technique is not as good as that of fluorescence techniques, but
it can be applied to a wider range of compounds and requires only methods which
are familiar to most chemists.

Reaction with Ozone

Screening. The screening test for reaction of ozone requires no
laboratory measurements. Instead, the rate constant for reaction is estimated
by comparing the reactive function(s) of the compound with those of other com-
pounds where the ozone rate constant has been measured. Table 5.7 lists the
reactivity of various reactive structures based on data from Table 5.14.
Saturated structures—such as alkanes, chloro and fluoroalkanes, simple alco-
hol, organic acids, esters, ketones, and aldehydes—all react very slowly with
ozone with kQ = < 1 M"1 s"1, which gives environmental half-lives on the order
of 100 years. On the other hand, olefinic compounds react rapidly with ozone
with rate constants of 1000 to 10,000 M""1 s~l, which corresponds to environ-
mental half-lives of about 1 to 20 days. In these cases it will be possible
to estimate the rate constant from the data in Table 5.7.

Detailed Tests. The determination of the rate constants for the re-
action of ozone with organic compounds may be obtained by following the change
of either reactant with an excess of the other reactant. The rate expressions
are

d[RH]/dt = k[03][RH]
ln[RH] /[RH] = k[03]
where [03] = constant;
d[03]/dt = k[03][RH]

ln[03]o/[03] = k[RH]
f\j
where [RH] = constant. A variety of techniques have been used to measure the
change in reactants (Japar et al. , 1974, Herron and Huie, 1974; Bufalini and
Altshuller, 1965). The method recommended in Section 5.6.3 has been selected
to minimize equipment requirement without significantly reducing accuracy.
198
-------
5.8 REFERENCES

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the Reaction of the OH Radical with H2 and NO (M = Ar and N2). J. Chem.
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Atkinson, R., R. A. Perry, and J. N. Pitts, Jr. 1976. Rate Constants for the
Reaction of OH Radicals with a-Methyl-2-butene over the Temperature Range
297-427°K. J. Chem. Phys. 64: 3237-3239.

Baldwin, A. C., J. R. Barker, D. M. Golden, and D. G. Hendry. 1977. Photo-
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2492.

Berger, M. I. L. Goldblatt, and C. Steel. 1973. Photochemistry of Benzalde-
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Blume, C. W., I. C. Hisatsune, and J. Heicklen. Gas-Phase Ozonolysis of cis-
and trans-Dichloroethylene. Intern. J. Chem. Kinet. 8: 235-258.

Bufalini, J. J. 1977. Opening remarks, 'Proceedings of Symposium on 1975
Northeast Oxidant Transport Study." Ed. by J. J. Bufalini and W. A.
Lonneman. EPA-600/3-77-017 p. 4.

Bufalini, J. J., and A. P. Altshuller. 1965. Kinetics of Vapor Phase Hydro-
carbon-Ozone Reactions. Can. J. Chem. 43: 2243-2250.

Cadle, R. D., and C. Schadt. 1952. Kinetics of the Gas Phase Reaction of
Olefins with Ozone. J. Amer. Chem. Soc. 74: 6002-6004.

Cadle, R. D., and Schadt, C. 1953. Kinetics of the Gas Phase Reaction Between
Acetylene and Ozone. J. Chem. Phys. 21: 163.

Calvert, J. G. 1976. Hydrocarbon Involvement in Photochemical Smog Formation
in Los Angeles Atmosphere. Environ. Sci. and Tech. 10: 256-262.

Calvert, J. G. and J. N. Pitts, Jr. 1966. Photochemistry. John Wiley & Sons,
Inc., New York.

Carter, W.P.L., A. C. Lloyd, J. L. Sprung, and J. N. Pitts, Jr. 1978. Com-
puter Modeling of Smog Chamber Data: Progess in Validation of a Detailed
Mechanism for the Photooxidation of Propene and n-Butane in Photochemical
Smog. Intern. J. Chem. Kinet.

Chang, J. S. and J. E. Penner. 1978. Analysis of Global Budgets of Halocar-
bons. Atm. Environ. 12: 1867-1873.
199
-------
Crutzen, P. J., and J. Fishman. 1977. Average Concentrations of OH in the
Troposphere, and the Budget of GHz,, CO, H2 and CH3CC13. Geophys. Res.
Lett. 4: 321-324.

Dave, J. V. 1972. Development of Programs for Computing Characteristics of
Ultraviolet Radiation. NTIS No. N75-10746/6SL.

Davis, D. D. Witteaps, and T. McGee. 1976. Direct Measurements of Natural
Tropospheric Levels of OH Via an Aircraft Borne Tunable Dye Laser. Geo-
phys. Res. Lett. 3: 331-336.

de Mayo, P., and H. Shizuka. 1976. Measurement of Reaction Quantum Yields.
"Creation and Detection of the Excited State." Vol. 4, W. R. Ware, Ed.
Marcel Dekker, Inc., New York.

Demerjian, K. L., J. A. Kerr, and J. G. Calvert. 1974. The Mechanism of
Photochemical Smog Formation. Adv. Environ. Sci. and Tech. 4:1-262.

Fishman, J., and P. J. Crutzen. 1978. The Origin of Ozone in the Troposphere.
Nature 274: 855-858.

Flamm, D. L. 1977. Analysis of Ozone at Low Concentrations with Boric Acid
Buffered KI. Environ. Sci. Tech. 11: 978-983.

Frank, A. J., R. J. Hanrahan. 1978. Gas Phase Photolysis of Ethyl Bromide
at 253.7 nm. J. Phys. Chem. 82: 2194-9.

Gandini, A., J. M. Parsons, and R. A. Back. 1976. The Photochemistry of
2-Furaldehyde Vapor. II Photodecomposition: Direct Photolysis at 253.7 and
313 nm and Mercury(3Pi) - Sensitized Decomposition. Can. J. Chem. 54:
3095-3101.

Gandini, A., P. A. Hackett, and R. A. Back. 1976a. The Photochemistry of
2-Furaldehyde Vapor. I Photophysical Processes: Phosphorescence Excited
in the ir* «- n Transition. Can. J. Chem. 54: 3089-3094.

Hage, K. D. 1965. Particle Fallout and Dispersion below 30 km in the Atmos-
phere. Final Report, Sandia Corp. P.O. 48-0648, Travelers Research Center,
Inc., Hartford, Conn.

Hampson, R. F., Jr., and D. Garvin. 1978. Reaction Rate and Photochemical
Data for Atmospheric Chemistry - 1977. National Bureau of Standards
Special Publication 513.

Harrison, R. M., and D.P.H. Laxen. 1978. Sink Processes for Tetraalkyllead
Compounds. Environ. Sci. Tech. 12: 1384-1392.

Heicklen, J. 1966. The Reaction of Ozone with Perfluoroolefins. J. Phys.
Chem. 70: 477-480.
200
-------
Hendry, D. G., A. C, Baldwin, J. R. Barker, and D. M. Golden. 1978. Computer
Modeling of Simulated Photochemical Smog. EPA-600/3-78-059.

Hendry, D. G., R. A. Kenley, B. Y. Lan, and J. E. Davenport. 1979. Reactions
of Oxy Radicals in the Atmosphere. Final Report EPA Grant 603864, in
press.

Hendry, D. G., and W. R. Mabey. 1978. Unpublished data.

Herron, J. T., and R. E. Huie. 1974. Rate Constants for the Reactions of
Ozone with Ethene and Propene, from 235.0 to 362.0 K. J. Phys. Chem. 78:
2085-2088.

K. Honda, H. Mikuni, and M. Takahasi. 1972. Photolysis of Nitromethane in
the Gas Phase at 313 nm. Bull. Chem. Soc. Jap. 45: 3534-3541.
Horowitz, A., and Calvert, J. G. 1978. Wavelength Dependence of the Quantum
Efficiencies of the Primary Processes in Formaldehyde Photolysis at 25°C.
Intern. J. Chem. Kinet. 10: 805-819.

Hoshino, M., H. Akimoto, and M. Okuda. 1978. Photochemical Oxidation of Ben-
zene, Toluene, and Ethylbenzene Initiated by OH Radicals in the Gas Phase.
Bull. Chem. Soc. Jap. 51: 718-724.

Howard, C. J., and K. M. Evenson. 1976. "Rate Constants for the Reactions
of OH with Methane and Fluorine, Chlorine, and Bromine Substituted Methanes
at 296 K." J. Chem. Phys. 64: 197-202.

Howard, C. J., and K. M. Evenson. 1976a. "Rate Constants for the Reactions
of OH with Ethene and Some Halogen Substituted Ethanes at 296 K." J.
Chem. Phys. 64: 4303-4306.

Japar, S. M., C. H. Wu, and H. Niki. 1974. Rate Constants for the Reaction
of Ozone with Olefins in the Gas Phase. J. Phys. Chem. 78: 2318-2320.

Japar, S. M., and H'. Niki. 1975. Gas-Phase Reactions of the Nitrate Radical
with Olefins. J. Phys. Chem. 79: 1629-1632.

Kenley, R. A., J. E. Davenport, and D. G. Hendry. 1978. Hydroxyl Radical
Reactions in the Gas Phase. Products and Pathways for the Reaction of
OH with Toluene. J. Phys. Chem. 82: 1095-1096.

Leighton, P. A. 1961. Photochemistry of Air Pollution. Academic Press, New
York.

Levy, H., II. 1974. Photochemistry of the Troposphere. Adv. in Photochemistry
9: 369-524.

Lonneman, W. A., J. J. Pufalini, and R. L. Seila. 1976. PAN and Oxidant
Measurement in Ambient Atmosphere. Env. Sci. Tech. 10: 374-80.
201
-------
Molina, L. T., S. D. Schinke, and M. J. Molina. 1977. U.V. Absorption Spec-
trum of Hydrogen Peroxide Vapor. Geophys. Res. Lett. 4: 580-582.

Morrissey, R. J., and Schubert, C. C. 1963. The Reactions of Ozone with Pro-
pane and Ethane. Combust. Flame 7: 263-268.

Murov, S. L. 1973. Handbook of Photochemistry. Marcel Dekker, Inc., New
York.

Nakagawa, T. W., L. J. Andrews, and R. M. Keefer. 1960. The Kinetics of
Ozonization of Polyalkylbenzenes. J. Amer. Chem. Soc. 82: 269-276.

Neely, W. B., and J. H. Plonka. 1978. Estimation of Trace-Average Hydroxyl
Radical Concentration in the Troposphere. Environ. Sci. Tech. 12: 317-
321.

Niki, H., P. D. Maker, C. M. Savage, and L. P. Breitenbach. 1978. Mechanism
for Hydroxyl Radical Initiated Oxidation of Olefin-Nitric Oxide Mixtures
in Parts per Million Concentrations. J. Phys. Chem. 82: 135-138.

Niki, H., P. D. Maker, C. M. Savage, and L. P. Breitenbach. 1978a. Relative
Rate Constants for the Reaction of Hydroxyl Radical with Aldehydes. J.
Phys. Chem. 82: 132-134.

Perner, D., D. H. Ehhalt, H. W. Patz, E. P. Roth, and A. Volz. 1976. OH-
Radicals in the Lower Troposphere. Geophys. Res. Lett. 3: 466-468.

Perry, R. A., R. Atkinson, and J. N. Pitts, Jr. 1977. Kinetics and Mechanism
of the Gas Phase Reaction of OH Radicals with Aromatic Hydrocarbons over
the Temperature Range 296-473 K. J. Phys. Chem. 81: 296-304.

Peterson, J. T. 1976. Calculated Actinic Fluxes (290-700 nm) for Air Pollu-
tion Photochemistry Applications. EPA 600/4-76-025.

Peterson, J. T. 1977. Dependence of the N02 Photodissociation Rate Constant
on Altitude. Atm. Environ. 11: 689-695.

Pitts, J. N., Jr. and B. J. Finlayson. 1975. Mechanisms of Photochemical Air
Pollution. Angew. Chem. Intern. Ed. 14: 1-74.

Pitts, J. N. Jr., A. M. Winer, K. R. Darnall, A. C. Lloyd, and G. J. Doyle.
1977. Hydrocarbon Reactivity and the Role of Hydrocarbons, Oxides of
Nitrogen, and Aged Smog in the Production of Photochemical Oxidants.
International Conference on Photochemical Oxidant Pollution and Its Con-
trol Proceedings: Vol. II, EPA-600/3-77-0016, p. 687-704.
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10: 783-804.

Ripperton, L. A., and H. E. Jeffries. 1972. Formation of Aerosols by Reaction
of Ozone with Selected Hydrocarbons. Advances in Chemistry Series 113:
219-231.

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Schubert, C. C., Pease, R. N. 1956. The Oxidation of Lower Paroffin Hydro-
carbons. I. Room Temperature Reaction of Methane, Propane, n-Butane, and
Isobutane with Ozonized Oxygen. J. Am. Chem. Soc, 78: 2044-2048.

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Hydroxyl Radical Concentration in the Troposphere. Geophys. Res. Lett.
4: 101-104.

Singh, H. B. 1977a. Preliminary Estimation of Average Tropospheric HO Con-
centrations in the Northern and Southern Hemispheres. Geophys. Res. Lett.
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Singh, H. B., J. R. Martinez, D. G. Hendry, R. J. Jaffe, and W. B. Johnson.
1978. Unpublished data.

Singh, H. B., L. J. Salas, H. Shigeishi, and E. Scribner. 1978. Global
Distribution of Selected Halocarbons, Hydrocarbons, SF6 and N20. EPA
Grant 803802.

Wang, C. C., L. I. Davis, Jr., C. H. Wu, S. Japar, H. Niki, and B. Weinstock.
1975. Hydroxyl Radical Concentrations Measured in Ambient Air. Science
189: 797-800.

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122.

Wiebe, H. A., A. Villa, T. M. Hellman, and J. Heicklen. 1973. Photolysis of
Methyl Nitrite in the Presence of Nitric Oxide, Nitrogen Dioxide, and
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203
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Williamson, D. L., and R. J. Cvetanovic. 1968. Rates of Reactions of Ozone
with Chlorinated and Conjugated Olefins. J. Amer. Chem. Soc. 90: 4248-
4252.
204
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Appendix 5 .A

STATISTICAL ANALYSIS FOR
In the proposed process, the concentrations of two substances, A and C
(where C is a standard with known reaction rate kc) , are measured initially
and after a lapse of time t. The final concentrations A and C are assumed
to be related as

A k. C
where A0 and C0 are the initial concentrations, and k^ and k^ are the reaction
rates. We assume that the concentration measurements are log normally distributed
with variances a2(£n$ = a? and a2 (Jin C) = a2., neither of which depends on t.
The parameter ratio R = k^/k^ is to be estimated. This could best be done by
measuring y = to 4^ and x = &r£o_ for a number of different values for t and
carrying out a regression of y t on x. However, current practice is to select
a suitable value of t and estimate R from y/x for the selected t.

From the assumptions made, y and x are normally distributed with variances
o2(y) = 2aj^ and oa/x\ = 2ac- Let y = E(y) and x = E(x) be the expected values
of y and x, respectively. Assuming that x and y are independent, the trans-
formations u = (x-x)/o~x and v = (y-y) /oy yield normally distributed variables
u and v with zero means and unit variances. Their probability densities are
p(u"> = -T^-e~-lu2 and p(v) = -Tx-e-^v2, with a joint probability density of p(u,v)
= -!j7e~i5(ua+v2) • The ratio R can now be expressed in terms of u and v
as

y + vo
R = Z - z
x + uox

We are interested in E(R) and a2(R) = E(R2) - [E(R)]2. We have E(R) = E(y)E(-|)
and oa(R) = E(y2)E(i2) - [E(y)E(^)]2 where

E(y) = y + a E(v) = y

E(y2) = E(y2 + 2a yv + a2v2) = y2 + a 2

since E(v) = 0 and E(v2) = 1. However, E(— ) and £(—5-) are given by
This analysis was carried out by Dr. Francis W. Dresch.

205
-------
du =
-oo(x + UO
-u
e du
X
for n = 1 and 2. Singularities enter when u = -^-. To avoid these, the assumed
normal distribution p(u)
tribution
can be replaced by a truncated normal dis-
p(u) =
.J^u'/^L -
1 In ~J->
0, otherwise
if -L < u < L
.,, n, 1« n -*5Uj
E(u ) = -fu e 2 du,
/ -kii2
e ^ du = E(u°)
-L
E(un) =I{[-u
3
-L
e'^du}
'-L
where b
n-1 a'
= (n-l)E(un~2) - b .L11'1
n—1
if n-1 is odd and 0 otherwise. We have

E(u°) = 1

E(u) = 0

by direct evaluation of ^•f_le~du. = f = 1 and — f ue'^du == i[-e~^u ] = 0.
From the recursion formula -L

E(u2) - E(u°) - biL - 1 - biL,

where b! = 2e /J e~ du
-L
E(u3) = E(u) - b2L2 = 0,
since E(u) * 0 = ba. All expectations of odd powers of u vanish, as can be
seen either from the recursion process or from symmetry
E(x} ~
ax
""" Li
206
-------
and
J^) =-L-fl
x2 ax2 -L
Expanding (1 + — ^u) n as binomial series for n = 1 or 2 gives
x
a

x
i i ° ° °
-) = -E{1 - -Ai + (—)2u2 - (—)3u3 ... }
a
= -{1 + (—)2(1 - biL) + (—)"E(O +..}
X
x
CTx
(-^
x
(-^
x
v
E(R) = E(y)E(-) = y--{l + (—
~* "™
1
-
~*
x
E(R2)
y2 + a2
— )
x
and
[E(R)]2 =
(-^
x
a2(R)
e
x
x y
(^
x
(^-)2{(-
xx
— )
x
..} Ml + 2(— )
x
207
-------
For L = 3, bj = 0.00675 and 1 - b1L = 0.979. For L = 5, bt = 3-1Q-6 and
1 - biL = 0.999985. Thus if 5^£ < 1 or x > 5a = 5v/2oc = 7a and if seco m
higher terms in °2 (x) and x _^2/vN> are neglected
gz(R) i q2(y) A CT'CX)
[E(R)]
Note that
E(R)

Thus, — as an estimate of *- is about 4% high if x > 50 or
X x x
a"(x) a"(y)
a2(x)a2(y)
This Includes terms such as -<, , -4 , and "2-2
x y x y
208
-------
CHAPTER 6. AQUATIC BIODEGRADATION

T.-W. Chou
6.1 INTRODUCTION 210
6.2 SUMMARY 210
6.3 CONCLUSIONS 210
6.4 RECOMMENDATIONS 211
6.5 SCREENING TEST 211
6.5.1 Purpose 211
6.5.2 Protocols 211
River Die-Away Test (RDA) 211
Semicontinuous Activated Sludge (SCAS) 213
6.5.3 Criteria for Screening Test 214
6.5.4 Rationale 215
6.5.5 Scope and Limitations 215
6.6 DETAILED TESTS 216
6.6.1 Purpose 216
6.6.2 Procedures 216
6.7 BACKGROUND 218
6.7.1 Definition and Nature of Biodegradation 218
6.7.2 Kinetics 219
6.7.3 Factors Affecting Biodegradation 222
6.7.4 A Review of Aquatic System Biodegradability Tests 227
6.8 REFERENCES 234
209
-------
6. AQUATIC BIODEGRADATION
6.1 INTRODUCTION

Biodegradation is one of the most important processes for transfor-
mation of chemical compounds when they enter into natural environments.
Many organic chemicals are used by living cells for carbon and energy
sources. Microorganisms metabolize a wide variety of organic compounds,
including man-made xenobiotic chemicals, and play major roles in bio-
degradation. It is important to determine biodegradation rate constants
for quantitative comparison with other, different pathways. This section
evaluates methods available for obtaining the data needed to calculate
rates of primary biodegradation in aquatic systems. From these methods
we have selected a few to use as screening test protocols for biodegrada-
tion. No recommendation is made as to selection of test protocols for
detailed study; however, principles of rate constant determination are
discussed in the section on kinetics.

6.2 SUMMARY

Screening test protocols for biodegradation of chemicals in water
have been tentatively prepared to enable investigators to obtain pre-
liminary information about primary biodegradation of chemicals. The river
die-away method (RDA) provides acclimation times and half-lives after
the initiation of biodegradation. The semicontinuous activated sludge
method (SCAS) provides data on the percent biodegraded in 24 hours of
fill-draw cycle. These two test protocols are widely used, simple, and
cost-effective, representing the best state of the art among many methods
developed. However, these procedures have limited value in estimating the
fate of toxic substances in the environment. A protocol of detailed testing
for biodegradation rates was not presented because of the complexities of
biodegradation. Relatively few investigations have been conducted to cor-
relate biodegradation and biomass. Kinetic descriptions which have been
developed and available methods are discussed in the text.

Many factors affecting biodegradation are discussed and aquatic
biodegradation test methods are reviewed.

6.3 CONCLUSIONS

The RDA and SCAS methods are recommended as screening tests for bio-
degradation protocol as the best test procedures currently available.
The procedures have some limitations for use as completely acceptable aquatic
biodegradation test protocols for all chemicals. Methods for obtaining the
data necessary to calculate rate constants and half-lives for biodegradations
are described, although no detailed test protocol is proposed. Further research
is needed in this area.
210
-------
6.4 RECOMMENDATIONS

The screening test methods should be evaluated in the laboratory for
applicability to several chemicals of environmental concern, which could then
be used as reference standards in testing other chemicals. The reference
chemicals should include representatives of a wide range of chemical groups.
The water samples should be collected from different places and at different
times, with selected chemicals being used for testing reproducibility of the
results. Research is needed to develop test procedures for detailed rate
constant studies.

6.5 SCREENING TEST

6.5.1 Purpose

The screening test protocols are intended to provide preliminary
information on primary biodegradation or persistence of chemicals in aquatic
environments.

6.5.2 Protocols

Many methods have been developed for testing biodegradability of
chemicals in aquatic systems (Howard et al., 1975). These methods differ
significantly in approach and in complexity of operation. The numerous
complicated environmental factors and the inherent lack of precision in
biological systems make the study of biodegradation complex.

Chemicals may be degraded in aquatic environments, such as rivers,
ponds, or lakes, with relatively low microbial populations; or in sewage or
waste biological treatment plants or in polluted waters with relatively high
microbial populations. River die-away tests and semicontinuous activated
sludge methods are representative of two different types of tests. These two
methods are recommended in this protocol for screening tests. However, these
methods have limited uses as a completely acceptable standard procedure for
testing biodegradability of all organic chemicals. Selection and modification
of a biodegradation test for a particular chemical should take into account the
chemical's major route of entry into the natural environment as well as
physical, chemical, and toxicological properties of the chemical. The
procedures described below are for testing relatively water soluble
nonvolatile chemicals of low toxicity.

For each set of tests, extra test vessels containing chemicals known to be
biodegradable should be included as reference standards for evaluating the
biodegradation capabilities of the water samples.

River Die-away Test (RDA)
Of all the tests, the RDA is the most simple and the closest to natural
environmental conditions. The test consists of adding test chemicals to natural
water samples; degradation is followed as a function of time. There is
variability in chemical compositions and microbial populations in natural waters,
and these may cause variation in the test results. However this method will
provide preliminary information about the acclimation periods and degradation

211
-------
rates. It will also provide acclimated mixed culture degradation systems
for enrichment processes that can be used for detailed studies.

The RDA test is as follows. Water and sediment (of about; 5 percent of
the volume of water) are obtained from a river that is large enough to have
only slight variability in quality and flow. The water and sediment are mixed
thoroughly and the sediment is allowed to settle. The supernatant is syphoned
off and filtered through a layer of glass wool or cloth to remove large float-
ing particles. Then 2 liters of the water sample is dispensed in a 4-liter
glass container (or 1 to 5 liters in a 2- to 9-liter vessel).

Concentrations of chemical depend on solubilities, realistic environ-
mental contamination levels, and sensitivities of analytical methods. Concen-
tractions in the neighborhood of 1 yg/ml"1 are recommended. Each chemical is
added in duplicate to water samples as aquatic stock solution. If the chemical
is low aqueous solubility compound, it may be added with a minimum amount of
solubilizing solvent, such as dimethyl sulfoxide, which is highly resistant
to microbial degradation but not toxic to microbes. Sterile water samples
with the test chemical added are used as controls for possible chemical degradation
and volatilization. Other chemicals known to be biodegradable may be added to
water in other vessels and included in the test run as reference standards moni-
toring their biodegradation to evaluate the biodegradation capability of the
water sample. Extra water samples containing the test chemical plus an analog
compound known to be biodegradable, and a possible pollutant present in the en-
vironment with the test chemical, may be set up if cometabolic biodegradation
is suspected.

At the start, the water sample containers should be agitated or shaken
to saturate the water with oxygen. The container is covered with a cotton plug
or loose lid to prevent excess evaporation. The water is incubated in the dark
at 25°C for up to 8 weeks. The water should be agitated before each sampling
for mixing and aeration.

An aliquot of the sample is withdrawn daily or on some other schedule
appropriate to the rate of degradation for the test chemical. The sample is
extracted with a proper organic solvent for chemical analysis to determine
the disappearance of the chemical. If the chemical has a specific visible or
ultraviolet (uv) absorption peak, spectrophotometric methods are used for a
quick check of the degradation so that the microorganisms may be transferred
for culture enrichment. If necessary, a more frequent sampling schedule
is set up for monitoring the degradation.

The experiment is completed when the parent chemical has > 90%
disappeared or when there has been no change in concentration for more than three
days after a period of biotransformation. From the chemical analysis, the
acclimation period and rate of degradation can be obtained if sampling is
sufficiently frequent to show changes in concentration of the chemical. Micro-
bial plate counts at the time of degradation may be made and used to estimate
degradation rate constants, although only a fraction of the microbial population
may be responsible for the biodegradation. When degradation is 50 to 80% com-
plete, the microorganisms are transferred into a shaker flask for development
of the enrichment culture to be used in detailed studies or for confirmation
of the biodegradation.

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Semi continuous Activated Sludge (SCAS)

The semi continuous sludge test is a modified confirmatory test of
the Soap and Detergent Association (1965). The 24-hour cycle of fill-
and-draw closely represents the biodegradation in sewage treatment plants
or continuously polluted, high-microbial-population environments. The
operation is more simple and less costly than the continuous method.

Aeration chambers consist of glass vessels (3-4 liters) with
cone-shaped lower parts, fitted with a gas diffuser at the inside bottom
of the conical end. The medium is aerated and mixed by passing glass
wool filtered sterile air through a glass diffuser into the medium.
The aeration period averages 23 hours per day. The aeration rate is
maintained at 500 ml/minute; temperature is maintained at 25° i 3°C.

Activated sludge samples for inoculum are collected from a sewage
plant that principally treates domestic wastes. Concentration of the sus-
pended solids is adjusted to approximately 2500 Mg/ml with tap water;
1500 ml of this activated sludge is placed into each chamber and the
f ill-and-draw routine (described later) is begun.

Synthetic sewage stock solution is prepared by dissolving 30.0
g of glucose, 20.0 g of nutrient broth, 13.0 g of K2HP01+, 2.5 g of
in tap water to make up to 1 liter.
The following incremental chemical feed schedule is used with
synthetic sewage to acclimate the organisms:

On Day 0 Feed 2 mg/liter
On Day 1 Feed 4 mg/liter
On Day 2 Feed 6 mg/liter
On Day 3 Feed 8 mg/liter
On Day 4 Feed 10 mg/liter
(finish)

With each run, at least one unit fed a reference standard chem-
ical is included as a control on sludge suitability and operation condi-
tions .

The daily routine is as follows. An aliquot of well-mixed sample
is withdrawn for solvent extraction and subsequent analysis (effluent) .
Aeration is stopped for 30 minutes to allow the material to settle; the up
per 1000 ml supernatant is then removed. Aeration is resumed and 10 ml
of synthetic sewage stock solution (with enough tap water to make up to
1500 ml) and 10 mg/liter of the test chemical are added. The pH is main-
tained at 6.5-8.0 with NaOH or HC1, and dissolved oxygen (at least 2
mg/liter) is maintained by the appropriate aeration.

Three days after the addition of chemical has reached the 10-mg/
liter level (Day 7), analysis of the chemical is begun. Synthetic sewage
stock solution (1 ml) plus the test compound, with the addition of dis-
tilled water to 150 ml, make up the influent solution sample for analysis.
Both the influent solution sample and the effluent are extracted with or-
ganic solvent and analyzed for the test chemical.

213
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Beginning on the fourth day on which chemical feed is 10 rag/liter
the percentage of chemical degraded is calculated as follows:

S.-S
% degraded (day X) = -£—e x 100
i

S. = influent analysis and S. = effluent analysis.

The daily acclimation program is continued until the percentage
of chemical degraded is constant (~t 10%) for three consecutive days or until
the 30th day of the acclimation period. The supernatant may be analyzed
to calculate percent removal due to biotransformation and biosorption.
Chemical degradation and/or volatilization may be checked by aerating
10 ppm aqueous solution in the chamber at a 24-hour cycle and analyzing
it for loss.

This acclimated activated sludge can be used for detailed rate
constant studies by centrifuging the sludge and testing It with basal
medium/test chemical; or it can be transferred into flasks for enrichment.

6.5.3. Criteria for Screening Test

In the RDA test, if there is no loss of the chemical in sterile
water samples, any loss in the nonsterile water samples is assumed to be
due to biodegradation. Any loss in the sterile water sample may indicate
chemical transformation, volatilization, or adsorption by vessel walls.
If the reference standard chemical known to be biodegradable is not degraded,
the result is questionable and the test should be repeated with a new water
sample. The plot of chemical concentration against time will show acclima-
tion time, biodegradation rate, and extent of parent compound consumption.
When biodegradation is apparent, a detailed study is needed to obtain biode-
gradation rate constants with regard to biomass. The biodegradation can
be validated by redosing the water sample with the test chemical or inoculating
the acclimated microbes into fresh water containing the chemical. In either
case, the chemical will be degraded after a much shorter lag period.

When the test chemical concentration is very low and microbial
populations responsible for biodegradation are high, the cell increase
due to consumption of chemical is negligible. Under these conditions,
a loss of chemical may follow a pseudo first-order transformation, and
the half-life can be easily obtained from the curve of chemical concen-
tration versus time on semilogarithmic paper. The half-life is counted
from the initiation of biodegradation and does not include: acclimation
time.

The pseudo-first order rate constant k£ can be obtained from
the slope or half-life (tt):

In2 0.693
214
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When cell plate counts were made at the time of degradation, the
second-order rate constant kb2 in terms of total cell count X can be
obtained from k^:

k= \r-f /Y
b2 b'

Thus, the biodegradation rate is:

JS - v'c - KuoYS
- -££ ~ KbS - Kb2Ab

where S is chemical concentration and t is time of degradation.

When cell populations are low and the level of test chemical added
can provide substantial cell growth, degradation will be a second order
reaction, depending on increasing biomass and decreasing chemical concentra-
tion. Under these conditions, after the initiation of biodegradation,
second half-life will be shorter than first half-life.

In the SCAS test, biodegradation is expressed as the percent
biodegraded in a 24-hour cycle. The chemical with a high percent degra-
dation value, greater than 90 percent, is likely to be biodegraded easily
in a sewage treatment plant or a natural environment, and the chemical
with the low percentage degradation value is expected to be slowly bio-
degradable in natural waters. A set of standard chemicals, representative
of different groups, should be tested in the future and used as reference
and to categorize the biodegradability of test chemicals. When a chemical
in the supernatant is analyzed, the percentage removal is the combined
result of biodegradation and adsorption by activated sludge.

6.5.4. Rationale

The screening tests recommended above are relatively simple,
cost-effective procedures for evaluating biodegradability of organic
compounds in two representative aquatic environments. The RDA method
most closely simulates natural surface waters and requires the simplest
equipment; in addition, the river water samples can be used as sources
of microorganisms and nutrients. The data obtained will provide infor-
mation about acclimation time, rate of biodegradation, and the amount of par-
ent chemical biodegraded. The SCAS method simulates wastewater treatment
operations and is simpler and less laborious than other dynamic methods.
The data obtained provide information about percent biodegraded in 24-
hour cycle operations.

6.5.5. Scope and Limitations

Two screening test protocols for biodegradation are recommended
for two different types of aerobic biodegradation: the RDA test simulat-
ing biodegradation in natural surface water, and the SCAS test simulating
biodegradation in activated sludge systems. The tests are designed to
investigate biodegradability of chemicals performed by microorganisms

215
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present in water samples at designated temperature and concentration of
the test chemical. The procedures are applicable to chemicals that are
relatively water-soluble, low volatility, and nontoxic at the level of
testing concentrations. Because biodegradation depends on activities of
organisms, and microbial populations vary with the site and time at which
the water samples are collected, reproducibility of the test results may
not be as good as in chemical transformation tests.

There are many other methods for testing biodegradability
of chemicals. Because of the many factors affecting biodegradation and
natural environments have many variable factors, each method has its
limitations. The choice and modification of test methods should consider
physical and chemical properties of chemicals as well as the usage and
disposal of the chemicals.

The test procedures measure primary biodegradation involving
disappearance of the parent chemicals. Because of the nature of biodegradation,
to understand how extensively the chemical is mineralized the study of ulti-
mate biodegradability is also important. For this purpose, a method of
testing C02 evolution, such as that of Gledhill (1975), may be used. The
test procedures for anaerobic biodegradation, generally slower than the
aerobic process, is not included in these protocols, but: this procedure
is important for compounds such as some chlorinated hydrocarbons.

6.6 DETAILED TESTS

6.6.1 Purpose

The objective of the test protocol is to provide a uniform
procedure for measurement of biodegradation rates and estimation of rate
constants under conditions that will enable the investigator to estimate
a biodegradation rate at any blomass level at a low concentration of
chemical.

6.6.2. Procedures

Relatively few investigations have been conducted to study
biodegradation rates in terms of biomass. Not enough information is avail-
able to prepare an acceptable protocol at this time, and future studies are
needed. In this section we will discuss the available test procedures
that can be used to obtain biodegradation rate constants.

Detailed biodegradation rate studies are conducted with acclimated
microorganisms. When biodegradation is apparent in screening tests, aliquots
of test water containing acclimated organisms may be transferred into shaker
flasks containing basal salts medium and test chemical. After several trans-
fers, these mixed populations of enriched culture systems may be used for
the rate study. If the biodegradation involves cometabolism, a cometabolic
substrate may be added to the medium; the possibility of eventually growing
in medium without cometabolic substrate may be studied by decreasing the
amount of cometabolic substrate during successive transfers of microbes.
The sludge from an SCAS test may be used directly for a rate study.

216
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The biodegradation rate is the function of microbial biomass and
chemical concentration. When microorganisms utilize chemical substrates as
sources of carbon and energy, there is an increase in biomass. When low
concentrations of chemicals are introduced into waters with relatively high
concentrations of cells, the microorganisms grown from consumption of test
chemical will not significantly affect the total population. However, when
microorganism populations are low and chemical concentrations are high enough
to alter those populations, the degradation will be a function of cell growth.
Specific microbial growth and specific rates of chemical utilization are not
linear relative to the chemical concentrations, as discussed in Section 6.7.2.

Several procedures for measuring kinetics have been used with
mixed culture systems in which the chemical serves as the sole carbon source:

• Batch degradation with low-level inoculum of microorganisms and
with several levels of chemical concentration.

• Continuous culture system biodegradation with several different
feeding rates.

• Batch degradation with large microbial populations and low substrate
levels.

Principles of these methods are discussed in the kinetics section
(6.7.2). Of the three methods, batch degradation with large microbial popu-
lations and low substrate levels is the most simple, cost-time-saving proce-
dure.
217
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6.7 BACKGROUND

6.7-1 Definition and Nature of Biodegradation

Biodegradation is a transformation of chemical compounds by the
action of organisms. Microorganisms play a key role in the biodegradation
of chemicals in aqueous and terrestrial environments because of their
abundance in nature, the numbers and types present, their metabolic
diversity, large surface-to-volume ratios, rapid multiplication, high
rate of mutation, and adaptability of many organisms to grow under a
wide variety of environmental conditions. Organisms require an energy
source, carbon, and other elements from their environments for their
growth and maintenance. In the process they transform many chemicals
introduced into the environment. The uniqueness of biodegradation of
organic compounds is that, on many occasions, chemical compounds are
metabolized by cooperation of a group of microorganisms to mineralized
end products—in contrast to other nonbiological processes that usually
result in only slight alteration of parent compounds. Metabolic reactions
are rapidly catalyzed by enzymes at ambient temperatures at which many
nonbiological reactions either will not occur or will do so at slow
rates.

Biodegradation can be divided into the following categories
(WPCF, 1967):

• Primary biodegradation - biodegradation to the minimum extent
necessary to change the identity of the compound.

• Ultimate biodegradation - biodegradation to a) water, b) carbon
dioxide and inorganic compounds.

• Acceptable biodegradation - biodegradation to the minimum extent
necessary to remove some undesirable property of the compound,
such as foaminess or toxicity.

Acceptable biodegradation is the practical goal of environmental
biodegradation. To determine that the chemical is environmentally safe,
studies of metabolites produced and their toxicity or undesirable char-
actistics are needed. The definition of undesirable properties may not
be clear and may be changed from time to time. Primary biodegradation
is the disappearance of parent compounds, and no ultimate conversion of
metabolites is considered. In the assessment of biodegradation, the kin-
etic data obtained are the relations between biomass in the environment
and the disappearance of chemicals when introduced. However, the meta-
bolites produced and their eventual transformation need to be understood
to accurately assess the overall environmental fate of chemicals.
218
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6.7.2 Kinetics

When an organic chemical is utilized by microorganisms as a sole
carbon source and its concentration limits the rate of microbial growth,
the widely used Monod kinetic equation (Monod, 1949) can be used to des-
cribe the relation between substrate concentration and rate of cell growth
in a well-mixed system:

^
(6.1)
X KS+S

where X is the biomass per unit volume, y is the specific growth rate,
Um is the maximum specific growth rate, S is the concentration of growth
limiting substrate, and Ks is the concentration of substrate supporting
half maximum specific growth rate (0.5 ym) .

The rate of substrate utilization is then:

f!±L = M = ^ . SX = k SX (6.2)
dt Y Y KQ+S b KC-HS
o o

where Y is the cell yield, kf, is substrate utilization constant and equal
to Um/Y- The constants ym, Ks, and Y are dependent on the characteristics
of the microbes, pH, temperature, other nutrients, and some other environ-
mental conditions, and are based on the rate of utilization of a growth
rate-limiting single substrate by pure microbial cultures. These kine-
tic expressions can be used to obtain rate constants with mixed culture
systems (Paris et al., 1975; Smith et al., 1977). It is possible to
choose culture conditions that allow simplification of the Monod expres-
sion by making one of its variables constant or one of its constants
insignificant. The results of the simplification allow a straightforward
estimation of the remaining constants.

When substrate concentration is high and S » Ks, then equation
(6.2) is reduced to:

(6.3)

The degradation rate is first order with cell concentration and zero order
with substrate concentration.

For many pollutants in the environment, substrate concentrations
are very low and S « Ks; then (6.2) is reduced to:

(6.4)
219
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where Kb2 is a second-order constant
kb? = ^- = i (6.5)
b2
YKS K_

The degradation rate is first order with both cell concentrations
and substrate concentrations.

Several procedures have been used for measuring kinetics param-
eters in which the chemical served as the sole carbon source:

• Batch degradation with low-level inocula of washed biodegrading
cells.

• Continuous culture degradation.

• Batch degradation with large microbial populations and low
substrate levels.

In batch degradation with low levels of inocula, the initial
conditions are chosen so that XQ, the original inoculum, is much smaller
than the total microbial growth that could be supported by the chemical
substrate. During most of the bacterial growth phase, the substrate con-
centration is practically constant at So, the initial substrate concentra-
tion. When organisms start to grow after a lag phase of growth, the cell
concentration is plotted against time on semilogarithmic paper, and the
specific growth rate y for particular initial chemical concentrations (So)
can be calculated from the slope. These tests are conducted with differ-
ent SQ values, and y is determined for each value of So. Then ym and KS
can be calculated by the method of Lineweaver and Burk (1934) as it is
used in enzyme kinetics. Inverting equation (6.1) and multiplying by So
results in the following equation:

— = ^i + — • (6.6)

When S0/y is plotted versus S0, the slope of the line is l/ym, and the
intercept on the so axis is -K kt_ anc^ ^b2 can be calculated from ym,
Ks, and cell yield Y, using (6.5).

The method described above is based on measurement of the spe-
cific growth rate of microorganisms, and actual consumption of substrate
is not considered. In some biodegradations, initial growth rate may not
result from assimilation of the test chemical due to, for instance,
diauxic utilization of contaminated substrate (e.g., methyl parathion,
Smith et al., 1978). In these cases, other kinetic analyses may be
used. When cell yield is constant,

X = XQ + Y(S0-S) = X0 + YAS (6.7)
220
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where AS is the substrate consumed and Y is AX/AS. Then the integration
of combined equations (6.2) and (6.7) provides:

I Ks il i K^ SX0
- lnx0 + __ ln _
t
_kbt

where t is the time after initiation of biotransf ormation, XQ is the bio-
mass of active organisms at the time of initiation, and SQ is the initial
substrate concentration. Stratton and McCarty (1967) and Knowles et al.
(1965) used these equations to obtain Kg and ^b •

When X0 « YS0 and S0 » Ks, equation (6.8) is reduced to
InAS = VJmt + ln(—-). <-D'
III I

A plot of InAS versus t should be a straight line with a slope ym.

By modification of (6.8) Moe (1970) obtained:

S2Xi

where Xi, X2, and Si, S2 are cells and substrate concentrations at
times ti, t2, respectively. Kg and k^ values can be obtained from ex-
periments with various SQ levels in which Xi, X2 and Si, S2 are measured
at tlf t2.

In continuous culture degradation systems, once steady-state is
established, dilution rate or (residence time)"1 at steady-state is equi-
valent to y at the concentrations of chemical present in the chemostats
or in the overflow from the chemostats. If the dilution rates are changed
and new steady-state concentrations are established, new values of y and
S are obtained. The values of Ks and ym are calculated by the Llneweaver-
Burk plot procedure.

Both batch degradation with low microbial populations and continuous
culture methods are labor intensive. In a mixed-culture system, the relative
components in the culture mixtures will change during the course of the exper-
iment. In Monod kinetics, cell yield Y is constant. However, due to the
production of the intermediate metabolites, which may not be assimilated
immediately during the growth, measurement of substrate disappearance does
not necessarily correspond to cell synthesis (Mateles and Chain, 1969).
This phenomenon is of particular concern at high dilation rates in contin-
uous culture when a significant portion of the metabolite may be washed out,
221
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resulting in low cell yield. Errors in kinetic constants may also develop
from parasitism or growth of organisms on autolysis products of dying, or
dead, organisms.

In batch degradations with large microbial populations and low sub-
strate levels, experiments can be performed in a relatively short time.
In these degradations, microbial populations would not change significantly
if all of the substrates were utilized for growth purposes. Degradation
rates under these conditions are pseudo-first order and can be described
by the equation

-¥-= khs (6-n)
dt b

where k^ is a pseudo-first-order rate constant. A choice of different
Xo would give a different value of k£. Therefore,

kfa/Xo = kb2 and - ~ = kb2xos. (6'12)

kb2 is the second-order rate constant for biodegradation. The
degradation rate can be calculated when XQ and S are given. The half-life
will be: 1 0
t-J- = ln2
2
Batch degradation with large microbial populations requires the
least time, needs no significant changes in total number or relative com-
ponents of organisms, and is mathematically simple to calculate. k^
can be used to estimate the persistence of a biodegradable chemical in
an acclimated environment where the level of pollution Is low.

6.7.3 Factors Affecting Biodegradation

Biodegradation involves enzymatic conversion of chemical compounds.
The environmental conditions that influence cell growth,, enzyme production,
and enzyme function will affect biodegradation rates. There are numerous
factors that affect biodegradation and their influences are interwoven.
Some of the important factors are:

• Physical and chemical properties of chemicals, such as solubility
volatility, adsorption, and chemical structure.

• Species, populations, and physiological states of the microorgan-
isms .

• Environmental conditions, such as temperature, pH, and light.

• Chemical components of water, such as dissolved oxygen and
inorganic and organic compounds.
222
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Microorganism Source

The microbial communities in natural environments differ signifi-
cantly in species and numbers present. They not only differ from place
to place, but also from time to time at the same place. No single micro-
organism species possesses all of the enzymes to catabolize all the
natural and synthetic compounds, and no environment contains all
species. Since biodegradation is performed by the action of organisms,
diversity of the microbial community in the environment is one of the
most important factors affecting the biodegradability.

In natural environments, microorganisms are always present as
complex mixed-population communities that interact with each other. Test
compounds may be competitively utilized by several different species, and
the metabolites may be utilized by other species and thus be removed from
the environment when a single species may not be able to accomplish this.
Fast removal of intermediates may either reduce the toxic effects or modi-
fy the chemical equilibrium and increase the degradation rate of the parent
compound. In the microbial communities, not only do the microorganisms
responsible for biodegradation of test chemicals interact with each other,
but other groups of organisms also interact with degradation microbes.
The interactions between microorganisms are neutralism, commensalism,
mutualism, competition, amensalism, parasitism, predation, and antibiosis
(Bungay and Bungay, 1968; Fredickson, 1977).

Microorganisms used for testing biodegradations in aquatic
environments are generally obtained from river, pond, lake, lagoon,
activated sludge, and raw sewage. Activated sludge normally contains
a wide variety and a high population of microorganisms and is considered
to be a good microbial source for biodegradation studies. River waters
have relatively low populations of microorganisms, but a greater varia-
tion of species. If it is expected that the chemicals will mainly
pollute rivers and lakes, then a river die-away test with natural water
will be a better choice.

Many synthetic chemicals to be evaluated are uncommon substrates
for microorganisms, and synthesis of enzymes capable of transforming
these compounds has to be induced or derepressed. Frequently there are
lag periods between the exposure of the chemicals to the organisms and
the initiation of biodegradation. A lag—or acclimation—period is re-
quired for the organisms to manufacture the enzymes capable of degrading
the chemical or for mutant organisms to develop that can degrade the
chemicals. A lag period may also result from too small numbers of degra-
dation microbes being initially present in the system. In the early
growth state, the substrate consumed is not significant until the cells
reach a high population level. When other readily utilizable organic
compounds are present in the system,.the acclimation period may be
caused by diauxic utilization of substrate by microorganisms. The length
of the acclimation period will vary with the structure and concentration
of the test chemical, the chemical compositions of the water, the types
and numbers of organisms present, and other environmental conditions.
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Monod kinetics is applicable if the lag period is caused by
too low a microbial inoculation (Braun and Berthauex, 1970) ; mathematical
treatment is difficult if acclimation is caused by physiological adjustments
of the microbial community. A biodegradation rate constant can be obtained
when the acclimation period is over and when the microorganisms are actively
consuming the chemical. However, when a chemical is first released into
a place where no previous history of exposure exists, the time required for
acclimation cannot be ignored. This information can be obtained through
the river die-away type of test with various water bodies.

Concentration of Test Chemical

The concentrations of test chemicals to be used are decided
by realistic pollution levels, solubilities, toxicities, and sensitivity
of analytical procedures. As expressed in Monod kinetics, the initial sub-
strate concentration in the growth media will affect the specific growth
rate, and the substrate utilization rates are slower at low substrate con-
centrations. Low chemical concentrations also affect acclimation periods
and extents of degradation (Pfeil and Lee, 1968). At too low concentra-
tions, high-adsorption compounds may not have enough "available substrate"
for microorganisms to grow. Certain microorganisms are apparently totally
unable to grow when their organic carbon sources are present in minute concen-
trations (Alexander, 1973; Boethling and Alexander, 1979). At high substrate
concentrations, the Monod equation predicted that the degradation rates are
independent of substrate concentration. Many chemicals are, however, toxic
or inhibitory at high concentrations, which decrease the utilization rate through
inhibition of enzyme action, repression of enzyme production, inhibition of
microbial growth, or killing of the organisms. Edwards (1970) discussed mech-
anisms causing substrate inhibition and used them to derive five mathematical
models.
Additional Organic Compounds

The presence of additional organic compounds in the test media
may either enhance or repress the biodegradation of testing compounds
in several different ways. For instance, some extra organic compounds
may provide energy and carbon for microorganisms to grow extensively and
increase both the biomass of microbes responsible for the biodegradation
and the utilization rate. They may also increase the growth of nonrelated
organisms. Monod kinetics will be hard to apply under these conditions,
since the equation is for the growth-limiting substrate concentrations
with regard to cultures responsible for degradation.

The additional organic compounds may be an essential nutrient
for the microorganism. A compound that is a structural analog of a test
chemical may help induce enzyme(s) and reduce the acclimation period.

An additional compound may act as a cometabolic substrate for
some compounds. Cometabolism is very important in biodegradation. This
is a phenomenon in which an organic compound may be transformed only when
another organic compound(s) is (are) present to serve as a carbon and
energy source. This cometabolic substrate may be a structurally analogous

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compound or may be unrelated. For example, it was demonstrated that
benzothiophene was not degraded unless naphthalene was also added to the
inorganic nutrient media (Chou and Bohonos, 1979). Various mixed organic
compounds are present in the natural environment, and very often pollu-
tants from industrial plants are mixtures of compounds of which many are
chemically related. Thus, test procedures to evaluate the biodegrada-
bility of a specific chemical as a sole carbon source may often under-
estimate the rate of biodegradation versus the rate in a natural water
or soil sample that contains many organic compounds capable of acting
as cometabolites (Horvath, 1972).

The presence of readily metabolizable carbon sources may be
preferentially utilized, cause catabolic repression or enzyme inhibition.
Degradation of test chemicals may not take place until this extra
carbon source is exhausted. This phenomenon is referred to as a diauxic
process. The diauxic effect of glucose in mixed substrate on other com-
pounds with heterogeneous mixed culture has been investigated extensively
(Gaudy et al., 1964; Stumm-Zollinger, 1966; Sikka and Saxena, 1973).
Even in a laboratory, the media prepared from distilled water may be con-
taminated with small amounts of organic compounds; although the concen-
trations are low, they may still be high enough to cause interference in
growth rate studies when low concentrations of a test chemical are used
with a low level of inoculum (e.g., methylparathion in Smith et al., 1978).

The possibility also exists that coexisting compounds or meta-
bolites at appropriate levels may be toxic or mutagenic to biodegradation
microorganisms.

Inorganic Salts

Microorganisms require elements other than carbon—such as
nitrogen, phosphorus, sulfur, magnesium, and some trace elements—for
their growth and functions. Some salts, such as phosphates, are added to
media for their buffering capacities. Many different mineral salts
media have been used in biodegradation studies. No attempts have been
made to determine whether variations in the composition of the mineral
salts medium affect the biodegradability of a chemical compound, but
the effect is probably small (Howard et al., 1975).

For biodegradation studies on some compounds, modification of the
protocol may be needed. For instance, phosphonate compounds are biode-
graded only when these compounds serve as a phosphorus source for bacteria
in phosphate-deficient media (Cook et al., 1978). In some studies on
biodegradation of dibenzothiophene, the heterocyclic sulfur was the only
supply of sulfur in the media (Hou and Laskin, 1975).

Dissolved Oxygen

Oxygen generally serves as the terminal electron acceptor in
oxidation of chemical compounds. Microorganisms are generally classified
as obligatory aerobic, obligatory anaerobic, or facultatively anaerobic,
depending on their requirements and sensitivity to molecular oxygen.

225
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The presence or absence of dissolved oxygen will decide the types of
microbial communities in the system. With low levels of organic 'compound
and low microbial populations, occasional stirring of the media water
may provide sufficient amounts of oxygen. With high microbial popula-
tions, extensive aeration is required. Generally, aerobic biodegradation
of organic chemicals is faster and more extensive than anaerobic processes,
but some compounds, such as chlorinated hydrocarbon pesticides, are more
susceptable to biotransformation under anaerobic conditions (Hill and
McCarty, 1967).
All microorganism species have their optimum pH for growth and
enzyme reactions. For most species the optimum is near neutral (pH 7) and
they cannot grow in a strongly acidic or a strongly basic environment.
Consequently, most biodegradations take place at a pH near neutral, al-
though some organisms can grow in either an acidic or a basic environment
and metabolize the substrate.

Changes in pH take place when microorganisms consume acidic or
basic compounds or produce sufficient concentration of ionic metabolites.
The pH is often maintained by adding buffer reagent to the test media.

Temperature

Temperature can also affect biodegradation in two ways: it can
cause a change in individual physiological activities, or a change in popu-
lation characteristics of mixed culture communities of microorganisms.
Under specific conditions, each microbial strain has an optimum temperature
for growth, which is not necessarily the optimum condition for each enzyme
system or physiological action of the microbe. Generally, the higher the
temperature, the more rapid is the biotransformation process. Biodegrada-
tions are very slow near freezing point. When the temperature rises to
above the optimum, inactivation of enzymes and a decrease in the reaction
rate result. Most organisms have optimal growth temperatures (and con-
sequently, normal overall metabolic action) at temperatures from 20 to
37°C, but some thermophilic or psychophilic organisms would exhibit growth
and/or survival at higher or lower temperature ranges.

A change in temperature will result in change in population and
composition of the microorganisms in the mixed culture system.

The Arrhenius relationship may be applicable to express biode-
gradation rates as a function of temperature over narrow ranges (Moe,
1970). However, this expression does not apply to the ranges above
optimum temperature and changing population of a mixed culture.
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6.7.4 A Review of Aquatic System Biodegradability Tests

Test procedures for conducting biodegradability tests have varied
considerably in equipment used, conditions controlled, and complexity of
operations. As discussed earlier, numerous factors may affect biodegrada-
tion. Attempts have been made to simulate many different environmental
conditions. Generally, there are two major types of test—static tests,
which simulate natural water systems; and dynamic tests, which simulate
biological wastewater treatment plant systems.

Typical methods include the river die-away test, the shaker flask
test, the continuous and semicontinuous activated sludge tests, and
the model ecosystem. Some of them use a simple glass container, but
others use highly complex, continuous culture equipment. A review of
the state of the art in biodegradation methods was made by Howard et
al. in 1975.
River Die-Away Test

This test has been used by many investigators because of
its simplicity and cost efficiency. It involves collection of raw
water from rivers, lakes, or other natural water bodies, addition of
a test chemical to the water, and analysis of water samples at various
intervals for disappearance of the parent compound or the product(s)
formed. The microbial populations are generally low, varying with the
site and the season of collection. The container used may be a 1-liter
mason jar, a 4-liter glass bottle, or a 5-gallon carboy bottle. The
water sample used may vary from less than 1 liter to 20 liters. The
incubation time for the sample may range from a few days to 8 weeks,
depending on time of acclimation and rate of biodegradation of the test
chemical. The containers are mixed and aerated by periodic shaking,
magnetic stirring, or sparger aeration.

The water samples vary in chemical and microbial compositions,
with the site or time of sampling in the same water body and with differ-
ent water bodies. However, the river die-away test is the closest simula-
tion of biodegradation conditions in natural aquatic environments.

The test, originally described by Hammerton (1955) in a
study of sodium lauryl sulfate, is employed by many investigators who use
water samples as microbial sources and growth media. Other investigators
have added microorganisms for faster biodegradation; for example,
natural water has been seeded with activated sludge (Garrison and
Matson, 1964), centrifuged sewage effluent or river water (Hitzman, 1964).
Others have added a pH buffer or extra nutrients (Sheers et al., 1967;
Smith et al., 1977).
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In some procedures, defined synthetic media have been used to
minimize the variability of the water components; in this case, the sewage
or natural water microorganisms are inoculated into the test media
(Bunch and Chambers, 1967; British STCSD, 1966). One special method of
doing this is the Biochemical Oxygen Demand (BOD) test, which measures
dissolved oxygen consumption (APHA, 1971).
Shaker Flask Test (SF)

In this test, microorganisms from natural sources are inoculated
into shaker flasks containing basal salts media with test chemicals. The
media are standardized to use defined nutrients, thereby reducing the
variability of the chemical components found in natural water. The
flasks used range from 250 ml to 2 liters in volume. Sources of inocula
used are water, activated sludge, sewage, soil, air-dried or lyophilized
sludge, and air microbes. Acclimated cultures developed by the shaker
flask test, the river die-away test, or the activated sludge test are
used with the shaker flask method to study the degree or rate of degradation
(Smith et al., 1977; SDA, 1965; Paris et al., 1975).

The flasks are normally aerated in shaker incubators, water
samples are withdrawn periodically, and degree of biotransformations are
determined. Gledhill (1975) used flasks equipped with ll4C02 traps for
ultimate biodegradation as well as for primary biodegradation studies.

The Soap and Detergent Association (SDA, 1965) adopted the
shaker flask method for a presumptive test of biodegradability of deter-
gents. The seed was adapted by making two 72-hour transfers, then
conducting the test in the third generation of flasks. The Organization
for Economic Cooperation and Development (1976) also adopted the shaker
flask method for a screening test without adaptation.

Swisher (1968) used a 2-week transfer for the shaker flask
adaptation and degradation studies because a 72-hour or a weekly transfer
was too short for some compounds that were tested.
Continuous Flow Activated Sludge (CAS) System

There are many kinds of equipment that attempt to simulate
different types of biological treatment plant conditions, or
biodegradation in water containing high microbial populations that are
continuously fed with chemical compounds and other nutrients, organic
and inorganic. In general, such equipment consists of either a
reactor that both agitates and aerates the material or a system that has
separate aeration and settling compartments. One typical continuous
system is the official method described by the German Government in
1962. The equipment consists of a 3-liter (working volume) aeration
vessel and a sedimentation vessel that has a feeding rate of 1 liter per
hour.

228
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Swisher (1964) designed a miniature continuous-flow vessel that
can operate in a much smaller space and requires smaller amounts of feed.

Semicontinuous Activated Sludge (SCAS) System

In this procedure, the feed is added periodically rather than
continuously. The operation is a fill-and-draw process. A typical
procedure is that used by the SDA (1965) as a confirming test. Detergent
in synthetic nutrient solution is fed into an aerated vessel; after
23 hours of aeration, the mixture is allowed to settle and the super-
natant is removed. New feed is then added and the process is
repeated. Synthetic "sewage" normally includes organic nutrients.

Nitrilotriacetic acid was the sole carbon source in the SCAS
method used in studies by Swisher et al. (1967).

Fitter (1976) used a 1-liter cylinder as semi-continuous
activated sludge equipment to adapt microorganisms for the die-away type
of biodegradation test. The SCAS method is used by some investigators
as an adaptation procedure for seed to be used in biodegradation studies
(Maurer et al., 1974).

Various other systems, such as trickling filters, septic
tanks, and cesspools are used to study aerobic and anaerobic biodegradation.
Official Procedures for Testing Detergents

Most of the early aquatic chemical biodegradability tests were
concerned with household detergents. Because of their widespread use and
the large amounts involved, standard testing methods for such detergents
have been adopted in many countries. In the U.S., the Subcommittee on
Biodegradation Test Methods of the SDA in 1965 adopted a two-step bio-
degradation procedure for aiiionic surfactants alkyl benzene sulfonate
and linear alkylate sulfonate. The shaker flask technique is used as
the presumptive test and the SCAS method is used for a confirming test.
The tests are conducted at 25° + 3° C. In the shaker flask test, the
chemical is considered to be adequately biodegradable when monitoring
by methylene blue colorimetric analysis on the 7th and 8th days if the
3rd-transfer flask shows 90% elimination fron 30 mg/liter; less than
80% elimination is not considered to be adequately biodegradable.
If reduction of surfactant is between 80 and 90%, its biodegradation
must be confirmed by another test. In the confirmatory test (the SCAS
test), the material (20 mg/liter) must be degraded by at least 90% to
be considered adequately biodegradable. This two-step degradability
test is a fail-safe type and does not provide the data for rate of bio-
degradation. The two 72-hour adaptations in shaker flasks may be justified
for testing the adequacy of biodegradation of a surfactant, but some compounds
require longer acclimation periods (Garrison and Matson, 1964; Swisher,
1968; Rogers and Kaplan, 1974). The 24-hr fill-and-draw SCAS method

229
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may not exactly simulate a sewage treatment plant, but it requires smaller
amounts of feed, simpler equipment, and less labor than does the continuous
method.

The West German Government in 1962 adopted a continuous sludge
system for testing anionic surfactant, in which synthetic sewage (organic
medium) containing 20 ppm methylene blue active surfactant was fed at
3-hour retention-time rates. Biodegradability was based on percent
removal of methylene blue active surfactant between influent and effluent.
This method more closely simulates sewage treatment plant operation.
However, it requires a long operation period, bulky equipment, large
volumes of feed, and a high labor cost. Another disadvantage to its
use is the difficulty in maintaining stable biochemical operations and
satisfactory circulation of sludge (Stennett and Eden, 1971).

The British Standing Technical Committee on Synthetic Detergents
(STCSD, 1966) recommended a sludge die-away type of rapid screening test
for anionic surfactant. The method used air-dried activated sludge as
an inoculum, which was incubated with BOD dilution water containing the
detergent (20 mg/liter). Aeration was by gentle stirring or by blowing
air across the surface of the liquid. This method is an attempt to use
standardized medium to reduce the variability of the river die-away test.

The Organization for Economic Cooperation and Development (OECD,
1971, 1976) adopted a. shaker flask method for a screening test (static
test) and a continuous activated sludge method for confirmatory test
(dynamic test) to determine biodegradability of anionic and nonionic
surfactants. In a shaker flask, medium containing mineral salts and
the surfactant (5 mg/liter) is inoculated with mixed aerobic micro-
organisms (preferably activated sludge) and incubated on the shaker for
up to 19 days at 25 C. The final percentage degradation is that
obtained when the degradation curve reaches a. plateau, or at the 19th day,
whichever is earlier. "Soft" and "hard" anionic standards are used as
references. The activated sludge method is the official German method,
except that filtered activated sludge is used as the inoculum. The
anionic surfactants (20 mg/liter in synthetic sewage) are measured by
methylene blue colorimetry; the nonionic surfactants (10 mg/liter) are
measured by precipitation with tetraiodobismuthate.
Comparison of Test Results

Cook (1968) compared the results of biodegradability tests of
several different alkyl benzene sulphonates (ABS) by the bottle die-away
test, the SDA shaker culture test, the official German method, the
SDA-SCAS method, and the recirculating filter method. The SCAS and
recirculating filter methods gave maximum results, and the German method
generally gave the lowest results. The bottle die-away and shaker culture
tests yielded average and similar removal percentages.
230
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Truesdale et al. (1969) studied British STCSD die-away tests,
the official German test, the SDA-SCAS test, and the recirculation filter
test and compared these with a pilot-scale percolating filter method.
The die-away method gave a high percentage of removal for "soft"
anionic materials, compared to other methods, but the percentage was low
for "hard" or "slow to acclimatize" ABS. Similar results were obtained
with the official German method. The SCAS and recirculating filter
methods yielded higher results.

Mausner et al. (1969) described the results of interlaboratory
biodegradability testing of several nonionic surfactants by SDA member com-
panies. After testing several different methods, they concluded that the
SCAS type seems to be the best approach because of its higher reproduci-
bility, but that no single standard method existed at that time for all
types of nonionic surfactants. They attributed part of the problem to
lack of a good general analytical method.

The reproducibility of the river die-away test was studied by
Weil and Stirton (1964), using several anionic and nonionic surfactants.
Sodium dodecanesulfonate was used as a standard to check the biological
activity of river water samples. They tested five samples taken from the
same spot in the Schuylkill River at various times. Except for one sample
taken after a severe summer drought, all the curves of disappearance of
the chemical versus time were nearly the same. In tests of waters from
three diferent rivers, biodegradation appeared to proceed at about the
same rate.

Setzkorn et al. (1964) presented data showing reproducibility
of linear alkylate sulfonate (LAS) in various river waters and in various
samples of Mississippi River water. They also reported large differences
between CIQ, C}2 and C^, C}6 LAS in the adaptation period; however,
when the compounds were readded to the water at 95% degradation time, their
degradation rate was not significantly different.

Borstlap and' Kortland (1967) pointed out that with the river
die-away test, data can be obtained on adaptation time, biodegradation
rate, and the amount of surfactant residue (if degradation is not
complete). In tests with alkylaryl sulfonate surfactants, the degra-
dation curves showed that some surfactants had different adaptation
times but comparable degradation rates.

The Office of Toxic Substances, EPA, is preparing guidelines
for premanufacture testing of new chemical substances (1979). The
EPA has also tentatively proposed biodegradation test methods for
assessing persistence of a chemical substance in a natural environment.
The methods include the shaker flask method, the C02 evolution test, the
BOD test, the SCAS method for aerobic biodegradation, and the methane
and CDs production test for anaerobic biodegradation. The recommended
acclimation method for shaker flasks is several 48- to 72-hour transfers,
up to 13 days. These biodegradations are monitored by disappearance
of dissolved organic carbon (DOC), C02 and/or methane evolution and

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uptake of oxygen. Although the proposed methods are the best available,
being simple and low in cost, they may have some drawbacks when used
in biodegradation rate studies. The evidence for biodegradation is
indirect and no information of disappearance of the parent compound is
obtained. The 48- to 72-hour transfers may be too short for chemicals
requiring long adaptation periods. In the SCAS method the SDA confirm-
atory method is used for acclimation and screening tests; then the
acclimated sludge is used for the degradation rate study with inorganic
salts and the die-away operation. The test chemical is added at levels
up to 100 and 200 mg/liter as a total organic carbon because DOC is used
for the measurement. This high test concentration may not be applicable
to many organic compounds that have low solubilities or high toxicities.
Biodegradation Rate Studies

Most biodegradability studies in the literature are qualitative
in nature. The investigations were undertaken a) to determine whether
biodegradation took place, b) to isolate microorganisms responsible for
the biodegradation, and c) to use these isolates to study the metabolic
pathways. Generally, quantitative studies were not made to obtain
degradation rates and kinetic constants. Research is needed for quanti-
tative measurement of biodegradation so that the rate constant can be
used for assessment of the environmental fate of chemicals.
Mathematical expression was first empirically obtained by
Monod (1949) to relate microbial growth rate to growth-limiting substrate
concentration with a pure culture. Some modifications have been proposed
(Contois, 1959; Powell, 1967) and different expressions have been used
(e.g., Kono, 1968; Verhof et al., 1972). The Monod kinetics have also
been applied to sewage treatment systems (Benedick and Horvath, 1967;
Gaudy and Gaudy, 1967; Jones, 1973). Several attempts have been made
to use substrate disappearance curves in batch systems to determine
values for Xo, Kg, and ym. Knowles et al. (1965) applied the computer
method, Gates and Marlar (1968) applied the graphical method, and
Stratton and McCarty (1967, 1969) applied both methods. Rapid measure-
ment of Ks with soluble substrates was proposed by Williamson and
McCarty (1975).

Uptakes of organic substrates such as glucose cind organic
acids were measured by adding C-labeled compounds to marine water or
lake water samples, incubating for definite periods of time, and
determining the amount of labeled carbon contained in the cells.
Although the relation between the substrate concentrations and uptake
rates is a hyperbola similar to the Michael-Menton equation (Parsons
and Stickland, 1962; Wright and Hobbie, 1965; Vacarro and Jannasch, 1967;
Robinson et al., 1973), the amounts of labeled carbon in the cells
differ from the amounts of parent compound metabolized (Hamilton and
Austin, 1967).
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Eichelberger and Lichtenberg (1971) studied the persistence of
28 common pesticides in river die-away testing over an eight-week period
at a concentration of 10 pg/liter. They determined the relative
persistence of these pesticides; however, the samplings were not frequent
enough to obtain degradation curves for a rate study.

Fitter (1976) adapted microorganisms in the SCAS method and used
them to study the degree and rate of biodegradation of 123 organic
compounds in terms of chemical oxygen demand (COD). The test chemicals
were used as the sole carbon source in the batch test system, which
contained 200 COD/liter, with 100 mg of dry matter/liter of adapted
sludge as inoculum. The rate of degradation was expressed in mg of
COD removed by 1 gram of the initial dry matter of inoculum per hour.
Moe (1970) used the modified Stratten and McCarty (1967) equation of the
Monod expression to obtain degradation constants for isopropyl carbanilate
and isopropyl m-chlorocarbanilate.

Paris et al. (1975) applied the Monod equation in a biodegradation
study of malathion. Several low levels of the pesticide in flasks were
inoculated with washed, acclimated, mixed microorganisms. The second-
order biodegradation rate constant kb2 obtained was compared with the
value calculated from the ym , K , and Y obtained. They found that these
values were in agreement at low bacterial and malathion concentrations.
They also applied this method to obtain second-order constants for bio-
degradations of the butoxyethyl ester of 2,4-dichlorophenoxyacetic acid
(2,4-D) and Methoxychlor .

Smith et al . (1977, 1978) studied chemical transportation,
chemical transformation, and biodegradation of 11 compounds, obtained
rate constants of each pathway, and used these values in a computer
model to predict the fate of the chemicals in ponds, rivers, and lakes.
Biodegradation -studies of several water samples were first conducted with
river die-away type screening tests in aerated bottles. Once biodegradation
took place, acclimated cultures were enriched in shaker flasks and trans-
ferred; one of the enriched mixed systems was used for a rate study for
each chemical. One or more methods, including batch biodegradation with
low level of inoculum, continuous culture method, and batch biodegradation
with high populations of microbes and low substrate concentrations,
were used to obtain rate constants for p-cresol, quinoline, benzoquinoline
9H-carbazole, and dibenzothiophene.

Paris et al . (1978 and 1981) collected several waters from rivers and
ponds and conducted the river die-away test with the butoxyethyl ester of 2,4-Dr
Malathion, and Chloropham to study the variability of different waters.
The amount of pesticides used was less than 1 mg/liter, and bacterial and
pesticide concentrations were monitored. Due to low concentrations of
substrate added, the investigators found no significant change in the bac-
terial populations caused by the metabolism of the pesticides. Malathion
and 2,4-D ester were readily hydro ly zed. Chloropham required long acclima-
tion periods. The degradation curves were pseudo-first order. Although bac-
terial populations are very different, the second-order rate constant cal-
culated from the curves and bacterial counts showed that variation of rate
constants among the natural waters were small.
233
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Rogers, M. R., and A. M. Kaplan. 1974. Biodegradation of Some Sulfur
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Setzkorn, E. A., R. L. Huddleston, and R. C. Allred. 1964. An Evaluation
of the River Die-away Technique for Studying Detergent Biodegradabil-
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Sheers, E. H., D. C. Wehner, and G. F. Sauer. 1967. Biodegradation of
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1410-1416.

Sikka, H. C., and J. Saxena. 1973. Metabolism of Endothall by Aquatic
Microorganisms. J. Agr. Food Chem. 21: 402.

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Smith, J. H., W. R. Mabey, N. Bohonos, B. R. Holt, S. S. Lee, T.-W. Chou,
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Soap and Detergent Association (SDA). 1965. A Procedure and Standards
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237
-------
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Stratton, F. P., and P. L. McCarty. 1967. Prediction of Nitrification
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Stratton, F. P., and P. L. McCarty. 1969. Graphical Evaluation of the
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238
-------
CHAPTER 7. VOLATILIZATION FROM WATER

J. H. Smith and D. C. Bomberger

7.1 INTRODUCTION 240
7.2 SUMMARY 240
7.3 CONCLUSIONS 241
7.4 RECOMMENDATIONS 242
7.5 SCREENING TESTS 242
7.5.1 Purpose 242
7.5.2 Procedure 242
7.6 DETAILED STUDIES 244
7.6.1 Purpose 244
7.6.2 Procedure for High Volatility Compounds 244
Introduction 244
Apparatus 245
Calibration of the Apparatus 245
Measurement of k^/k° 247
Data Analysis 248
Calculation of k^/k0 250
7.6.3 Procedure for Low Volatility Compounds 251
Introduction 251
Apparatus 251
Calibration of the Apparatus 251
Experimental Procedure 252
7.6.4 Procedure for Intermediate Volatility Compounds 254
Estimation of Environment Rates of Volatilization 255
7.7 BACKGROUND 256
7.7.1 Equilibrium Thermodynamics of Dilute Non-Ideal Solutions 256
7.7.2 Two-Film Theory 260
High Volatility Compounds 264
Low Volatility Compounds 266
7.7.3 Penetration Theory 269
7.7.4 Summary of Experimental Results 272
7.7.5 Estimation of Diffusion Coefficients 273
Diffusion in Liquids 273
Diffusion in Gases 274
7.7.6 Calculation of Environmental Volatilization Rate Constants .... 275
High Volatility Compounds 275
Low Volatility Compounds 275
7.8 REFERENCES 278
239
-------
7. VOLATILIZATION FROM WATER
7.1 INTRODUCTION

Volatilization of a chemical that is dissolved in a water body is the
transport of the chemical from the water body to the atmosphere. The concen-
tration of the chemical in water decreases even though a transformation does
not occur, but the water body serves as an "area source" of emission of the
chemical to the atmosphere. Thus, while the exposure of the aquatic environ-
ment to the chemical decreases, the exposure of the air environment increases.
However, the amount and rate of dilution of the chemical in the air may be so
fast that the atmosphere exposure is not a significant hazard.

Current evidence suggests that volatilization is likely to be the major
aquatic fate of low molecular weight, nonpolar compounds that are not rapidly
biodegraded or chemically transformed. Volatilization rates of higher molec-
ular weight compounds can also be significant under certain conditions. The
protocols of this chapter represent the current state of the art methodology
for predicting the volatilization rates of chemicals in aquatic environments.
The background section is a critical review of the bases for the proposed
methods.
7.2 SUMMARY

Screening and detailed laboratory test protocols for volatilization of
chemicals have been prepared to enable the investigator to estimate the vola-
tilization rate constants and half-lives of chemicals in several representative
water bodies. Only chemicals with half-lives of less than three months in
small rivers are considered for detailed studies.

The test protocols are based on an extensive body of chemical, chemical
engineering, limnological, and oceanographic literature on mass transport
phenomena. The screening studies are made by predicting the volatilization
rate constant from the physical and chemical properties of the chemical. The
recommended protocols for the detailed tests are cost-effective and simple to
use for a wide range of chemicals.

The screening tests for volatilization of the chemical from water require
data for the following physical properties: melting or boiling point, solubil-
ity in water at 20°C, vapor pressure at 20°C (which can often be estimated),
and, if possible, the Henry's law constant. The heat of fusion is usually
required for solids, if the Henry's law constant has not been measured. These
data, plus the chemical structure, are used to estimate the volatilization
rate constant.

240
-------
The protocols for the detailed laboratory tests require first that the
compound be classified as a low or high volatility compound, which is done on
the basis of the screening test. For high volatility compounds, the ratio of
the volatilization rate constant of the chemical, k^ , to the oxygen reaera-
tion rate, k0,, is measured over a range of stirring rates. Then, since values
of k for representative water bodies are available, k^ in the environment can
be calculated, since

(k°) = (kC/k°)1 , (k°) (7.1)
v env v v lab v env
C 0
Similarly, for low volatility compounds, the fiatio of k to k and the gas-
phase mass transport coefficient for water, kg, is measured at several
stirring rates. Then, k^ in the environment is

f.C
k
(kC) =l^\ nab .Wx
\ v/env I , W I L \ g /env
<. I, , env &
g /lab
where L.. , is the solution depth of the laboratory apparatus and Lenv is the
depth or the water body. These procedures are applicable to any well-mixed
water body for which the values of k and k can be estimated.
' v g

7.3 CONCLUSIONS

The present knowledge of the theory and experimental aspects of volatili-
zation of high volatility compounds when liquid phase mass transport resistance
controls the volatilization rate provides a sound basis for the recommended
protocols. These protocols have been evaluated in our laboratories during
several research programs. However, the protocol for medium and low volatil-
ity compounds are based on our assessment of the theoretical aspects of vola-
tilization when gas phase mass transport limits the overall volatilization
rate plus preliminary laboratory validation studies. These procedures have
not been adequately verified in the laboratory. In both cases, the laboratory
measurements are relatively simple to perform and require common laboratory
equipment.

The screening test protocol can be used to determine if the chemical
should be classed as high or low volatility. It can also be used to calculate,
with good accuracy, the volatilization rate constant ratio, ky/k°. Values of
ky/k for low volatility compounds can be estimated, but the accuracy of the
estimation procedure is known for only a few chemicals.

The detailed test protocols can be used to measure k /k and k^/k with
good accuracy and precision in the laboratory. The accuracy of the predicted
values of (k~) depends on the accuracy of the literature or estimated val-
ues of (k^) or (k^) for the specific water body. The techniques are
excellent for estimating (k^) for streams and rivers. The corresponding
procedures are inadequate for ponds and lakes.

241
-------
7.4 RECOMMENDATIONS

The protocol recommended for medium and low volatility compounds should
be subjected to an extensive laboratory validation program. Measurements of
ky, k^, and kg should be made at several temperatures, stirring rates, and
wind velocities.

0 W
The techniques for predicting ky in ponds and lakes and k in streams and
rivers should be reviewed. Field studies should be devised ana carried out to
validate the procedures.

7.5 SCREENING TESTS

7.5.1 Purpose

This screening test protocol is intended to classify chemicals as high,
medium, or low volatility and to identify chemicals with volatilization half-
lives of less than three months.

7.5.2 Procedure

The following physical property data for a chemical must be available
or measured before proceeding with the screening test.
• Melting point (Tm, °C)
• Solubility in water at 20°C (Csat, g liter"1 and mole liter"1)
Either
• Henry's law constant, at 20°C (HC, torr liter mole )
or
• Vapor pressure at 20°C (P , torr)
« Heat of fusion, if the chemical is a solid at 20°C and if the
vapor pressure data used to calculate Hc (next section) is for
the liquid (AH,., cal mole"1).
The screening test consists of calculating the value of the Henry's law con-
stant, HC, which is used to determine if the environmental half-life for
volatilization is less than about three months.

Henry's law is expressed as

PC = Hc[C] = HcCw (7.3)

where P is the partial pressure (in torr) of the chemical C above an aqueous
solution (that is, at or below the solubility limit of the chemical) at a
*
A series of aromatic compounds, such as naphthalene, anthracene, pyrene, and
benzfV]anthracene, are being studied at SRI under a grant from the National
Science Foundation.
If a measured value of the Henry's law constant of the chemical in water is
available, the calculation steps should be omitted.

242
-------
concentration [C ] = Cr, (in moles liter ^= M). . Then H is the Henry's law
constant expressed in units of torr M~ .

The value of H for a gas is obtained by measuring solubility of the
gas in water at several partial pressures. Then H is the slope of a plot
of the partial pressure (torr) versus its concentration of C in solution (M)
(plotted as the abscissa) as the concentration approaches zero, using a
graphical method. If measurements of gas solubility are required, the reader
is referred to the review by Mader and Grady (1971) for specific measurement
techniques.

The value of H at 20°C can be measured (Mackay et al., 1979) or
estimated from the vapor pressure and the solubility in water, using equation
(7.5)

H = PC/C t (7.5)
c v sat

where Pv is the vapor pressure of pure C and C is the solubility of pure C
in water (M) at 20°C, provided the values of P^ and Csat are for the
same phase (both solid or both liquid).

If the vapor pressure of the chemical is available only at some temper-
ature other than 20°C, the integrated form of the Clausius-Clapeyron equation

AH
r f I III
(7.6)
1.987 T 293
can be used to estimate the vapor pressure at 20 C provided there is no phase
change; P~ is the vapor pressure at temperature T~ (K) , P-^ is the vapor pressure
at 293 K, and AR^ is the heat of vaporization (cal mole~l). This extrapolation
may not be accurate over a wide temperature range. Therefore, if possible, the
vapor pressure should be measured at 20°C. Methods for measuring vapor pressure
(Thomson and Dovslin, 1971) and solubility (Mader and Grady, 1971) have been
reviewed.

If the chemical is a solid at 20°C and the vapor pressure data at T~
are for the liquid phase of the chemical
An alternative definition of Henry's law, which is often used, is

Cg=HCw (7.4)

where C is the concentration of the chemical in the gas phase. In this
case, Cg and CL, are expressed in the same units of concentration, such as
g liter~l, and H is unitless. Other units of H, such as torr and atm m^
mole~l can be used, provided appropriate units for the partial pressures
and concentrations in the liquid are also used.
243
-------
H =
c
2£
exp
"sat
1.987
exp
582.2
(7.7)
where P~ is the vapor pressure of the chemical in the liquid phase at temper-
ature T2, Tm is the melting point (K), and Hf is the heat of fusion (cal
which is easily measured with a differential thermal analyzer.
The volatilization behavior of a chemical can be divided into three
classes that depend on the value of H
High volatility:

Intermediate volatility:

Low volatility:
These are:

.-1
H > 1000 torr M
c
10 < H < 1000 torr M
c
H < 10 torr M'1.
c
Volatilization is likely to be an important environmental fate for
chemicals that fall into the high and intermediate volatility classes. In
these cases, detailed studies should be carried out. The case of low vola-
tility compounds is not as clearcut.

In Section (7.7.6) it is shown that if H is greater than about
2 torr M"1, the half-life for volatilization of £he low volatility compound
may be less than about 3 months. If screening studies suggest that other
processes, such as photolysis and biodegradation, are slow, detailed vola-
tilization rate studies should be carried out. Clearly, the researcher must
exercise careful judgment in deciding if detailed volatilization studies are
needed if H is between 0.5 and 10 torr M"1.
7.6 DETAILED STUDIES

7.6.1 Purpose

This detailed test protocol is intended to provide estimates of the
volatilization rate constant of a chemical from typical natural water bodies.

7.6.2 Procedure for High Volatility Compounds

Introduction

The basis of the test procedure for high volatility compounds is the
measurement of the ratio of the volatilization rate of the chemical to the
oxygen reaeration rate constant,
(7.8)
The oxygen reaeration rate, R , is
R
v
dt
244
-------
where k is the oxygen reaeration rate constant, [02 ]s is the concentration
of oxygen at saturation and [02]t is the oxygen concentration at time t.
Q
The volatilization rate of the chemical, RV> is defined by
(7'9)

where kC is the volatilization rate constant of the chemical' and [C]t is the
concentration of the chemical in moles liter"1 (M) .
C C
The value of k in the environment Ck ) , can be calculated, pro-
vided estimates (or measurements) of (k ) ¥o?n^he specific water body are
available, since

(k°) = (kC/k°), ^ (k°) (7.1)
v' env v v lab v env

Apparatus

The recommended apparatus, which is shown in Figure 7.1, consists of
a 2-liter beaker modified with two 0.635-cm (1/4-in.) O.D. tubing connections
at the bottom. The probe of the dissolved oxygen analyzer is mounted in a
glass holder to maximize the flow velocity past the membrane and minimize the
hold-up volume. The water is circulated past the oxygen probe with a small
pump. The Cole Palmer All-Teflon metering pump No. 7180 is recommended be-
cause it is all Teflon; other pumps might be satisfactory. The aqueous
solution is stirred with a constant-speed stirring motor, such as Scientific
Products Catalog No. 47980-1 equipped with a propeller stirrer. Close
temperature control is not required because the value of k^/k^ is independent
of temperature, within experimental error (Smith et al., unpublished results).

Calibration of the Apparatus

The relationship between k and the stirring rate for the system
should be determined before measurements of k /k^ are made. The procedure
is as follows. Calibrate the dissolved oxygen analyzer in air, according to
the manufacturer's instructions. (This calibration is not critical, since
the instrument is recalibrated at the end of the experiment.) Place the
probe of the dissolved oxygen analyzer in the glass holder. Fill the beaker
with about 1600 ml of distilled water. Start the recirculation pump. Purge
the oxygen from the water using reagent grade nitrogen, which is bubbled
through a glass frit on the end of a long glass tube that has been placed at
the bottom of the beaker. Monitor the decrease in the oxygen concentration
with the dissolved oxygen analyzer. When the oxygen concentration is less
than 1.5 ppm, remove the sparger and start the stirrer motor. Adjust the
stirring speed to a preset value, which can be the revolutions per minute or
an arbitrary setting on the motor speed controller. Begin monitoring the
oxygen concentration as a function of time. At least 15 observations of the
oxygen concentration [62 ]t should be taken, and the dissolved oxygen concen-
tration should be greater than 8 ppm before the experiment is ended. At the
end of the experiment, increase the stirring speed and allow the oxygen con-
centration to reach a constant value, [02 ]s and note this value.
245
-------
co
Q
Z
o
o
<
o
CC
o
LL
in
cc

S
Q.
<
at

5
oc
<
O
r»
LU

246
-------
A plot of log (L02]S - [02 ]t) versus t (in hours) should be a
straight line. The slope of this line is -0.434 k^. The value of k^ is cal-
culated using a linear least squares analysis of the data, which is described
in the Data Analysis subsection below.

It should be possible to choose stirring rates with this apparatus
that give k°, values between I and 15 hr"1. A plot of k^ versus stirring rate
should be prepared for the convenience of the operator.

C 0
Measurement of
A stock solution of the chemical in methanol or acetonitrile should be
prepared. The concentration of the chemical in the stock solution should be
adjusted so that a dilution of 0.1 ml to 1 liter of water will give a concen-
tration of the chemical in water that is at least 10 times the detection limit
but is less than 50 ppm and less than about one-half of the solubility limit
of the chemical in water.

Calibrate the dissolved oxygen analyzer in air, according to the
manufacturer's instructions. (This calibration is not critical, since the
instrument is recalibrated at the end of the experiment.) Place the probe
of the dissolved oxygen analyzer in the glass holder. Fill the beaker with
about 1600 ml of distilled water. Start the recirculation pump. Purge the
oxygen from the water using reagent grade nitrogen, which is bubbled through
a glass frit on the end of a long glass tube that has been placed at the
bottom of the beaker. Monitor the decrease in the oxygen concentration with
the dissolved oxygen analyzer. When the oxygen concentration is less than
1.5 ppm, add the chemical to be studied in the stock solution. No more than
about 0.16 ml of stock solution should be added to the water.

Start the stirring motor at the preselected speed. Remove the sparger
and start the stirrer motor. Adjust the stirring speed to a predetermined
value which can be the revolutions per minute or an arbitrary setting on the
motor speed controller. For convenience, the initial runs should be made at
stirring speeds that give k°, values of approximately 2 to 5 hr"1. Begin
monitoring the oxygen concentration with the dissolved oxygen analyzer, and
withdraw aliquots of the solution for analysis of the chemical. If the
withdrawn aliquots are not analyzed immediately, they should be stored in
the refrigerator in sealed containers without headspace and should not be
poured from container to container to minimize losses by volatilization.

Two criteria for data collection should be met. At least 10 measure-
ments of the concentration of the chemical, [cl, should be made. The final
concentration of C should be less than 25% of the initial concentration.
Also, at least 15 observations of the oxygen concentration [0~]t, should be
made, and the dissolved oxygen concentration should be greater than 8 ppm
before the experiment is ended by increasing the stirring speed. At the end
of the experiment, increase the stirring speed and allow the oxygen concentra-
tion to reach a constant value, [02] , and note this value.
247
-------
This experiment should be repeated at least six times at stirring
rates corresponding to a range of ky from about 1 to 15 hr

Data Analysis

Estimation methods for error analysis of the test protocol are based
on certain assumptions concerning the accuracy of specific measurements and
relationship between variables. The test protocol for high volatility com-
pounds proposed here requires measurements of concentrations of chemical and
dissolved oxygen as a function of time from which the ratio k /K is calculated.
r
The estimate of the volatilization rate constant ky is related to the
measured variables, concentration and time, by the following regression
equation
V nZt2 - (It)2

where C is^the concentration of chemical measured at time t and the hat signi
fies that k^ is an estimate of k^. This version of the regression equation
does not require that InCC/C^) = 0 at t = 0; that is, the line is not forced
through the origin and any significant departure from the origin indicates
bias in the values of C at t > 0.
The intercept, C , the concentration at t = 0, is obtained from the
equation

l-nCQ = ^ (IlnC - kCEt) (7.11)

The preferred measurement of error in experiments of this kind is the 95%
confidence limit, CL(95%)
CL(95%) = t
n-2,a
Z(lnC) - InC ZlnC - k (SlnC)Et
o v
(n-2) [Zt2 - (Et)2/n]
(7.12)
where t _ is the t-statistic for n observations and (l-a)lOO confidence
limit (S). (see Table 7.1).

r
Then, the confidence interval of k is

kC - CL < kC < k° + CL (7 .13)
v v v
243
-------
TABLE 7.1 VALUES OF t
n-2,5%
n
10
11
12
13
14
15
16
17
18
19
20
un-2,5%
2.31 2.26 2.23 2.20 2.18 2.16 2.14 2.13 2.12 2.11 2.10
The simplest way to fit the data is to use the linear regression pro-
grams that are built into some hand-held calculators. The values of ln[C]t are
entered as the ordinate, y, and the time, in hours, is entered as the
abscissa, x. The hand-held calculators will calculate the slope, k^, the
intercept, In CQ, and the correlation coefficient for the data. The values for
the terms E(t)lnC, ZlnC, Et and £t2 will be stored in the memory of the calculator
and can be recalled to simplify the calculation of CL(95%). Least squares
routines on larger computers could also be used.

*0
The estimate of the oxygen reaeration rate constant k is calculated
from the following regression equation:
n£(t)[ln(C -C)] - Et£ln(C -C)
S fi
2 2
nZt - (Et)
(7.14)
where C and C have been substituted for [0™] and [On]t to simplify the nota-
tion. This version of the regression equation does not require that
ln[(Cs-C)/(Cg-Co)] = 0 at t = 0; that is, the line is not forced through the
origin and any significant departure from the origin indicates bias in the
values of (CS~C) at t > 0.

The intercept, (CS-C ), the oxygen deficit at t = 0, is obtained from
the equation
- k° St]
(7.15)
The preferred measurement of error in experiments of this kind is the
95% confidence limit, CL(95%):
CL(95%)
"n-2,a
E[ln(C -C)] - ln(C -C )Zln(C -C) - k, EtIln(C -C)
s s o s v s
(n-2)[EtZ -

Then, the confidence interval of k is

kv ~ CL < kv < kv + CL
1/2
(7.16)
(7.17)
249
-------
Hand-held calculators can be used for these calculations by entering ln(C -C)
for the ordinate y. and t for the abscissa x.. s

Calculation of kv/kv

C 0
A plot of ky versus ky (abscissa), including the 95% confidence limits
for each value of k0, and k^ from equation (7.16), is made. The best straight
line is drawn through the data points, using a linear least squares fit forced
through the origin. Then an estimate of the average value of ky/kv can be
calculated from
Kk1
02
(7.18)
where the subscript j refers to the
confidence limit on k
j measurement of
CL', is
, C,,0
k /k .
v v
The 95%
and
CL'
n-l,a
(kc\

*\
(n-1)
I1*
(7.19)
(7,20)
Our experience has shown that the 95% confidence limits on the average value
of kc/k for high volatility compounds is about 5 to 10% of the magnitude of
Strictly speaking, a nonlinear least squares analysis, using all of the
concentration versus time data should be used. However, this would be very
expensive, and, in our experience, would not give substantially different
values of k /k .
v v
250
-------
7.6.3 Procedure for Low Volatility Compounds

Introduction

The basis of the test procedure for low volatility compounds
(H < 10 torr M ) is the measurement of the ratio of the volatilization
rate constant of the chemical, kv, to the water evaporation mass transfer
coefficient, k^. This ratio should be constant for low volatility compounds.
The volatilization rate of low volatility compounds is limited by gas phase
mass transport; therefore, the wind speed above the water body determines the
rate. However, since in many cases the chemical may be either a low or inter-
mediate volatility compound the ratio k^/k^ is also measured at several water
turbulence levels to provide an estimate of the liquid phase mass transport
coefficient.

C 0
The rate constants ky and ky are defined by equations (.7.8) and..
(7.9 ), respectively, in the previous section. The value of k^ (cm hr~ ) is
estimated from

/i/, ft/. \
(7.21)
where NW is the flux of water evaporating through the gas phase boundary layer
and is measured as the weight of water lost per unit area per unit time
(g cm" 2 hr"1), P$ is the vapor pressure of water (torr) at temperature T (K),
and Pw is the partial pressure of water in the bulk gas phase (torr). Thus,
values of k^ for both laboratory and environmental conditions can be calculated
from measured values of NW, provided average temperatures and relative humidities
are also available. Then
Ac\
-I— \
lkw)
\ g a
(7.22 )
env | , W I L \ K /env v
• /, env
g 'lab

Apparatus

The recommended apparatus consists of a 19 x 10 cm crystallizing dish,
a constant speed stirring motor equipped with a propeller stirrer, a dissolved
oxygen probe, a balance capable of weighing up to 8 kg at ± 0.5 g, and a 4-in.
"muffin fan". The laboratory air temperature and relative humidity should be
measured with a psychrometer.

Calibration of the Apparatus

The procedure for correlating the propeller stirring speed with ky
was given in Section 7.6.2. In this case, the stirring rate should be ad-
justed so that k^ is greater than 2 hr . The balance is used to weigh the
dish at regular time intervals to determine water loss rates. The muffin
fan is located either 10 cm or 30 cm from the surface of the beaker, in a

251
-------
horizontal direction. The water loss rate should be measured at several
stirring rates, without the fan and at the two fan locations to determine N T
under the various conditions. Nw should be nearly independent of the stirring
rate (Mackay and Cohen, 1976).
*
Experimental Procedure

The procedure is designed to evaluate k , k^, and Ic; in the same
experiment. The experimental plan is to determine the volatilization rate
using three conditions: no fan, a fan at 10 cm, and a fan at 30 cm at a
turbulence level that produces an oxygen reaeration rate constant of ~2 and
~15 hr"-"- for each condition.

A method for analyzing the chemical in water must be developed.
Chemicals in the low volatility class will either be very ssoluble in water or
have both a low vapor pressure and a very low solubility in water; thus,
special analytical techniques may be necessary. Also, if the solubility is
less than about 40 pg liter~l, problems with sorption of the chemicals to the
apparatus and detection system may be encountered. Whenever possible, direct
analysis of the aqueous solution is desirable.
C 0
In most cases, the value of k will be much less than that for lc .
In fact, the experiment may take several days. Therefore, the measurements
of [C ].j_ and the weight of the beaker, W^, should be made at: approximately
t = 0, 0.5, 1, 2, 3, 4, 6, 8, 10, 15, 20, 30 and 40 hours. The change in
weight of the crystallizing dish for the itn time interval, W^, is

W. = W° - WC (7.23)
111 '

where W? is the initial weight of the crystallizing dish and w| is the weight
of the dish at time t. After the amount of water lost in the itn time interval
is measured, an amount of distilled water equal to W. is added to the
crystallizing dish. The solution is then stirred briefly, and an aliquot is
withdrawn for analysis of the chemical. The concentration of the chemical is
C^. Measurement of T and the relative humidity should be made at the same time.
Measurements of k~, which will increase as the water evaporates, should be
made at t = 0, 6, 20 and 40 hours. The speed of the stirring motor can be
reduced slightly each time to maintain k^ approximately constant during the
experiment. The depth of the vortex created by the stirrer should also be
recorded.

The average value of k^ for each interval between weighings of the
beaker is calculated. First, the wet and drv bulb temperatures of the lab-
oratory air are used to calculate T,, P , and P where T. is the dry bulb
temperature (converted to degrees KJ, Pg is the vapor pressure of water at
the dry bulb temperature (torr), and Pw is the actual vapor pressure of water
in the laboratory atmosphere (torr). The conversion of wet and dry bulb temp-
eratures to vapor pressures of water is conveniently done by using standard
psychrometry tables (for instance, see List, 1958). Then, for the ith measure-
ment (at each value of t)
3464 W.T.
kW. = „ i \ (7.24)
§x A (PW - PW).
252
-------
,th
where W is the weight of the beaker (g), t is the time of the i and i+1
measurement (hr), and A is the area of the surface of the water (cm ), I
the water surface is flat, A is

2
th

If
irr
(7.25)
where r is the radius of the beaker (cm). However, if a vortex is formed,
then the surface area of the vortex is approximated by the surface area of a
cone
A = irr(r2 + h2)*5

where h is the depth of the vortex. The average value of k, k , is
O 5
7w i _.w
k = — Ik .
g n gi
(7.26)
(7.27)
TJ w
Both k and its standard deviation, a(k ), can be calculated conveniently
using nand~held calculators.

The concentration of chemical observed at each sampling, C., is used
to calculate k^, using equations (7.10-7.13). The value of k^/kw twhich is
k /kg for the experiment and has units of cm" ) is then calculated. This
procedure should be repeated for at least six measurements at no fan, the fan
at 10 cm and the fan at 30 cm and at least two liquid stirring speeds.
If the compound is in the low volatility class, then ky/kg should be
nearly independent of k^. Then an estimate of the average value of
can be calculated from
(7.28)
where the subscript j refers to the jfc measurement of k /k . The 95%
confidence limit on k^/k^, CL, is 8
CL
n-l,a
.2 /?\

-------
and
(7.30)
7.6.4 Procedure for Intermediate Volatility Compounds
The measurements described in Section 7.6.3 should be performed as a
first step in the test for intermediate volatility compounds. In this case,
both terms of the two-film theory expression of k^ must be used (see Section
7.7.2). Estimates of k., and k are required to calculate kS .
.,
RT
k o H k
£ c gJ
-1
(7.31)
where R is 62.4 & torr K mol . The approximations
(7.32)
and
kC » (DC/DW)°-7 x, a egg

,W
k .
gJ J
T -1
Then, for the j
vj
Solution of equation (7.35) for several measurements of
"•V
and k
(7.35)
w.
gj
would require iterative techniques. Since the procedure is speculative, we
have not attempted the solution at this time. Experimental verification of
the procedures for intermediate and low volatility compounds is clearly
required.
254
-------
7.6.5 Estimation of Environment Rates of Volatilization

The value of (kv)env for high volatility compounds is estimated from

equation

(\e } = (1r /1r 1 (k } (1 'H
VK.7 ~VIN./1\.J...\R./ I / • .L J
v env v v lab v env

Representative values of (k ) are summarized in Table 7.2.
* • v env
TABLE 7.2 OXYGEN REAERATION RATES IN REPRESENTATIVE WATER BODIES

Pond
River
Lake
Literature values
(day'1)
0.11 - 0.23b
0.2,° 0.1 - 9.3d
0.10 - 0.30b
Sugj
(day-]
0.19
0.96
0.24
o
'ested values
C) (hr'1)
0.008
0.04
0.01

aSmith et al. (1977).

bMetcalf and Eddy (1972).

CGrenney et al. (1976).

Langbein and Durum (1967); taken from Table 2 for rivers such as the

Allegheny, Kansas, Rio Grande, Tennessee, and Wabash. Values for other

rivers as well as a method for calculating k? in rivers are given in this

reference.

Equation (7.2) is used to estimate (kv)env for low volatility compounds

for a representative water body. In this case, there are literature reports

of measurements of k^ only for lakes. A reasonable value for (k) is

2100 cm hr-1 (see SeStion 7.7). g
,.C. I "v I Llab nW, ,, „,
(k ) = I — I r— — (k ) (7.2)
v env I ,W I L g env ^
1 i' IT , env &
'lab
In both cases, these numbers provide rough estimates of (kv)env. The

precision of the estimate of (kv)env depends on the precision of the estimates

of (k^)env and (kg)env. More precise estimates can be made if the hydrological

and meteorological characteristics of a specific water body are known.
255
-------
7 . 7 BACKGROUND

7.7.1 Equilibrium Thermodynamics of Dilute Non-Ideal Solutions

The fundamental thermodynamics of ideal and real solutions, which
includes the concepts of fugacity or escaping tendency, f, activity, a, and
activity coefficient, Y, are described in any elementary physical chemistry
text. We assume that the reader is familiar with these terms and will follow
the thermodynamic development suggested by Lewis and Randall (1961) and
Prausnitz (1969) .

The fugacity is the escaping tendency of a real vapor from a real
liquid and approaches the vapor pressure of the substance as the pressure
approaches zero. Consider the equilibrium between a pure liquid, component i,
its vapor phase, and its solution in water. Then, by definition, the
fugacities of component i in all three phases are equal
f - fi = (-7.36)

V o
where f^ is the fugacity of i in the vapor phase, f^ is the fugacity of
pure i, and f , is the fugacity of i in solution.

It is well known from experimental observations that for very dilute
solutions of ideal gases in ideal solutions

P± = H±X± (7.37)

where P. is the vapor pressure of solute i above the solution and X^ is the
mole fraction of i, H. is a constant. Equation (7.37) is known as Henry's law.
This observation is a major foundation of the volatilization theory we are
developing. Deviations from ideal behavior (H. is not a constant) are observed
at higher pressures and concentrations. Equation (7.37) can be extended to
dilute real solutions by recognizing that fY is nearly equal to P^.

From the definitions of the activity, a., and the activity coefficient,
Y . , for solute i

ai = YiXi = fi/fi (7>38)
where f^ is the fugacity of an arbitrary reference state of component i
in
256
-------
the liquid phase. t Then, for solute i dissolved in a solvent,
(7-39)
V
By combining equations (7.36) and (7.39), and assuming that P. = f,, we obtain

Pi% f i = YiVi (7>40)
By comparison with equation (7.37)
The activity coefficient can be defined in two ways. In the sense of
Raoult's law,

Yj-*-! as X±— »~1 (7.42)

for both the solute and solvent. Then, the reference fugacities are equal to
the fugacities of the pure liquid solute and solvent.

In the sense of Henry's law, for the solute

Y* - 1 as Xj-H^O (7.43)

but for the solvent

Yt = 1 as X±— >-l (7.44)

In this case, the reference fugacity is not the fugacity of the pure liquid.
Prausnitz (1969) shows that for the solute

Ii.5 (7-45)
Y* f± (pure i)

For the purposes of this development, the Raoult's law convention is
more convenient, for two reasons. First, the reference fugacity is equal to
the vapor pressure of the pure liquid (at low pressures). Second, the value
of Y., can be measured easily, since for a saturated solution,

fl - Yis Xis fi (
Equation (7.37) assumes that a is independent of pressure, which is usually
true if the total pressure is about 1 atm or less.
257
-------
where the subscript s indicates the saturated solution. Since
Then
and
fi = fi = fi * p°(Pure liquid) (7.47)
X.s P. (7.48)
y.s = l/X.s (7.49)

Definition of the references states is required to estimate values of y and
to predict solubilities (see Lewis and Randall, 1961, cpt. 20). However, we
are interested in estimating values of H only, which can be estimated with-
out knowing f . .

For gases,

fl =^i Xis f i * Pi C7'50)
H. = y. f = P,/X. as X. +0 (7.51)
i i i is is
where X is the solubility of the gas in water (moles liter ) at the gas
pressure P..

For liquids in solution at saturation

fl - Y± Xis f I * P±t (7.52)

H.=Pu/Xis (7.53)

where X is the solubility of the liquid and P. is the vapor pressure of
the pure liquid.

For solids, we consider a saturated solution in equilibrium with the
solid phase. Then

fl " *± Xis f i ^ Pis <7'54>

In this case, f. is approximately the vapor pressure of the supercooled
liquid i. Then

H. = Pis/Xis (7.55)

253
-------
where P is the vapor pressure of the solid i and X. is the solubility of
i . j .is is
solid i.

A more convenient form of equation (7.55) and (7.57) is to use the
solute concentration in moles liter"! (M.). Then, for liquids
Hci = V[Ci]sat
(7.56)
and for solids
H , - P. /[C.] .
ci is i sat

which are equivalent to equation (7.5)
(7.57)
If vapor pressure data are available for the chemical above the
melting point, T , but the chemical is a solid at temperature T, = 20°C =
293 K, then, if ™he vapor pressure is extrapolated to T.., the vapor pressure
is that of the supercooled liquid, P. , which is the reference state for
solids in equation (7.54). Prausnitz8 (1969, section 9.2)has shown that
In
"is
RT..
--^-InjUl
m ' is
(7.58)
where AHf-is the heat of fusion. Then
is
'isi
AH,
exp
m
(7.59)
Substitution of equation (7.59) in equation (7.57) and conversion of X« to
[Ci]sat, which is a units change, gives the correct expression for H . Then
the Clausius-Clapeyron equation is used to extrapolate the vapor pressure,
P2t for the liquid at temperature T2, co T.. = 20° C, or P. . and converting
P to the vapor pressure of the solid, gives equation (7.7)
IS J6
H
'21
sat
AH
exp
AHf / i i_\
R \ Tm"Tl/
(7.7)
where R = 1.987 cal rnol" and T
293 K.
259
-------
In summary, estimates of Hci can be made, provided the gas solubility
versus pressure curve is measured or the liquid or solid vapor pressure and
solubility in water are measured. These measurements are required at either
25°C or, preferably, 20°C, and at ambient laboratory pressures.

The implicit assumptions in the calculations are that the solutions
are dilute (interactions between dissolved solute molecules do not occur)
and that the gases or vapors are ideal gases (fV = p.). The errors intro-
duced by these assumptions are not significant for the volatilization
screening tests.

7.7.2 Two-film Theory

The two-film mass transport theory is the simplest mathematical
description of the evaporation process from a liquid phase to a gas phase.
This theory was originally developed by Whitman (1923) and. was recently
applied to the problem of the evaporation rate of chemicals from water by
Liss and Slater (1974), Mackay and Leinonen (1975), Smith et al. (1977),
and Smith and Bomberger (1978). The results of recent studies by Smith and
Bomberger (1978) suggest that the two-film theory is not a complete descrip-
tion of the volatilization process of organics from water. However, it is
outlined here because it is conceptually useful and because the more correct
theory is too complex to describe in detail in this protocol.

The basic concept is that there are three regions near the gas-liquid
interfacial surface, s: these are the liquid phase boundary layer; the
Knudsen region, which is one or two mean free paths in the gas phase immed-
iately above the gas-liquid interface; and the gas phase boundary layer.
These regions are schematically depicted in Figure 7.2.

The transport of a substance through a boundary layer is assumed to
be by molecular diffusion, because the fluid flow is laminar. The diffusion
process can be described by Pick's law in one dimension, where the flux of
the substance, N (moles cnf^sec"!) is
N = - D|| (7.60)
260
-------
BULK GAS PHASE<
GAS PHASE BOUNDARY LAYER^
KNUDSEN REGION^
GAS-LIQUID INTERFACE

LIQUID PHASE BOUNDARY LAYER
-------
where D is the diffusion coefficient and z is the vertical distance. If the
concentration gradient 9C/3z is constant within the boundary layer, then
equation (7.60) can be rewritten

N = kAC (7.61)

The mass transport coefficient k has the units of velocity (cm sec )
and is

k = D/6 (7.62)

where 5 is the boundary layer thickness.

The flux through the gas-liquid boundary layer, Ng£, is

N „ = kn(Cn - C „) (7.63)
where kpis the mass transport coefficient of the chemical in the liquid phase,
C is the concentration of the chemical in the liquid phase at the gas-liquid
interface. For convenience, all concentrations are expressed in units of
moles cm~ •

For the Knudsen region, which is just above the liquid surface and is
the region where molecular velocity limits the mass transport rate, the flux,
Nk, is

Nfc = aS(Csg - Ck) (7.64)

where
(7.65)
where ct is the accommodation coefficient, R is the gas constant (8.31 x 10 erg
mol~l K ), T is the absolute temperature (K), Mc is the molecular weight of
the chemical, C is the concentration of the chemical at the gas phase side
of the gas-liquid interface, and C^ is the concentration'of the chemical at
the boundary between the Knudsen and the gas phase boundary layers (Fuchs,19591.

The flux through the gas phase boundary layer, N2, is
Ng=kg
where kg is the gas phase mass transport coefficient (cm sec~l) and C is
concentration of the chemical in the bulk gas phase. 8
262
-------
For any substance, the flux through each boundary layer must be equal
to the overall flux from the bulk liquid to the bulk gas phase, N. Henry's
law relates CSg and Cs^
sg
H C
sSL
where H is the Henry's law constant (unitless, as defined here)
stituting equations (7.64), (7.66), and (7.67) into (7.63)
N =
Collecting terms in N, and solving for N gives
H
(7.67)

Then, sub-

(7.68)
(7.69)
In the laboratory, C K 0. The volatilization rate of the chemical, R , is
&
and
R = N
v V
k = •"• I —
v T I k.
k C.
-1
0.6H Hk
(7.70)
(7.71)
g
For a molecule of molecular weight 150 at 20°C, g = 5 x 10 . For pure
compounds, including water, a is between approximately 0.1 and 1.0 (Hickman,
1954; Pound, 1972). Hence, the second term of equation (7.71) is always
small.* Therefore, equations (7.69) and (7.71) reduce to
(7.72)
(7.73)
Henry's law can also be written as

T^*"* T* n
(7.3)
X
o may be several orders of magnitude lower if a surface active chemical is
present. Then the second term may be significant.
263
-------
where C is the concentration of the chemical in solution in moles liter = M.
The Henry's law constant, H , is in units of torr M , and

HC = RT H (7.74

Making the conversion to H and C (M), equations (7.72) and (7.73) become
C W

Typical values of k and k for molecules are 10-50 cm" and
1000-4000 cm hr'1 (Liss and Slater f 1974). The value of RT is 18,300 torr M
at 20°C. Therefore, if HQ ~ 103 torr M . the second term in equation (7.31)
is small and k will be determined by the value of k . This means that the
rate of mass transport (volatilization) is limited by diffusion through the
liquid phase boundary layer. We have called compounds that fit within this
class "high volatility compounds." Similarly, if H < 10 torr M~^, then the
second term in equation (7.31) dominates and the rate of volatilization is
limited by mass transport in the gas phase. We have called these "low vola-
tility compounds." If H is between 10 and 1000 torr M"1, then both terms
are important. We have called these intermediate volatility compounds."

High Volatility Compounds

For high volatility compounds, equation (7.31) becomes

k - f k, (7'76)
v L a

The ratio of k for two high volatility chemicals, 1 and 2, is
(7.77)
k *
k.
v SL
1 2
assuming that k and k are measured simultaneously. Note that (1/L) cancels.
v v
A very convenient choice for the second chemical is oxygen (H = 5.5 x
10^ torr M at 20°C, Tsivoglou, 1967). The oxygen reaeration rate is the
rate at which oxygen in the atmosphere dissolves in water that has a concen-
tration of dissolved oxygen lower than the equilibrium concentration with the
atmosphere. The value of the oxygen reaeration rate constant, k^, which is
defined by

<7-8)
264
-------
where £0-] is the concentration of oxygen in water, [°2lsat is the Oxv8en
concentration at saturation (in equilibrium with the atmosphere), and [C>2
is the oxygen concentration at time t. The integrated form is
(7'78)

where [0~3 is the initial oxygen concentration. Tsivoglou has shown
(Tsivoglouet al. , 1965; Tsivoglou, 1967) that the ratio of the volatilization
rate of several rare gases to the oxygen reaeration rate, is a constant over
a wide range of turbulence conditions. Therefore, if the value of the ratio
of the volatilization rate constant of a chemical, k^, to the oxygen reaeration
rate constant can be measured in the laboratory, then

(kC) = (kC/k°). . (k°) (7.1)
v env v v lab v'env

Hill et al. (1976) used this procedure to estimate the volatilization rate
of vinyl chloride in the environment. Smith et al. (1977) and Smith and
Bomberger (1978) have extended this procedure to a wider range of compounds.
The literature data for the ratio k^/k^v for high volatility compounds are
summarized in Table 7.3. The available experimental results suggest that the
ratio kC/kO is a constant over a range of k° from 0.2 to 15 hr~l.
In dilute solutions when the amount of material being transferred
across the interface is small, the mass transfer coefficients for both gas
and liquid phase mass transport can be approximated by

\ = V6£ (7'79)

kg = Dg/6g (7.80)

2 -i
where D is the diffusion coefficient (cm hr ) and 6 is the thickness of the
mass transfer film or boundary layer in the liquid or gas phase. Increasing
the turbulence decreases 6 and therefore increases the mass transport rate.
Then, by combining equations (7.77) and (7.79) for the chemical and oxygen,
we obtain

kC k° DC
_y. = li _i
,0 = .0 ~ _0 (7.81)
kv k* D*

The validity of this equation and techniques for estimating D£ are discussed
in Sections 7.7.4 and 7.7.6.
265
-------
TABLE 7.3 COMPARISON OF PREDICTED AND
MEASURED VALUES OF ky/k°

Compounds
Benzene
Carbon dioxide
Carbon tetrachloride
Chloroform
1 , 1-Dichloroethane
Dicyclopentadiene
Ethylene
Krypton
Propane
Radon
Tetrachloroethylene
Trichloroethylene

a a
0.45
0.84
0.43
0.47
0.47
0.31
0.70
0.78e
0.53
0.66e
0.40
0.44

i a

£ £
0.67
0.92
0.66
0.68
0.68
0.56
0.84
0.88e
0.73
0.8le
0.64
0.66
Measured

kC/k°
V V
0.57 ± 0.02b
0.89 + 0.03°
0.63 + 0.07°
0.57 ± 0.05b
0.71 ± 0.117
0.54 ± 0.02b
0.87 ± 0.02
0.82 ± 0.08^'
0.72 ± 0.01 f
0.70 + 0.08^'
0.52 ± 0.09^
0.57 ± 0.15°

o
Range of k
(hr-1)
0.4 - 15.5
0.07 - 0.5
0.4 - 10.7
0.4 - 10.7
0.3 - 12.0
1.6 - 10.4
0.1 - 2.2
0.06 - 2.9
0.2 - 1.6
0.08 - 0.5
1.6 - 10.7
1.6 - 10.7

aDC/D° predicted as (V°/v£)0'6, which is the result of the Othmer-Thakar
approximation (Reid and Sherwood, 1966, p. 550). V^ was estimated from
critical properties or the method of LeBas (Reid and Sherwood, 1966, p. 86-87,
v£ = 25.6 cm3 g-1 mole"1.
SRI unpublished data.

CTsivoglou, 1967.

Rathbun, 1978.

from Handbook of Chemistry and Physics.
Tsivoglou, 1965.

Low Volatility Compounds

For low volatility compounds, only the second term in equation (7.31)
is significant. Then
s
°-82)
Combining equations (7.80) and (7.82) gives
V
2
a constant
(7.83)
which should be a constant and should be valid for low volatility compounds.
We are not aware of any experimental verification of this expression.
266
-------
If the volatilization rate is gas phase mass transport resistance
limited, a useful equation would have the form of equation (7.1), where the
ratio of the volatilization rate constant of the chemical to a second chemical
found in the environment could be measured in the laboratory. The obvious
choice of the second chemical is water. Thus, the water evaporation rate
would be measured in the laboratory and used to estimate (lei) using the
environmental rate for water evaporation. This concept is complicated by
the fact that the rate of water evaporation is, for dilute solutions, a zero
order process, since the concentration of water does not change during evapo-
ration. Water evaporation ra.tes are usually expressed in units of depth
(length) time , which is equivalent to units of flux, volume area"-1- time" .

W
The value of kg is calculated from the water evaporation rate or
flux, N . For dilute aqueous solution, the equilibrium partial pressure of
water above a solution, PQ , is expressed by Raoult's law (which, like Henry's
law, cannot be derived from first principles.),
PWXW
o
(7.84)
W W
where P0 is the vapor pressure of water at the surface temperature, and X is
the mole fraction of water, which approximately equals 1 for very dilute
solutions. Then
,W = _s
"sg RT
pw
^
RT
(7.85)
Also, for water C
limited. Then
If the terms are separated,
hence, mass transport of water is only gas phase
(7.86)
(7.87)

(7.88)
W
where P is the actual pressure of water vapor in the air. Since awl for
water (Hickman, 1954), term 1/ocg is
1-1
17.89)
-L = C1>/(8.31xl07)(293)\is
<*e r 'y 2Tr(i8) 1
= 6.8 x 10 5 sec cm'1
267
-------
W —4 —1 !
which is small compared to 1/k » 3.3 x 10 cm hr (Liss and Slater, 1974)
Therefore, equation (7.88) can^be rewritten

k^ = Nw RT/ (P^-PW) . (7.90)
To derive the expression for (ky) for low volatility compounds, it
must be assumed that the ratio k^/k is a constant for a wide range of labor-
atory and environmental condition's. ^ This assumption is reasonable, since
film theory suggests that the ratio should be proportional to the ratio of
the gas phase diffusion coefficients (see Section 7.7.3), but it has not been
validated by laboratory experiments. Therefore, from equation (7.85)
(7.91)

lab
From equation (7.82)
k = k L RT/H (7.92)
g v c

Substitution of equation (7.92) into equation (7.91) for k in the laboratory
and the environment gives

(kC) RT L /H (kC)1 , RT. , L ,_v/H,
v env env env c v lab lab lab c
_ _ _ (,/.yj)
W W
(\e ^ (\e ^
Ug;env Ug;iab

and

(kCx = /iv \ Llab Tlab ( W
v env I . W | L T g
\kg/lab env
*
This term may be significant if a surface-active chemical is present,
because a will be several orders of magnitude lower.
268
-------
7.7.3 Penetration Theory

The classical two-film theory predicts that the mass transport co-
efficients are proportional to the diffusion coefficient (equations 7.79 and
7.80). Thus, in principle, the ratios k^/k°v and kg/kg can be calculated from
the ratio of the diffusion coefficients. Later theories and experimental
evidence have shown that the mass transport coefficients are proportional to
Dn where n may vary from 1 to % depending on the turbulence. These theories
are described in this section.

Penetration or surface renewal theories of mass transfer across an
air-water interface are based on a different model of the interface than two-
film theory. Most studies, both experimental and theoretical, have focused
on the liquid side of the interface; therefore, this discussion will also
focus on the liquid side. The theories assume (Treybal, 1968) that instead
of a fixed liquid film that sits next to the interface, packets of bulk
liquid are transported to the interface, where they stay for a period of time
and are then displaced by other packets from the bulk liquid. The displaced
packet is mixed into the bulk liquid and loses its identity. While the
packet is at the interface, material diffuses into it from the gas (or out
of it, depending on the gas phase concentration). Penetration theory assumes
that all of the packets reside at the interface for the same time. Surface
renewal theory assumes that the residence time of packets is described by a
probability distribution (Danckwerts, 1955) such that the probability of a
packet being displaced is independent of its previous time history.

Both of these theories assume that the liquid packets do not reside
at the interface for a time period long enough for the materials to diffuse
completely through them. This is illustrated in Figure 7.3 for the case
where material is being transported into the liquid. At to, a packet with
the bulk concentration C arrives at the interface. At a larger time, t-,
material has started to diffuse into the packet but by time t~, when the
packet is displaced by another packet, it has not yet diffused through the
packet.

The results of both theories are similar. Penetration theory yields

6)ls (7>95)
where 9 is the fixed time period that packets reside at the surface. Surface
renewal theory yields

\ - (Ds)*5 (7.96)

where s is the fractional rate of packet displacement. The important aspect
of these two theories is that they both show that k is proportional to the
square root of the diffusion coefficient, whereas film theory shows that k,,
is directly proportional to the diffusion coefficient.

269
-------
GAS-LIQUID
INTERFACE
INTERFACE BETWEEN

SURFACE PACKET AND

BULK LIQUID
< 'u

UJ
GC

CO
m
D
CO
BULK LIQUID
FIGURE 7.3
DISTANCE FROM GAS-LIQUID INTERFACE
SA-4396-90

CONCENTRATION PROFILES USED TO DEVELOP PENETRATION AND

SURFACE RENEWAL THEORIES OF MASS TRANSPORT
270
-------
Dobbins (1964) proposed a modification of surface renewal theory that
allows some packets to remain at the surface long enough for material to
diffuse completely through the packet. This is illustrated in Figure 7.3
by the concentration profile at t-j. The consequence of this change is that
kj, is given by

k^ = (Ds)1* coth (sL2/D)15 (7.97)

where s is again the fractional rate of packed displacement and L is the
actual packet thickness. L is very similar to the film thickness parameter 6.
This expression has two limiting forms: when L is small or D is large,
k* = D/L (since coth (x) = 1/x as x -> o) , and when L is large or D is small,
k = (Ds)^ (since coth (x) = 1 as x -> °°) .
X*

Therefore, in the combined theory, under different extreme circum-
stances either film theory or surface renewal theory obtains, and under other
circumstances the dependence of k« on D is intermediate. Dobbins (1964)
showed by experiments that highly agitated conditions yielded kj= D where
n -» 1/2, meaning that surface renewal dominated mass transport. Under less
agitated conditions k,, = Dn, n -» 1, meaning that diffusion across a film
dominated mass transport. Lee (1973) used a capillary microelectrode to
measure oxygen concentrations in a stirred liquid a few millimeters below the
gas-liquid interface. He could detect regular concentration fluctuations,
which he interpreted in terms of surface renewal theory. With this inter-
pretation, he could estimate a value of the diffusion coefficient of oxygen
in water of 2.3 x 10 cm^sec", which he felt compared well to a literature
value of 2.2 x 10 cm^sec" . Dobbins and Lee's work raises some questions
about Tsivoglou's conjecture (1965, 1967, 1968) that the ratio of mass trans-
port rates of gases into lakes and streams is the same as the ratio of their
diffusion coefficients, namely

k£ DC
_± = »- = constant (7.98)

k£ °
The true relationship is probably
-^ =1 -7; I = constant, 0.5
c I,M
n * 1.0 (7.99)
n
reflecting a combination of film and surface renewal theory. Therefore,
it is common to speak of a two-resistance theory, since the resistance
to volatilization is the sum of resistances in the gas and liquid phases.
271
-------
7.7.4 Summary of Experimental Results
C O
Table 7.3 summarizes the measured and predicted values of k^/ko for
a number of gases and organic compounds. Predictions of kj/k§ have been made
using molar volumes at the normal boiling point to estimate diffusion coeffi-
cients. This procedure is described in Section 7.7.5. Estimates were made for
film theory and penetration theory. It is apparent that the measured value
of kjjVk0, is consistent with k^/k° = (Dc/D°)n where n is a value somewhere
between 1 and 1/2. Only for one compound, ethylene, does the measured value
fall outside the predicted range and even then, the error is minor.

For a number of compounds in Table 7.3, including the gases, benzene,
propane and ethylene, actual values of diffusion coefficients have been
measured but these values have not been used in calculating ratios. Estimated
diffusion coefficients were used in all cases for two principle reasons:
first, in cases where one diffusion coefficient was known and the other had
to be estimated, it was felt that forming a mixed ratio might bias the results.
Second, in cases where both diffusion coefficients had been measured, there
was still a large potential error. Rathbun (1978) pointed out the difficulty
of using diffusion coefficients measured by different investigators to calcu-
late ky/ky. He calculated a k /k^ ratio for ethylene using film theory (ji=l)
and diffusion coefficients for oxygen and ethylene measured by the same inves-
tigator. The ratio was 0.77. If oxygen diffusion coefficients and ethylene
diffusion coefficients from different investigators were used, the ratio
varied from 0.57 to 0.96. This is a wider range than the range predicted by
using the estimated values of the diffusion coefficients and varying n from 1
(film theory) to 0.5 (penetration theory).

C CO
In predicting (k^)env from (kv/kv)lab ratios, there are two poten-
tial sources of error. First, conditions of mixing and flow in the natural
environment (streams, ponds and lakes) will probably be different from
conditions in the laboratory where k^/ky. was measured. Under laboratory
conditions n may be close to 1/2 because the turbulence is relatively high,
whereas in the environment, where the turbulence is lower, n may be closer
to 1 in value. Some error then results in the prediction of k^ or kv under
environmental conditions. Second, if laboratory experiments are not con-
ducted, but instead k^/k0, is estimated using diffusion coefficients, the
same kind of error can occur if the wrong value of n is used. The error can
be on the order of ± 30% if the compound of interest is similar to those
shown in Table 7.3 where k^/k° « 0.6.

When H < 1 torr M"1 (low volatility class), volatilization is con-
trolled by mass transport in the gas phase. Mass transfer in the gas phase
has been modeled by film theory, penetration theory, and surface renewal
theory. Some recent work by Tamir (1978) has demonstrated for the gas phase
what Dobbins demonstrated for liquid phase—namely, that a combination theory
is probably required. For a series of gases, Tamir found that kg is propor-
tional to Dn, where n varied between 0.7 and 0.9 depending on the turbulence
level. At high turbulence levels n was 0.7 and at low turbulence it was 0.9.
It is expected that a wider range of turbulence conditions than those used by

272
-------
Tamir would show 1/2 < n < 1. Again, the possible difference between labor-
atory and environmental turbulence levels could introduce error in the pre-
dicted values.

For the protocol, we have assumed an n value of 0.7 as a compromise,
because the data in Table 7.3 indicate that the error introduced for liquid
phase transport control is not severe. Therefore, equation (7.91) should be
rewritten as
= constant = ( -a | (7.100)

env \ "g/lab

Any prediction error introduced by choosing n as 0.7 would not change the fate
assessment for the compound. Similarly using estimated diffusion coefficients
instead of laboratory measurements probably would not change the fate
assessment.

7.7.5 Estimation of Diffusion Coefficients

There are numerous ways to estimate or measure diffusion coefficients.
In volatilization theory where ratios of diffusion coefficients are required,
most investigators have used Tsivoglou's suggestion (1965, 1967, 1968) for
diffusion in water and have estimated D /D as d /d where d is the molecular
diameter of the compound being considered. For cases where gas phase diffus-
ion is important, investigators have followed Liss' suggestion (Liss and
Slater, 1974) and estimated D^VD2 as (M2/M )^ where M is the molecular weight
of the compound.

Neither of these approaches is correct. Reid and Sherwood (1966) have
thoroughly reviewed the literature on predicting diffusion coefficients using
other physical properties of materials. They observe, for example, that
diffusion coefficients in solution are inversely proportional to molecular
diameter only for large spherical molecules. Gas molecules and most organics
of concern are too small for the approximation to be correct. It is true,
however, that for most compounds the estimates of the ratio of mass transport
coefficients based on molecular weight or molecular diameters are within a
factor of 2 or 3 from the correct result.

Diffusion in Liquids

Most methods for estimating diffusion coefficients in solution use the
solute molar volume at its normal boiling point. When the solvent is water,
the Othmer-Thakar relation is the most convenient (Reid and Sherwood,1966,p.550)

DC (cm2/Sec) - "-° * ™~* (7.101)
1.1 TT U. D
yw Vb
where u is the viscosity of water (centipoise) at the temperature of concern,
and V, is the molar volumeOcmrg-lmol~l) at its normal boiling point of the

273
-------
solute C. This relation has beem compared to measured diffusion coefficients
and found to be accurate within ± 11%. When the molar volume is not known,
it can be estimated from the critical pressure (Reid and Sherwood, 1966, p.87)
or assembled from molar volume increments proposed by LeBas (Reid and Sherwood,
1966, p.
n = 0.7
86). Then,
and (7.101)
can be estimated from equations (7.99) where
0.7
V.
,0 \0.42
V,
(7.102)
For the light gases, molar volumes have been estimated using equation
(7.101) and diffusion coefficient measurements. When critical pressure meas-
urements are absent, critical pressure can be estimated by the increment
method of Lydersen (Reid and Sherwood, 1966, p. 9). Critical pressure esti-
mation errors are typically ±3% as are the molar volume estimates. This
means that diffusion coefficient estimates in water should be accurate within
±15%.

Diffusion in Gases
There are several rather complex methods for estimating diffusion
coefficients in gases based on statistical mechanics. All the methods
require knowledge of the Lennard-Jones parameters a and e for the diffusing
species and the stationary phase. For many compounds these parameters would
have to be estimated, which in turn would require information on critical
pressure and volume. A much simpler procedure when the stationary phase is
air is to use (Reid and Sherwood, 1966, p. 531)
DC(cm2
sec )
P x 2.52 x 10
7 2.74
. 23
(V
(7.103)
b,A
where P is the pressure (atm), y. is the viscosity of air (centipoise) at the
system temperature, V^ is the molar volume at the normal boiling point, M.
is the molecular weight of air, and M_ is the molecular weight of the
compound. This correlation has an average error of ±9%.

Liss and Slater (1974) have assumed that kg and Dg are inversely
proportional to the square root of the molecular weight of the chemical. In
view of the uncertainties in the estimates of H and D , this assumption may
be adequate for many purposes. Thus,
(7.104)
274
-------
7.7.6 Calculation of Environmental Volatilization Rate Constants

High Volatility Compounds

If the volatilization rate is liquid phase mass transport resistance
limited, equation (7.1) is used to estimate (k)e . The following

(kv>env= (kX>lab ^>env

equation, which is the combination of equations (7.81) and (7.99),

(kX>env = (kX>lab - (DX>°'7 <

Values of (kv)env are given in Table 7.2.

Low Volatility Compounds

If the volatilization rate is gas phase mass transport limited,
equation (7.2) is used to estimate (kg)env
C W
We believe that the ratio ky/K should be constant for low volatility
compounds.

W
The value of (kg) must be estimated from field data. The water
evaporation rate, which is gas phase mass transport resistance limited
(Liss and Slater, 1974), has been carefully measured for several lakes. The
results are shown in Table 7.4.

_ TABLE 7.4 WATER EVAPORATION RATES FOR LAKES _
_ . Average evaporation rate
Location _ (cm sec-1 x 106) _ Reference

Lake Hefner, Oklahoma 4.8 Marciano and Harbeck (1952)
Lake Mead 6.8 Harbeck, et al. (1958)
Pretty Lake, Indiana 3.8 Ficke (1972)

Average 5 . 1
275
-------
Assuming that the average relative humidity is 50%, then the average
value of k for freshwater lakes is,

k^ = Nw RT/(P* - PW) (7.90)

= (5.1 x 1Q~6)(62400)(293)

(18) (17.5) (0.5)

= 0.59 cm sec"

= 2100 cm hr"1

r Equations (7.82) and (7.104) can be used to estimate values of
, since

kC = -£—£ (7.82)
v L RT

-j* = constant «|-^ } (7.100)
k
g

kC L H kC » /nC\0.7

v .1 ah , - c & = _iii _&. i (7 -in*)
TT w RT I w ' v/.iu3;
kW RT kW Ki \ DW
2 g \ g
C W
Thus, values of H , Dg, and Dg must be estimated or measured. Then the
t f *(j/Xi/»»v*" PT*T «^ 4.«..i* .* f^ f\\. •
value of lc/(A/V), , k can be substituted in equation (7.2) to give an
estimate of (kC> a. 8 Liss and Slater (1974) suggested that
Using this approximation,

,7 L
(7.107)
MW
These equations have not been verified in the laboratory.
276
-------
Then, substituting equation (7.105) or (7.107) into equation (7.2), we

obtain

(A/V) „
env ,, W,

(A/V)lab ^Venv
H /1; vu. / 2. u

R*HS) W (Venv (7.108)

(7.109)

The following procedure was used to estimate the lower limit of H

that would cause the environmental half-life for volatilization of a low

volatility compound to be less than 3 months. The half-life for volatiliza-

tion of the chemical, t, ,?, can be calculated from

t1/2 = In 2/(kJpenv (7.106)
If the half-life is less than 3 months, thenlk^l must be greater than

9 x 10-8 sec-l. \ Venv

Substituting the following representative values into equation (7.109), and

solving for H , we obtain
(kC) >.9 x 10~8 sec
v env
MC = 250

3 -1 -1
R = 62 ,.400 torr cm mol K

Lenv - 20° cm

T = 20°C = 293 K

(kW) = 2100 cm hr~l = 0.59 cm sec'1
g env

„ ^ (9 x 10~8) (62. 4) (293) (200)
i

C (18/250K (0.59)

> 2.1 torr M"1
Thus, if Hc is greater than about 2 torr M'1, the environmental volatilization

half-life of the chemical may be less than 3 months.
277
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7.8 REFERENCES

Danckwerts, P. V. 1955. Gas Adsorption Accompanied by Chemical Reaction.
AIChE Journal 1(4): 456-463.

Dobbins, W. E. 1964. Mechanism of Gas Adsorption by Turbulent Liquids.
Advances in Water Pollution Research. The MacMillan Co., New York.

Ficke, J. F. 1972. Comparison of Evaporation Compution Methods, Pretty Lake,
Lagrange County, Northeastern Indiana. USGS Professional Paper 686-A.

Grenney, W. D., D. B. Porcella, and M. L. Cleave. 1976. Water Quality
Relationships to Flow Streams and Estuaries, in Methodologies for the
Determination of Stream Resource Flow Requirements: An Assessment,
C. B. Stalmaker and J. L. Arnette, eds. Utah State University, Logan,
Utah.

Harbeck, G. E., Jr., M. A. Kohler, G. E. Koberg, and others. 1958. Water
Loss Investigations: Lake Mead Studies, USGS Professional Paper 298.

Hickman, K.C.D. 1954. Maximum Evaporation Coefficient of Water, in Ind.
Eng. Chem. 46: 1442.

Hill, J. IV, et al. 1976. Dynamic Behavior of Vinyl Chloride in Aquatic
Ecosystems, in U.S. Environmental Protection Agency, EPA-600/13-76-001,
January.

Langbein, W. B., and W. H. Durum. 1967. The Aeration Capacity of Streams,
in Geological Survey Circular 542.

Lee, D. D. 1973. Effect of Surfactants on the Surface Adsorption of Oxygen
into Water. Masters Thesis, Department of Chemical Engineering,
Iowa State University, Ames, Iowa.

Lewis, G. N., and M. Randall. 1961. Thermodynamics, 2nd revised edition,
McGraw-Hill.

Liss, P. S., and P. G. Slater. 1974. Flux of Gases Across the Air-Sea
Interface. Nature, 247: 181-184.

List, R. J. 1958. Smithsonian Meteorological Tables, Smithsonian Miscella-
neous Collections. Vol. 114, publication 4014, Table 94,95, p. 351-369.

Mackay, D., and Y. Cohen. 1976. Prediction of Volatilization Rate of
Pollutants in Aqueous Systems, presented at Symposium on Nonbiological
Transport and Transformation of Pollutants on Land and Water National
Bureau of Standards, Gaithersburg, Maryland, May 11-13.

Mackay, D., and P. J. Leinonen. 1975. Rate of Evaporation of Low-Solubility
Contaminants from Water Bodies to Atmosphere. Environ. Sci. and
Tech. 9(13): 1178-1180.

278
-------
Mackay, D., W. Y. Shiu, and R. P. Sutherland. 1979. Determination of Air-
Water Henry's Law Constants for Hydrophobia Pollutants, in Environ. Sci.
Tech. 13(3): 333-337.

Mackay, D., and A. W. Wolkolf. 1973. Environ. Sci. and Tech. 7: 611-614.

Mader, W. J., and L. T. Grady. 1971. Determination of Solubility, in
Techniques of Chemistry, Vol. 1, Physical Methods of Chemistry, Part V,
Determination of Thermodynamic and Surface Properties, A. Weissberger and
B. W. Rossiter, eds., Wiley-Interscience, p. 258-308.

Marciana, J. J., and G. E. Harbeck, Jr. 1952. Mass-transfer Studies, in
Water-Loss Investigations: Lake Hefner Studies.
USGS Professional Paper 269, pp. 46-70.

Metcalf and Eddy, Inc. 1972. Wastewater Engineering: Collection, Treatment,
Disposal. McGraw-Hill, New York, New York , p. 671.

Pound, G. M. 1972. Selected Values of Evaporation and Condensation Coeffi-
cients for Simple Substances, in J. Phys. Chem. Ref. Data 1(1): 135-146.

Prausnitz, J. M. 1969. Molecular Thermodynamics of Fluid-Phase Equilibria.
Prentice-Hall, Inc., Englewood Clifts, New Jersey.

Rathbun, E., et al. 1978. Laboratory Studies of Gas Tracers for Reaeration.
in Journal of the Environmental Engineering Division, ASCE 104(EE2):
215-229.

Reid, R. C., and T. K. Sherwood. 1966. The Properties of Gases and Liquids.
2nd ed. McGraw-Hill, New York

Smith, J. H., et al. 1977. Environmental Pathways of Selected Chemicals in
Freshwater Systems, Part I: Background and Experimental Procedures.
EPA Report No. 6001/7-77-113, October 1977; Part II: Laboratory Studies,
EPA Report No. EPA-600/7-78-074, May 1978.

Smith, J. H., and D. C. Bomberger. 1978. Prediction of Volatilization Rates
of Chemicals in Water, presented at the AIChE 85th National Meeting,
Philadelphia, June 4-8, 1978. To be published in Water, 1978.

Tamir, A., and J. C. Merchuk. 1978. Effect of Diffusivity on Gas-Side Mass
Transfer Coefficient, in Chem. Eng. Sci. 33 1371-1374.

Thomson, G. W., and D. R. Dovslin. 1971. Determination of Pressure and
Volume, in Techniques of Chemistry, Vol. 1, Physical Methods of Chemistry,
Part V, Determination of Thermodynamic and Surface Properties, A.
Weissberger and B. W. Rossiter, eds., Wiley-Interscience, p. 23-104.

Treybal, R. E. 1968. Mass-Transfer Operations, second edition- McGraw-Hill
Book Co., New York.
279
-------
Tsivoglou, E. C., et al. 1965. Tracer Measurements of Atmospheric
Reaeration-I Laboratory Studies. J. Water Poll. Control Fed. 37(10):
1343-1362.

Tsivoglou, E. C. , 1967. Tracer Measurement of Stream Reaeration. Federal
Water Pollution Control Administration, U.S. Department of the Interior,
Washington, B.C.

Tsivoglou, E. C., et al. 1968. Tracer Measurements of Atmospheric Reaeration-
II Field Studies, JWPCF 40(2) part 1: 285-305

Whitman, W. G. 1923. Preliminary Experimental Confirmation of the Two-Film
Theory of Gas Absorption. Chem. Metall. Eng. 29:146-148; CA17:3118.
280
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CHAPTER 8. SORPTION OF ORGANICS ON SEDIMENTS

J. H. Smith and D. C. Bomberger

8.1 INTRODUCTION 282
8.2 SUMMARY 282
8.3 CONCLUSIONS 283
8.4 RECOMMENDATIONS 283
8.5 SELECTION AND PREPARATION OF SEDIMENT SAMPLES 283
8.5.1 pH 284
8.5.2 Cation Exchange Capacity 284
8.5.3 Organic Carbon 284
8.5.4 Size Distribution 284
8.5.5 Preparation of the Sediment 286
8.6 SCREENING TESTS 286
8.6.1 Purpose 286
8.6.2 Procedure 286
Estimation of K 287
Preparation of the Stock Solution of the Chemical 287
Experimental Plan for the Screening Isotherm 287
Measurement of the Screening Sorption Isotherm 292
Centrifugation Conditions 292
Data Analysis 296
8.7 DETAILED TESTS 296
8.7.1 Purpose 296
8.7.2 Procedure 297
8.7.3 Data Analysis 299
8.8 BACKGROUND 311
8.8.1 Theory . .- 311
8.8.2 Sorption Mechanisms 313
8.8.3 General Design of Sorption Isotherm Measurements 314
8.8.4 Sediment Particle Size 316
8.8.5 Prediction of Soil or Sediment Partition Coefficients 317
8.8.6 Equilibration Time 318
8.8.7 Effect of pH on Sorption 319
8.8.8 Effect of Other Dissolved Organics on Sorption 320
8.8.9 Comparison of Using Wet and Dried Sediments for
Isotherm Measurements 321
8.8.10 Derivation of Equations • 321
Equations (8.6), (8.7), (8.15), (8.25), and (8.27) 322
Equations for Centrifugation Time 322
Equation (8.21) 325
8.8.11 Theory of Nonlinear Least Squares Estimates of
Isotherm Parameters 325
8.9 REFERENCES 327
281
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8. SORPTION OF ORGANICS ON SEDIMENTS
8.1 INTRODUCTION

Sorption of organic substrates into sediments and biota can be a very
important phenomenon in the aquatic environment. The sediments can act as
sinks for sorbed materials, removing them from the water column. However,
since the substrate can also be released (desorbed) from the sediments at a
later time, contaminated sediments can also be a source of pollution. Sorption
of pollutants by sediments often results in high concentrations of low-solubil-
ity pollutants in a part of the water column where uptake by biomagnification
may become significant.

The use of the terms "sorption" and "adsorption" deserves special comment.
Sorption includes any type of process whereby the substrate is physically or
chemically bound to a solid surface (chemisorption). Adsorption implies to us
that the process that holds the substrate on the sediment is strictly physical,
such as the van der Waals type of attraction. However, sorption of ionizable
substrates such as amines may include chemical bonding interactions as well as
physical processes. While other authors have used adsorption to include chemi-
cal interactions (Hamaker and Thompson, 1972), we will use "sorption" to avoid
confusion.

These protocols are designed to provide necessary information on the extent
of sorption of organic and organometallic compounds on naturally occurring sed-
iments. The procedures can also be used to measure the sorption isotherm on
soils.
8.2 SUMMARY

Screening and detailed test protocols for sorption of chemicals on sedi-
ments have been prepared to enable the investigator to estimate the equilibrium
sorption partition coefficient of a chemical on suspended or bottom sediments
in natural waters. Only chemicals with a sorption partition coefficient greater
than 100 are considered for detailed studies.

The test protocols are based on a review of the extensive body of litera-
ture on sorption and an analysis of the kinetics and equilibria of the sorption
process. The recommended test protocols meet the criteria of quantitation,
accuracy, and applicability to experimental systems. They are cost effective
and are simple to use for a wide range of chemical structures.
282
-------
The sorption partition coefficient, K , is defined as

concentration of chemical sorbed on sediment (ng g"1') /-o •<<.
p concentration of chemical dissolved in water (vtg ml"1)

= F K
oc oc

where F is the fraction organic content and K is the sorption partition
coefficient normalized for the sediment organic content. The screening proto-
col consists of estimating KQC from the solubility of the chemical in water
and measuring K and K at one concentration of chemical and two sediment
loadings, using a standard sediment. If the value of K is greater than 100,
the detailed test protocol should be used.

The detailed protocol consists of the experimental plan for measuring the
partitioning between sediment and water at several sediment concentrations and
total concentrations of the chemical. A nonlinear least squares procedure is
used for calculating the best estimate of K .

8.3 CONCLUSIONS

Present knowledge of the theory and experimental aspects of the sorption
of chemicals on soils and sediments provides a sound basis on which to propose
protocols for evaluating the extent of sorption in natural waters. The
recommended sorption protocols represent a balance between the economic need to
minimize laboratory work and the scientific requirements for sufficient and
accurate data.

The general protocol has been evalua ted under laboratory conditions (Smith
et al., 1978). Measurements of the sorption partition coefficient on the
sediment of specific water bodies that may be exposed to the chemical are
recommended.
8.4 RECOMMENDATIONS

The basic protocol has been evaluated (Smith et al., 1978) using a limited
range of sediments. We recommend that a series of test soils and sediments
spanning a reasonable range of cation exchange capacity and total organic carbon
be selected, stored, and maintained in large enough quantities so that samples
can be made available to researchers.

8.5 SELECTION AND PREPARATION OF SEDIMENT SAMPLES

At the time of preparation of this protocol, no reference soil or sediment
samples are available for standardized measurement of sorption isotherms.
Therefore, we recommend that the user collect approximately six freshwater sedi-
ments from a variety of sources, including, if appropriate, a sample from a

283
-------
proposed receiving water body. Natural sediments change on a daily basis, due
to chemical and biological transformations of the organic matter, sediment
transport within the water column, and changes in the hydrological properties
of the water body that occur on a seasonal basis. They also vary as a function
of the depth and location. Therefore, enough of each sediment: should be col-
lected to permit all the experimental work to be performed on a given sample.
It would be nearly impossible to obtain a duplicate sample later.

The sediments should be chosen to uniformly span the range of organic
content (OC), cation exchange capacity (CEC), and pH commonly found for sedi-
ments and soils. Sediments should be obtained from streams, rivers, eutrophic
lakes, and oligotrophic lakes. Special care should be taken to follow uniform
and consistent methods of sampling, preservation, and transport of sediments.
At the time of sampling, detailed records should be made of the exact sampling
locale and the representativeness of the sample collected in relation to the
size of the water body, depth from water surface, local topography, and any
special feature peculiar to that area.

The chemical and physical characteristics of a natural sediment depend on
the type of soil upstream from a given location because soil runoff forms the
sediment. Data regarding the surrounding soils can be obtained from the local
soil survey, hydrologic/geological survey, water resources board, and public
health departments to help select sediments that cover the required range of
OC, CEC, pH, and clay mineral compositions. Information from these sources will
cover the parent material, soil physical and chemical properties, and clay
mineral composition. Background soil survey data of the land from which the
sediment orginated, such as the crop, fertilizer, and insecticide/herbicide
history of that land, and the rate of sedimentation and the microbial life of
the water body should be obtained, if available.

The collected sediments should be analyzed for pH, cation exchange capacity,
organic carbon, and size distribution, using the methods outlined and refer-
enced below.

8.5.1 JDH

Measurement of the pH of a sediment is important when working with com-
pounds whose ionization state is affected by pH. The strength of sorption will
depend on the degree of ionization, particularly where the sorption mechanism
is ion exchange.

The pH of the sediments should be measured by the method described by
Peech (1965). Two parts of a solution of 0.01 M CaCla are added to one part
of a sediment to adjust the ionic strength of the suspension. The suspension
is stirred several times during the next 30 minutes. The suspension is left to
settle for 30 minutes and the pH of the supernatant is measured with a glass
pH electrode containing an internal calomel reference electrode.

8.5.2 Cation Exchange Capacity (CEC)

An important parameter of the sediment when dealing with ionizable com-
pounds is CEC. The degree of sorption of the compound by the sediment can be

284
-------
directly related to the CEC of the sediment. The method used consists of
saturating the sediment with NH^+, washing away excess NH^+, distilling NH-j
into dilute l^SC^. This method is based on one developed by Mackenzie (1951).
8.5.3 Organic Carbon
The organic matter of sediments is a major source of sorption of non-
ionized compounds on sediments. The amount of organic matter can be determined
by an organic carbon (OC) analysis. This value can be correlated with the
degree of sorption by different sediments. The analytical methods for organic
carbon are not specific and yield varying results depending on the method used.
However, the trend between sediments should be in the same direction.

One method is that of Walkley and Black (Hesse, 1971). The organic
carbon is oxidized by a wet dichromate digestion, and the excess dichromate
is titrated with ferrous ion in the presence of barium diphenylamine sulfonate.
The organic carbon obtained from the analysis is multiplied by a correction
factor of 1.33.
The second method is a dry combustion technique (Hesse, 1972). The
dried sediment sample is placed in a combustion tube through which oxygen is
passed, and the tube is heated to 1000°C. The evolved CC>2 is collected and
weighed. To rid this analysis of interferences by carbonate, the sediment
is first acidified before drying. Several commercial laboratories routinely
make this measurement.

8.5.4 Size Distribution

The size distribution of the sediment is determined using ASTM Methods
D421 and D422-63 (ASTM, 1978). The sample is prepared according to ASTM
Method D421. The size distribution of the fraction of the dry sediment that
is retained on the No. 10 (2.00-mm) sieve is determined by further sieving and
then by sedimentation, using ASTM Method D422-63. The weight percent of the
size fractions shown in Table 8.1 should be reported for each test sediment,
using the format suggested in this table.
Table 8.1. SEDIMENT SIZE FRACTIONS

Fraction
Gravel
Coarse
Medium

sand
sand
Fine sand
Coarse silt
Medium
silt
Retained
sieve
No. 4
No. 10
No. 40
(4.8
on
mm)
(2.0 mm)
(425
No. 200 (75

_
Mm)
Mm)

Fine silt
Clay
o
Size Range
(cm)

4
2
4
7
2
5

.8
x
.2
.5
x
X
> 4.8 x
x 10~1-2
10"1-4 . 2
x 10-2-7
x 10~3-2
10~3-5 x
10~4-2 x
Time to settle 10 cm
(sec) (min)
ID'1
x
X
.5
x
10
10
10-1
10-2
x 1Q-3
10~3
i-4
-4
0.03
0.63
19.8
278 4.6
4450 74.2
2.8 x 104 464
< 2 x 10-4
Particle diameter. The size of the silt and clay fractions are the
equivalent Stokes diameters for spheres.
285
-------
8.5.5 Preparation of the Sediment

Each sediment sample should be sieved wet through a No. 10 (2.0-mm)
sieve to remove the large organic debris, rocks, and gravel. It should then
be quartered and stored in small polyethylene jars at 4°C.

It is very difficult to make reproducible transfers of whole sediments
if the sediments are in suspension. The sand fractions settle rapidly, and
they constitute a significant portion of the total mass of many sediments.
Therefore, only the particles smaller than 60 ym (6 x 10~^cm) should be used.
The less than 60-um sediment fraction (silt and clay) can be reproducibly
transferred as a slurry. Also, the majority of the sorption occurs on these
fractions and not on the sand and gravel fractions. The less than 60-pm
sediment is prepared by adding the wet sediment to a 2-liter bottle, mixing
it thoroughly by shaking for several minutes, and settling the screened sedi-
ment for 30 seconds to remove the sand and gravel. The discarded fractions
are dried and weighed. The calculations will assume that the discarded
fractions contribute mass to the sediment, but not to sorption.

To determine the concentration of sediment in the suspension, Css, the
sediment is resuspended by shaking for 1 minute. The suspension is allowed
to settle for 30 seconds, and the suspended portion is drawn off into another
container using a syphon. A 10-ml aliquot of this suspension is added to an
aluminum weighing dish using a 10-ml measuring pipet with a large tip opening.
The suspension is constantly stirred during this process with a magnetic
stirrer to ensure the homogeneity of the suspension. The dish is placed in
a drying oven at 110°C and then weighed to constant weight after the sediment
is completely dry. Three determinations are made and the mean taken as the
value of C .
ss

8.6 SCREENING TESTS

8.6.1 Purpose
This screening test protocol is intended to identify chemicals with
n partitic

8.6.2 Procedure
sorption partition coefficients K greater than 100.
It is essential to measure the solubility of the chemical in distilled
water before beginning the sorption test protocol. If solid (or liquid)
phase pure chemical remains suspended in the aqueous phase, erroneous values
of the sorption partition coefficient will be obtained.

The sorption partition data will be fit to a Freundlich isotherm with an
exponent of 1.
286
-------
where
and
C = K C = (K F )C (8.2)
s p w oc oc' w v '
K = K F (8.3)
p oc oc
C = concentration of chemical on the sediment
S 1
at equilibrium (yg g~x sediment)

K = sorption partition coefficient

K = sorption partition coefficient normalized

by the organic content

F = fraction organic content (weight basis)

C = concentration of chemical in the water
W T —1
at equilibrium (pg ml"-1- = mg liter ) .

Estimation of K
_ oc

es t
An estimated value of KQC, which is called KQC , is used to calculate

the concentrations of chemical and sediment for the screening isotherm.

Express the solubility of the chemical in distilled water, C •. , in moles

liter"! (M) . Equation (8.4), which is the least squares fit to the data

plotted in Figure 8.1, is used to calculate
log K = -0.27 - 0.782 log(C ,) (8.4)
O C SO -L

cstz
The available data suggest that K should be within an order of magnitude

of Koc'

Preparation of the Stock Solution of the Chemical

A stock solution of the chemical in distilled or distilled-deionized

water is used to prepare all the chemical-sediment mixtures used in the

isotherm experiments. The initial concentration of the chemical in the stock

solution, C , should be saturated or 1 mg liter"1, whichever is lower.

Experimental Plan for the Screening Isotherm

The experimental plan for the screening isotherm is given in Table 8.2.
287
-------
108
107
106
105
o
LL
LL
LLJ
8
p 103
cc
102
= •
A Karickhoff et al. (1978)
o Smith et al. (1978)
• Kenaga and Goring (1978)
..-2*A.'-
null
Elinniil i i mini i i Mini iiinid iiiimd iiimul iiiiinil liSum! MI
IITT
TO'9 ID"8 10~7 10"6 ID'5 10~4 TO"3 10'2 10'1
SOLUBILITY — moles liter1
SA-4396-85
FIGURE 8.1 SOIL OR SEDIMENT PARTITION COEFFICIENT OF CHEMICALS VERSUS
SOLUBILITY IN WATER
288
-------
TABLE 8.2. EXPERIMENTAL PLAN FOR SCREENING SORPTION

ISOTHERM MEASUREMENTS3

Concentration of chemical
None
Low
Number of
No sediment Low
1
1
flasks
sediment
0
2

High sediment
1
2

a
Replicate measurements should be made of C and C at equilibrium in each

flask. W S
To set up the screening isotherm, the following quantities must be de-

fined and either chosen or measured:

C = concentration of the chemical in the stock solution

° (mg liter"1)

V = total volume of suspension after adding a volume of the sedi-

ment suspension (V ), a volume of the chemical stock solution

(V ), and the volume of makeup water (V) (liters). All

volumes must be expressed in ml.

' Vs+Vc+Vm

C = g sediment per ml of sediment stock suspension
ss

F = estimated fraction of chemical sorbed
S

F = fraction organic carbon of the sediment selected for
oc
the screening isotherm

V = volume of sediment stock solution.
s

The equations that describe the quantities that must be used are:

C = (K est F ) C = Kest C (8.5)
s oc oc w p w

CVF _ CV(l-F)
PCS _ , est . o c s/ ,ft ,,

C^T^ - (Koc Foc) V~ (8'6)
ss s t

and, solving equation (8.6) for V , we obtain
s

F V

V = 5— (8.7)

(Kest F ) (1 - F ) C
oc oc s ss

289
-------
We chose V = 0.5 V for convenience. Also, to be sure that the change
of the concentration of the chemical in the water can be measured reliably,
the values of F at low and high sediment concentrations should be approxi-
mately 0.15 and 0.85, respectively. Then
Vc = 0.5 V (8.8)

1 °'15 Vt
V = —ggj (low sediment) (8.9)
S (K F ) (1 - 0.15) C
oc oc ss

0.85 V
..h (high sediment) (8.10)
S = (1 - °'85> Css

Vm = Vt-Vs-Vc (8'U)

where Vm is the volume of water added to make up the volume to V . The super-
scrips, 1 and h, are used to indicate high or low sediment or chemical
concentrations.

Note that to prepare the sediment-chemical mixtures as recommended
here,

Vh < V - V (8.12)
s t c

To meet this requirement, the concentration of the sediment stock suspension
must be adjusted so that

FsVt
C > — — (8.13)
SS " - V (Vs>

The greatest amount of sorption, F - 0.85, will occur in the high sediment
flask. Then,

0.85 V.
C > E r (8.14)
38 (K F ) (0.15) Vn
oc oc s

The following values were selected for illustration.
290
-------
V = 100 ml

Kest = 105
oc
F = 0.05
OC
Then, since Vh ^ 0.5 V.
s t
0.85 V
(105) (0.05)(0.15)(0.5) Vfc
> 2.27 x 10~3 g ml'1

If C = 0.004 g ml" , then substituting in equations (8.8) through (8.11)

give!3

V1 = , (0.15) (100) = 0>88ml

S (10^) (0.05)(0.85)(0.004)

vh _ (0.85)(100) _
V = r ' = /o. j ml

s (KT) (0.05)(0.15)(0.004)

For convenience, V = 1.0 ml and V = 30.0 ml could be selected. If this were
S ^
done, the actual fractions sorbed would be 0.167 and 0.86 in the low and high

sediment flasks, respectively. This calculation was made by solving equation

(8.6) for F and substituting the appropriate values.
S

(K6St F )C V

F = oc oc ss s (8.15)

S V.. + (KSSt F )C V
t oc oc ss s
Also,
V = V. - V - V (8.16)
m t s c
and therefore
V1 = 100 - 1.0 - 50 - 49.0 ml
m

Vh = 100 - 30.0 - 50 = 20.0 ml
m
291
-------
Measurement of the Screening Sorption Isotherm

To prepare the no chemical/no sediment blank, place V liters of water
in a clean flask.

To prepare the low chemical/no sediment blank, add V liters of chemical
stock solution to a flask, then add (V - V ) liters of distilled water.

To prepare the no chemical/high sediment blank flasks, dilute V liters
of sediment stock solution* with (V - V ) liters of distilled water.
t s
To prepare the chemical/sediment flasks, add to the flask V liters of
chemical stock solution, V or V*1 liters of sediment stock solution, and
either V1 = V - V - Vl or Vh s= V - V - Vh liters of distilled water.
mtcs m tvs
All three blanks should be shaken, extracted, and analyzed at the same
time as chemical/sediment flasks are analyzed. Replicate flasks containing
chemical and sediment are required; single, blank flasks are required for the
screening isotherm.

All solutions, suspensions, and blanks should be made up in clean 500-ml
Erlenmeyer flasks, which are then sealed, covered with aluminum foil to exclude
light, and shaken gently on a wrist-action shaker for 12 to 16 hours (that is,
overnight). If shorter equilibration times are used, the sorption equilibrium
may not be attained. If longer equilibration times are used, transformation
processes, mainly biodegradation, may occur. In some cases, biodegradation
may occur within 12 hours (Smith et al., 1978). In that case, a 2- to 4-hour
equilibration time should be used.

Centrifugation Conditions

At the end of the equilibration period, the contents of each flask must
be centrifuged to separate the sediment from the supernatant. The centrifuga-
tion conditions should be chosen to remove particles greater than about 0.5 J-ira
(5 x 10-5 cm) equivalent diameter (to settle all but the fine clay fraction).
There are two ways uo specify the conditions: by determining the relative
centrifugal force, RCF, or by calculating the centrifugation time, t£.

The RCF is defined as

RCF = u)2 R/g (3-17)

= 1.117 x 10~5 RN2 (8.18)
where
a) = angular velocity of the centrifuge spindle radius(sec~ )
R = radial distance of the particle from the center of rotation
g = gravitational constant (980.1 cm sec )
N = number of revolutions (min~ ).
*0ne sediment is used for all screening isotherm experiments.
292
-------
The value of RCF as a function of RPM and the centrifuge head is usually given
in the centrifuge manual. The value of RCF x g can be used to specify the
centrifugation conditions; the conditions needed to centrifuge particles
greater than 0.5 um (5 x 10 cm) diameter may be determined from Figure 8.2.

The centrifugation time determined from Figure 8.2 is approximate
because the gravitational force exerted on a particle increases as it settles
in the centrigute tube. A more accurate procedure is to use equation (8.19)
to calculate the centrifugation time, t :

4n ln(R,/R ) K -
t (sec) = -=—= — = 4.04 x 10° In (R /R )/
-------
LU
1000
800
600
500
| 400
I 300

200
100
80
60
50
40
30

20
O
10
I
I
8 10 12
RCF (x ID'3)
14 16 18
20
SA-4396-86
FIGURE 8.2 MINIMUM CENTRIFUGATION TIME VERSUS RCF (AT THE TUBE TIP)
REQUIRED TO REMOVE 0.2-jum-DIAMETER (2 x 1
-------
CENTRIFUGE SHAFT
FREE SURFACE WHEN ROTATING
SEDIMENT DEPOSITED
AT AN ANGLE
SA-4396-87
FIGURE 8.3 DEFINITION OF RADII OF A CENTRIFUGE
295
-------
for the chemical.) Standard solutions of the chemical must also be
analyzed.

If the distilled water blank contains more than 5% of the amount of
chemical measured in the low sediment flask, the experiments should be re-
peated to see if the glassware, water, or solutions were contaminated or
a new analytical method must be devised (presuming that the interference is
not the chemical of interest).

Data Analysis

A preliminary estimate of the partition coefficient from the screening
isotherm data (Kscr) is obtained by substitution into equation (8.5), based
only on the averlge of the measurements of C in one set of flasks.
w

C V - C V
Kscr m Kscr=^ - w_t
oc oc p c V C
ss s w

The data for C from either the high or low sediment flask should be used.
The actual values of V and V added to each flask should be used in these
C S
calculations. The appropriate data set should meet the following criteria:

0.15 C V /X < C < 0.85 C V /V.. (8.22)
octw oct ^ '

which is equivalent to specifying that only data from flasks? where the
fraction of chemical adsorbed falls between 0.15 and 0.85 should be used so
that C has been measured reliably. The experiment has been designed so that,
in the other flask, either C » 0.0 (100% of the chemical was sorbed) or
C ~ C V /V (no measurable sorption occurred) .

If the value of Kscr is less than 1500, no additional sorption measure-
ments are required because sorption on sediments will not be a significant
environmental fate. If the value of K^§r is greater than 1500, the value of
C should be measured for the sediment in whichever set of flasks gave partial
sorption. A new value of Kscr is calculated:

KSCr = F KSCr - C /C (8.23)
p oc oc s w
SClT
This value of K is used to plan the detailed isotherm.

8.7 DETAILED TESTS

8.7.1 Purpose

This detailed sorption isotherm test protocol is intended to measure
the value of the sorption partition coefficient, K = K F , on natural

296
-------
soils or sediments. Detailed sorption isotherm measurements should be made
on a chemical if the value of KQC obtained from the screening test is greater
than about 2000.

8.7.2 Procedure

The experimental plan for each isotherm, which should be run on at least
three sediments or soils, is shown in Table 8.3. The initial concentration of
the chemical in the stock solution should be saturated or 1 mg liter , which-
ever is lower. It is essential to assure that all isotherm measurements are
conducted with pure solutions of the chemical in water. Procedures for
preparing these solutions are given in Section 8.6.2.
TABLE 8.3. EXPERIMENTAL PLAN FOR THE DETAILED
SORPTION ISOTHERM MEASUREMENTS3
Concentration Number of flask
of chemical
None
Low
High
No sediment
1
1
1
Low sediment
1
2
2
High sediment
1
2
2
a
Four replicate measurements should be made of C and C at equilibrium in
1. £1 1 S W
each flask.

Next, the amount of sediment required in each flask must be calculated.
The experiments are designed so that the concentration of chemical remaining
in solution spans a tenfold concentration range at equilibrium. The equations
needed to calculate the amount of stock solution of chemical and stock sedi-
ment suspension are

F = fraction of chemical sorbed (8.24)
s

predicted value of C , based on value of F selected (8.25)
s &

= C V F /C V
o c s ss s

Vt Fs
V = — (8.26)
S (1 - F ) KSCr C
v s' p ss

V F
= — (8.27)
(1 - F ) (KSCr F ) C
^ s oc oc' ss

est
The values of F and C are selected to span a range of concentrations of
both C and C . TheseSselections then dictate the values of V and V for
s w s c

297
-------
each flask. The equations for V and V for each flask of the detailed

isotherm are given in Table 8.4.
TABLE 8.4. CALCULATION OF VOLUMES OF STOCK SOLUTIONS

FOR DETAILED ISOTHERM MEASUREMENTS

No chemical
F
s
cest
w
V
s
V
c
Low chemical
F
s
cest
w
V
s
v1
c
High chemical
F
s
cest
w
V
s
Vh
c
No sediment

0
0

0.4 C
o
0
0.35 V
t

0.6 C
0
0
0.6 V
t
Low sediment

0.33 V^/KSCr C
t p ss
0

0.25

0.26 C
o
0.33 V /KSCr C
t p ss
0.35 V..
t

0.25

0.45 C
o
0.33 V_/KSCr
t P
0.6 V_
t
High sediment

3.0 V_/KSCr C
t p ss
0

0.75

0.088 C
o
3.0 V /KSCr C
t p SS
0.35 V
t

0.75

0.15 C
o
3.0 V /KSCr C
t p ss
0.6 V
t

The concentration of sediment in the stock sediment suspension. Css

(in g liter"-'-) , must be adjusted, depending on the value of K^ = Ko£r FOc»

so that Vs < 0.4 Vt for the high sediment/low chemical flask. Otherwise,

the experiments cannot be carried out. Therefore, C00 must be adjusted so
. So
that
C >
ss
F v.
s t
F V,
(KSCr F )
oc oc
- F ) V
s s
- V Vs
(8.28)
293
-------
If V = 100 ml, F = 0.8, KSCr = 50, and V = 0.4 V , then C > 0.2 g ml"1.
L S P o L. oo

Blanks are prepared using appropriate volumes of only one stock solution.
In all cases, the volume of distilled water that must be added to make up the
volume to V. is
V = V_ - V - V (8.29)
m t s c
At least four sediments, spanning a range of organic content, cation
exchange capacity, and predominant clay mineral, should be used for detailed
isotherm measurements.

All solutions-suspensions, and blanks should be made up in clean 500-ml
Erlenmeyer flasks, which are then sealed, covered with aluminum foil, and shaken
gently on a wrist-action shaker for 12 to 16 hours. If shorter equilibration
times are used, the sorption equilibrium may not be obtained. If longer equil-
ibration times are used, transformation processes, most likely biodegradation,
may occur. If biodegradation is observed, which may be the cause of a poor
mass balance (see below), a 2-hour equilibration time may be used.

At the end of the equilibration period, the contents of each flask must
be centrifuged to separate the sediment from the supernatant. The centrifuga-
tion conditions used for the screening isotherm should also be used for the
detailed isotherms (see Section 8.6.2).

After centrifuging, the aqueous phase is decanted carefully from the
sediment. About 1 ml of solution will probably be retained in the centrifuge
tube. One extraction and four replicate analyses of the chemical in the ex- ^
tract must be performed on both the supernatant and sediment from each flask.
Appropriate standard solutions that span the concentration range of the chemi-
cal in the extracts must also be analyzed.

A simple check of the mass balance in each flask should be made to
determine if significant losses (or gains) of the chemical have occurred. At
least 80% of the total amount of chemical (but less than 120%) should be re-
covered, which is true if equation (8.30) is satisfied:

1.2 CV>CCV + C V > 0.8 C V (8.30)
o c ~ s ss ss wt oc
If equation (8.30) is not satisfied, the source of the error should be deter-
mined and the experiment repeated.

8.7.3 Data Analysis

The data analysis is carried out in two stages. First, a linear least
squares regression analysis is performed to estimate K for each sediment.
We have presumed that the analytical method developed for the screening
isotherm can be used for the sediments used for the detailed isotherms.
299
-------
The average values of C and C for each flask are calculated. The regression
equations are: w
Zx.y.
b = 1 * = K = K F
Zx 2 P oc oc
yx
Ex.
(n - 1)
-1
(8.31)
(8.32)
*
95% confidence interval = (t , n)S (£x)
n^ _L j ** y
(8.33)
where b = K is the slope, x. and y^ are the individual or eiverage measurements
from each flask of C^, and Cs, respectively, S is the standard error, and
cn-l a is t'ie t-value from Student's t-test for n measurements at a = 0.05
confidence. These expressions are in the form suitable for use in hand calcu-
lators, such as the Hewlett-Packard Model 65. This procedure is used to
estimate K for each sediment tested.

When both C and C are measured, the linear least squares procedures
using average values for C and C are not statistically correct because re-
sponse variables appear on both sides of the regression equation. In addition,
the averaging procedure throws away valuable information about experimental
variance. To deal more correctly with this situation, we use pairs of simul-
taneous nonlinear regression equations, one pair for each experimental condi-
tion. One of the pair utilizes concentrations of chemical on the sediment,
C,,,
C = K C.
s pi
(8.34)
and the other of the pair utilizes the concentrations measured in the super-

(8.35)
natant, C ,
w'
C = C.
w i
where C^ is the estimated value of supernatant chemical concentration for a
particular experimental condition, i. With this formulation, the response
variables appear only on the left-hand side of the regression equation.
The common parameters K and C^ tie the simultaneous regressions together and
assure that the resulting estimate for K is conditioned on both the sediment
and supernatant concentrations measured.
300
-------
The method is superficially similar to the simple linear least squares
procedure used to estimate Kp. The regression equation (8.35) use the super-
natant concentrations to estimate a single concentration that best represents
the concentration in the flasks for each different substrate and sediment
level. This representative concentration is then used with the concentration
of supernatant on the sediment in equation (8.34) to estimate K . An impor-
tant difference between the two approaches, however, is that, with the non-
linear appraoch, the supernatant concentration, C., that represents a particular
substrate and sediment levej. is not necessarily the average supernatant con-
centration. The values of C. determined by the method are almost always
very close to the average except when concentration measurements are highly
scattered.

An important feature of nonlinear approach is that it does not require
that the same number of observations of both C and C be made in each flask.
s w
The formulation also does not require that individual measured values of Cs
and GW from a particular flask be paired. This is an important feature because
any pairing of data points is artificial and could bias the estimate of K .

The non-linear approach can be formulated compactly if the sorption
isotherm experiments are thought of in terms of two factors: total mass of
chemical and sediment level. Let the subscript i correspond to a particular
combination of sediment level and chemical mass level. For example, a possible
experimental setup is shown below in which the numbers represent the value of
the test condition identification variable i to be used in the regression
procedure described below.

Concentrat ion
of chemical No sediment Low sediment High sediment

None 147

Low 258

High 369
In general, suppose there are p total experimental conditions. Each
condition may be represented by one or more flasks. Then the regression
model may be written as:
Y. = VUK, C.U - 6J + K C^M I (8.36)
301
-------
where
!1 if data are from the sediment

0 if data are from the water

Y. = predicted concentration of chemical for observation j,
j = 1, ..., n. When 6. = 1, Y. is the predicted value of
the chemical concentration on the sediment. When 6. = 0,
Y. is the predicted value of the chemical concentration in
tne water phase.

i = test condition identification

!1 if observation j corresponds to test condition i

0 otherwise i = 1, ..., p
^
C. = estimate of chemical concentration in the water phase,
corresponding to test condition i

K = estimate of partition coefficient, K > 0

M = grams of sediment per liter of water.
s
There are then p + 1 parameters to be estimated, C. (i = l,...,p) and
K . Note that there need not be data in all the cells indexed by i. The
indicator variables u>,., if properly specified, will prevent any inconsis-
tencies due to missing-1 observations.

The BMDP3R program (from the Biomedical Computer Programs package,
P-series) may be used to obtain the necessary parameter estimates. This
program uses a modified Gauss-Newton algorithm (described in Section 8.8.10).
Input variables for the BMDP3R routine are Y., t (the test condition iden-
tification), 6., and M . The ui. . are computed by the program, using the
value of t.(w -] = 1 for i = t., J0 otherwise). The BOP3R program requires
(as a minimumr1 the following tUrds on the IBM370:

(job card)
(key card)
// EXEC BIMEDT, PROG + BMDP3R
// FUN DD *

DIMENSION IW (50)
NT = NPAR-1
F - 0
DF(NPAR) = 0
DO 1 I = 1, NT
IW(I) = 0
1 CONTINUE
302
-------
ICOND = X(2) + .01
IDELT = X(3) + .01
IW(I COND) = 1
DO 2 I = 1, NT
F = F + IW(I) * (P(I)*(1-IDELT) + X(4)*P(NPAR)*P(I)*IDELT)
DF(I) = IW(I)*((1-IDELT) + X(4)*P(NPAR)*IDELT)
DF(NPAR) = DF(NPAR) + IW(I)*X(4)P(I)*IDELT

CONTINUE
/GO.SYSIN DD *
/PROBLEM TITLE = ' (problem title)' .
/INPUT VARIABLES ARE 4 .
FORMAT IS '((input format))'.
/VARIABLES NAMES ARE CONG, TCODE, SOURCE, MASS .
/REGRESSION DEPENDENT IS CONG .
INDEPENDENT ARE TCODE, SOURCE, MASS .
PARAMETERS = (p+1) .
/PARAMETERS INITIAL = (p) * 0.0, ^initial estimate of K )
Minimum = (p+1)* 0.0 P
/END
(formatted data goes here)
/*
Note: The variables must be input in the order shown for the function to be
properly evaluated.

The information within the angle brackets (( )) is to be replaced by
the information specific to an individual run of the program. The brackets
themselves are not typed.

An example of the computer input stream and output listing corresponding
to the input shown above is given on the following pages. Note that data are
available only for six cells (2, 3, 5, 6, 8, and 9). The output listing shows
that the estimates for the parameters corresponding to empty cells are zero.
Obviously, these cells could have been omitted entirely from the model, but
they are included for illustrative purposes.

In this example of an input stream, the name card has been included to
give meaningful names to the parameters. If this card is omitted, the param-
eters are referred to in the output as P(l), P(2), and so on where the numbers
in parentheses correspond to the cell identification code, and P(p + 1) cor-
responds to K . The names used here identify the sediment level (second
character) an8 the chemical level (third character). For example, CLH corres-
ponds to low sediment concentration and high chemical concentration.

The first several cards of the input (those beginning with "//") may
differ at various installations and various modes of input (this run was sub-
mitted through a time-sharing terminal).
303
-------
// JOB
// EXEC BIMEDT,PROG«BHDP3R
//FUN DO «
DIMENSION IW(IO)
NT-NPAR-1
F»0
DF(NPAR)«0
DO 1 1-1.NT

1 CONTINUE
ICOND«X(2)+.01
IDELT'X(3)+.01
IW(ICOND)'1
DO 2 I'l.NT
F»F+IM(I)«(P(I)»(1-IDELT)+X(4>«PCNPAR)»PCI)«IDELT)
DF
-------
13.500 600.0000358
13.400 600.0000358
14.700 600.0000358
It.300 600.0000358
1M.800 600.0000358
16.200 600.0000358
16.000 600.0000358
15.900 600.0000358
6.7304610.0000358
6.7304610.0000358
7.8402610.0000358
8.640 900.0000717
8.910 900.0000717
8.380 900.0000717
8. 1 10 900.0000717
8.380 900.0000717
8. 110 900.0000717
9. 180 900.0000717
9. 180 900.0000717
8.910 900.0000717
8.060 900.0000717
7.940 900.0000717
7.690 900.0000717
6.7255910.0000717
6. 1017910.0000717
7.740 500.0000358
7.350 500.0000358
7.740 500.0000358
7.810 500.0000358
7.680 500.0000358
7.420 500.0000358
8.640 500.0000358
8.510 500.0000358
8.640 500.0000358
7.320 500.0000358
7.320 500.0000358
7.180 500.0000358
3.8664510.0000358
3.8664510.0000358
3.8664510.0000358
4.290 800.0000717
4.290 800.0000717
4.150 800.0000717
5.160 800.0000717
4.900 800.0000717
4.900 800.0000717
4.580 800.0000717
4.580 800.0000717
4.450 800.0000717
5.580 800.0000717
5.710 800.0000717
4.620 800.0000717
4.4813810.0000717
INPUT STREAM, page 2
305
-------
PROGRAM REVISED DECEMBER 1977
MANUAL DATE — 1977
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The output listing shows that, even for a very poor initial guess for
K (the guess was zero and the actual estimate was 12,247), the sequence con-
verged in only seven iterations (page 2 of the output listing), at a total
computer cost of 73c. Page 3 of the output summarizes the parameter estimates
and the estimated asymptotic standard deviations of the estimates. The latter
may be used to construct confidence intervals for the parameters (assuming
normality). Pages 4 and 5 of the output list the input data, the predicted
values, and the residuals.

The refined values of Kp for the soils or sediments tested can then be
used to estimate a KQC value for the chemical. The linear least squares
approach embodied in equations (8.31), (8.32), and (8.33) is used where y is
identified as the measured values of K and X is identified as F . Solution
to the linear least squares regression yields a value of b that is identified
^ Koc.

8.8 BACKGROUND

Sorption of organic substrates onto sediments and biota can be a very
important phenomenon in the aquatic environment. The sediments can act as
sinks for sorbed materials, removing them from the water column. However, the
substrate can also be released (desorbed) from the sediments at a later time.
In this way sorbed material can also be a source of pollution. Sorption of
pollutants by sediments can also be a source of pollution. Sorption of
pollutants by sediments often results in the concentration of low solubility
pollutants in a part of the water column where uptake by a biomagnification
becomes significant, as has been the case with Kepone in the James River and
in Chesapeake Bay.

The use of the terms "sorption" and "adsorption" deserves special comment.
Sorption includes any type of process whereby the substrate is physically or
chemically bound to a solid surface (chemisorption). Adsorption implies to
us that the process that holds the substrate on the sediment is strictly
physical, such as the van der Waals type of attraction. However, sorption
processes of ionizable substrates such as amines may include chemical bonding
interactions as well as physical processes. While other authors have used
adsorption to include chemical interactions (Hamaker and Thompson, 1972) we
will use "sorption" to avoid confusion.

Several excellent reviews of the sorption of organic substrates on soils
and sediments are available. Hamaker and Thompson (1972) have prepared an
excellent review of sorption of pesticides on soil, clay, sediments, and the
like. Theng (1974) has written a prize-winning text entitled The Chemistry
of Clay-Organic Reactions. This section provides only a brief overview of
sorption on soils. The reader should consult the two references cited above
for detailed discussions.

8.8.1 Theory

Sorption takes place, in general, when solution containing a dissolved
chemical contacts a solid phase surface. If the total amount of chemical is
increased, the amount of chemical that is sorbed is also increased. Experi-
mental data have generally been found to fit one of two mathematical forms:
the Langmuir and Freundlich isotherms.
311
-------
The Langmuir isotherm can be derived theoretically from kinetic con-
siderations by assuming that:

• The energy of sorption is constant for a particular sorbent
and independent of the surface coverage.

• Sorbed molecules do not interact.

• Sorbed molecules form a monolayer on the sorbent surface; the
amount sorbed is limited by the surface area of the sorbent.

First, we define C and C as
w s

weight substrate in solution (ug)
w ml solution

_ weight substrate sorbed (yig)
C = - - r — i - ^^ = ppm
s g sorbent rr

at equilibrium. The substrate weights must be in the same units (e.g., ng,
yg) . The Langmuir isotherm equation is defined as
a b C
(8-37)
s

where a and b are constants and

a = X (8.38)
c

K
b = ^ (8.39)
c

where X is the sorption capacity of the sorbent and K is a partition
coefficient. Equation (8.37) can be rewritten as
K C
p w
C = 1 4- K C /X (8.40)
s p w c
or

X K C
c p w

Data for gas-solid sorption generally and for organic substrates sorbed on
clay minerals usually fit the Langmuir isotherm. However, natural sediments
are inhomogeneous—sorbed complex organic materials such as humic substances
are already present on the clay particles—and sorption by these sediments
usually fails to fit the Langmuir isotherm because the first assumption is
violated.

312
-------
Data for sorption of multiple substrates from solution on nonuniform
surfaces generally fit the Freundlich isotherm, which is an empirical
equation

C = K C 1/n (8.42)
s w

where K and n are experimentally determined constants, and again, it is
assumed implicitly that the system is at equilibrium.

At low substrate concentrations, n is often very nearly equal to 1.
If n = 1, the units on each side of equation (8.42) cancel and K becomes a
partition coefficient, as defined by

C = K C (8.43)
s p w

Since sorption of organic molecules is often correlated with soil and
sediment fraction organic content (F ) (see Section 8.7), a useful form of
equation (8.43) can be defined as

C = K C (8.44)
s oc w
where
K = K /F (8-45)
oc p oc
The F can be measured by several analytical procedures (Hesse, 1971).

8.8.2 Sorption Mechanism

Sorption of a chemical (the sorbate) onto a solid surface (the sorbent)
is due to the intermolecular forces between the sorbate and sorbent. In the
case of sorption of organic chemicals dissolved in water on natural sediment
sorbents, many types of interactions are possible, including:

• Van der Waals/London forces.
• Hydrophobic bonding induced by the unusual lattice structure of
liquid water.
• Charge transfer, including II-cloud and lone electron-pair donors
and acceptors, and hydrogen bonding.
• Ligand exchange and chelation, ion exchange, and other forms of
chemisorption.
Hamaker and Thompson (1972) also point out that the exponent in equation
(8.42), 1/n, is an "archaic remnant of an attempt to give the Freundlich
equation physical meaning and is retained only because its use is embedded
in the literature."

313
-------
Van der Waals-type interactions arise as a result of very rapid fluctuations
in the charge distribution of the electron clouds of molecules that induce
an instantaneous dipole that averages out on longer times. On a molecular
level, however, the instantaneous dipole results in weak attractive forces
that decrease as a function of d~^, where d is the distance; between molecules.
At distances less than the van der Waals radii, strong repulsive forces
produced by the nuclear charge limit the distance of approach.

Liquid water is considered to be a combination of ice-like structures
and more compact but random orientations of water molecules within and
around the ice-like structure. The hydrophobic portions of dissolved organic
molecules disrupt the structure of liquid water and raise the entropy of the
solution. If sorption is possible, the water is able to revert back to its
normal structure, thereby reducing the entropy of the system. Hence, sorption
is thermodynamically favored. This sorption mechanism has been called
hydrophobic bonding. The combination of van der Waals and hydrophobic bonding
may be largely responsible for the strong sorption characteristics of chlor-
inated organic molecules such as DDT (Hamaker and Thompson, 1972) , disulfotone
(Graham-Bryce, 1967), and high molecular weight polynuclear organic molecules
(POMs) on soils (Smith et al., 1978).

Charge transfer reactions, such as TT electron donation by aromatics
and lone-pair interactions of amines, may be important interaction mechanisms
with soil and sediment organic matter. However, formation of charge-transfer
complexes is also an equilibrium process

A + D = A • D (complex)

and, at the very low concentrations of organic pollutants found in the envi-
ronment, the equilibrium should lie far to the left.

Chemisorption, which may include ligand exchange, chelation, and
ion exchange may be very important processes, especially with ionizable sub-
strates such as carboxylic acids and amines. An excellent example is the
herbicide paraquat, l,l'-dimethyl-4,4'-bipyridylium ion, which possesses two
permanent positive charges. It is strongly sorbed (or, more correctly,
chemisorbed) to the cation exchange sites of clays and sediments (Karickhoff
and Brown, 1977; Hamaker and Thompson, 1972).

8.8.3 General Design of Sorption Isotherm Measurements

The general procedure for measuring sorption isotherms consists of
equilibrating a solution of the chemical with the sediment for a period of
hours. Then C and sometimes C is measured by an appropriate analytical
technique. The concentration of chemical and/or sediment is adjusted so
that C spans a reasonable range, say, from a factor of 2 to more than 10.

To fit the isotherm data to the Freundlich isotherm equation, a plot
of C versus C (for n ^ 1) is prepared. The slope of the line is K . If
the IxponentiaY form is used (n = 1), a plot of log C versus log C should
w
314
-------
be a line with slope 1/n and log C = K when log C = 1. Statistical
procedures for calculating K or 1/n and K are described in Sections 8.7.3
and 8.8.10. P

Several experimental designs are possible to obtain data over a
range of values of C . One approach is to vary the total amount of chemical
present and hold the sediment loading constant. Then the fraction of the
chemical adsorbed, F , will be nearly constant. Two major advantages of
this approach are that it is relatively convenient to set up and that satura-
tion effects can be observed if C is high enough. An alternative approach
is to hold the total concentration of chemical constant and vary the sediment
loading. This second approach has the advantage that, if the value of K or
K is affected by the sediment loading, the effect can be observed. Either
or these approaches will be unsatisfactory if the solubility of the chemical
is very low or the precision and accuracy of the analytical are poor.

When sediment loading is held constant and total chemical concentration
is varied, C will be low at low total chemical concentrations. When the
total chemical concentration is held constant and sediment loading is varied,
then at the low sediment loadings, the amount of chemical adsorbed will be
low and C « 0. Similarly, at the high sediment loadings, most of the chemi-
cal will Be on the sediment and C « 0. If the accuracy and precision of
the measurement of C and C are poor at very low levels, the precision of
the estimates of K or K will also be very low.

For these reasons, we recommend the experimental design suggested in
Table 8.3, which is a combination of the two approaches. The levels of
sediment and chemical have been adjusted to span a range of C of a factor of
about 4 (see Table 8.4). W

Many of the isotherm measurements reported in the literature are based
on measurements of C only, plus the known total amount of chemical and sedi-
ment added. This approach is particularly convenient when radio-labeled
samples of the chemical are available. However, our experience with sorption
isotherm measurements suggests that direct, independent measurement of C and
C is essential to obtain accurate and precise estimates of K or K . If
w p
both C and C are measured, losses due to sorption on the walls or the
vessel, volatilization, and chemical and biological transformation processes
will be detected when low mass balances are observed. The statistical pro-
cedures recommended in this protocol are not affected by such losses, and
estimates of K or K can be obtained (unless C = 0 or C = 0).
p s w
The remaining subsections address specific problems that arise when one
attempts to design a suitable test protocol for determining the sorption and
desorption of organic chemicals by sediments. The most important questions
involve the kinetics of sorption and desorption, the effects of sediment
particle size, equilibration time, system pH, indigenous dissolved organics,
and the use of natural wet or dried sediments. Experimental work has been
done in these areas, and the results are available from various sources.
Unfortunately, little attention has been given to the detailed reporting of
experimental procedures.
315
-------
8.8.4 Sediment Particle Size

Sediment particle size is an important parameter in the description
of an experimental protocol because there is considerable evidence that the
value of K varies strongly with the size fraction of a particular soil or
sediment sample. Experimentally, it would be very convenient to use only
particles less than 100 ym in diameter. The work done in this area indicates
that the large particles will not significantly affect sorption characteris-
tics of the sediment. Meyers and Quinn (1973) fractionated clays and natural
sediments into five sizes ranging from 1 mm to less than 44 ym. They found
that the 1-mm to 250-ym fractions sorbed essentially no heptadecanoic acid
and that the 250 to 105-pin fractions sorbed only 1% of the acid sorbed by the
fractions smaller than 105 ym.

Karickhoff and Brown (1977) studied the sorption of paraquat on natural
sediments that had been fractionated by size. The experiment suffers from
low total recovery of the paraquat (54% - 90%). It was noted, however, that
the low paraquat recovery was due mostly to the loss of small particles that
had been retained on the larger particles after the first separation and
were later washed away. Because the low recovery is due primarily to the
loss of fine particles, the data for the larger particles should still be
useful. It was found that only 1% - 9% of the total sorbed paraquat was on
the particles larger than 64 ym in diameter.

It has been shown by Huang et al. (1974), Wang et al. (1972), Pierce
et al. (1973), Karickhoff et al. (1978), and Saltzman et al. (1971), that
increased sorption occurs in sediments with an increased CEC or organic car-
bon content, depending on the nature of the sorbate. The greater sorption
on small particles is due primarly to their large ratio of surface area to
mass. A larger surface area will provide more sites on which sorption
can occur. To cite one example, Karickhoff and Brown (1977) measured the
CEC and organic carbon content of the various fractions. They found that
the CEC and the organic carbon content were greater for smaller particles.

Another potential problem concerning sediment particle size is that
very small particles are difficult to remove from suspension. Karickhoff
and Brown (1977), using natural clay sediments, found that after 4 hours
of centrifugation at 10,000 rpm, the paraquat absorption spectrum of the
supernatant was still dominated by sorbed paraquat, indicating that the
presence of paraquat in the supernatant is due mostly to a fine clay
(>0.08 ym), which is only very slowly removed from suspension. Consequently,
care should be taken to determine that all the particles are removed from
suspension.

For most natural soils and sediments, the fine clay fraction repre-
sents a small percentage of the total soil or sediment mass. Thus, although
Karickhoff and Brown (1977) found that the partition coefficient for paraquat,
K , was extremely large for the fine clay, for the five natural sediments they
tlsted, less than 0.5% of the total amount sorbed was in the fine clay frac-
tion. Most of the sorption occurred on coarse clay 0.2 ym s d *• 2 ym. They
also found that more than 99% of the paraquat was sorbed by particles larger

316
-------
than 0.08 ym (8 x 10 cm). Their data for one natural sediment are shown in
Table 8.5. The sorption of paraquat is strongly dependent on the CEC.
TABLE 8.5 PARAQUAT DISTRIBUTION IN A NATURAL SEDIMENT0

Fraction
Sand
Coarse silt
Medium silt
Fine silt
Coarse clay
Medium clay
Fine clay
Size range
(cm x 1(T)
>64
64-20
20-5
5-2
2-0.2
0.2-0.08
<0.08
Sediment
(g)
833
45
32
14
14
0.53
0.40
fraction
(%)
88.7
4.8
3.4
1.5
1.5
0.06
0.04
Paraquat
(mg)
0.7
0.9
1.8
4.6
14.1
0.4
0.06
on sediment fraction
(%)
3.1
4.0
8.0
20.4
62.5
1.8
0.3

Karickhoff and Brown (1977). The data are for Georgia local stream I,
Karickhoff et al. (1978) also studied nonpolar organics, which have K
values that are strongly correlated with F
given in Table 8.6.
oc
An example of this data is
TABLE 8.6 PYRENE DISTRIBUTION IN A NATURAL SEDIMENT'

Fraction
Sand
Coarse silt
Medium silt
Fine silt
Clay
Size range

(cm x 104)
>64
'64-20
20-5
5-2
<2
„ Sediment fraction

P
42
3000
2500
1500
1400

(%)
50
}"
1
Calculated pyrene on
sediment fraction

(%)
1.8
\96.9
1.2

Data for Hickory Hill sediment; Karickhoff et al. (1978).
The data in these references suggest that most of a chemical by weight, will
be sorbed on the silt and coarse clay fractions of the sediment.
8.8.5 Prediction of Soil or Sediment Partition Coefficients

The most convincing basis for predicting sediment partition coeffici-
ents is contained in an extensive review by Kenaga and Goring (1978). They
collected data from more than 100 sources on the partition coefficients,
solubilities, and octanol-water partition coefficients for a wide variety of
organic chemicals. Included were compounds that are neutral, anionic, or
317
-------
cationic in solution. All partition coefficients were converted to K
values, and K was correlated with compound solubility and with octanol-water
partition coefficients. Low water solubilities and high octanol-water
partition coefficients were associated with large values of K . It was
found that K could be predicted within an order of magnitudeCfrom either
the solubility or the octanol-water partition coefficient. These results
are quite similar to correlations found by Smith et al. (1978) and Karickhoff
and Brown (1978). A more complete correlation of K versus water solubility
using all three sets of data was presented earlier as Figure 8.1 and equation
(8.4).

It is not possible to completely explain the success of the correla-
tion, since the chemicals involved probably do not all interact with the
soil by the same mechanism. The various interactions probably include
van der Waals-London interactions, hydrophobic bonding, hydrogen bonding,
charge transfer, ligand exchange, ion exchange, and chemisorption. A partial
explanation may be simply that soil and sediment organics (humic and fulvic
acid) are complex materials that contain enough different chemical groups
that they can interact in all of the above ways with dissolved organic
chemicals. Humic material appears to be a highly aromatic polymer that
contains carboxyl, phenolic, alcoholic, carbonyl, and methoxyl groups, as
well as amino acids and polysaccharides (Schnitzer and Khan,. 1972).

An additional factor is that both solubility and KQW indicate how much
affinity a particular chemical has for water. Low solubility or a large
octanol-water partition coefficient indicates that the chemical is adverse
to water, and since humic material is so chemically heterogeneous, it pro-
vides an almost universal other place to be.

8.8.6 Equilibration Time

The length of time required for a sorption system to come to equili-
brium is another point that needs to be considered. In most: cases there will
be an initial rapid approach to sorption equilibrium (1-24 hours), followed,
in some cases, by a prolonged, slow (+ 4 days) increase in sorption.
Doehler and Young (1960) found that quinoline reached approximately 97% of
its equilibrium concentration within 100 minutes of initial contact with
Na-montmorillonite. The quinoline then continued to be sorbed and reached
its equilibrium state after 4 days. Hamaker et al. (1967) reported that
sorption of picloram increased for 23 days with no sign of having reached
equilibrium.

The matter of reaching an equilibrium state is even more important
when considering desorption proceeses. It has been shown that the longer a
chemical has been in contact with sediment, the more difficult it is to
desorb, which indicates a slow approach to equilibrium. In a study by
Hamaker et al. (1966), it was found that, after an incubation period of
28 hours, picloram was much more difficult to remove from sediment than after
an incubation of 2 hours. Meyers and Quinn (1973) took bentonite on which
heptadecanoic acid had been sorbed and resuspended it in saline water,
allowing desorption to occur. This process was repeated several times on
the same bentonite, and the supernatant was analyzed after each suspension

313
-------
and desorption. Analysis showed that a smaller percentage of the acid re-
tained on the bentonite was desorbed during each successive resuspension.
Saba et al. (1969) also did desorption experiments with dieldrin sorbed on
soil. They found that when dieldrin has been incubated for several months
it is harder to extract from the soil than when it has been incubated for
several days.

The different sorption rates and the fixation of organic chemicals on
sediment is probably due to the concurrent action of two sorption mechanisms.
Initially, there is a rapid physical sorption onto the organic sediment
matter. Then, the chemicals diffuse more slowly into the interstitial clay
(Saltzman and Yaron, 1971). Highly ionic material may have a higher affinity
for the inorganic part of a soil or sediment than for the organic fraction.
Burns and Audus (1970) sorbed paraquat which is highly ionic, on the
separated organic fraction of a natural soil and suspended this in a dialysis
bag. The bag was placed in a water suspension of the inorganic fraction of
the soil. Within six hours, nearly all of the paraquat had moved through
the dialysis bag and was sorbed onto the inorganic fraction. When the
dialysis bag was suspended in distilled water, only 30% of the paraquat was
released from the organic fraction.

8.8.7 Effect of pH on Sorption

Since different sediment-water suspensions frequently have different
pH values, it is very important to know how pH of the system affects the
adsorption characteristics. It is not expected that neutral compounds or
strong acids and bases will be affected by changes in pH, because their
form is not dependent on the pH of their environment. Weak acids and bases,
however, can be present in two forms, depending on the pH of the environ-
ment. At low pH, weak acids are in the free acid form and weak bases are
in the cationic form. Nearly all sediments have negatively charged sites;
therefore, the free acid will be more highly sorbed than the anionic acid
and the cationic base will be more highly sorbed than the free base. As
the pH of the sorption system decreases the sorption of weak acids and bases
increases. The pH dependency of adsorption has been demonstrated by several
groups. Doehler and Young (1960) sorbed quinoline on various clay materials
and found that quinoline sorption increased with decreasing solution pH.
The solution pH was controlled by use of buffer solutions.

It has been shown that sorption increases rapidly as the pH approaches
the pKa of the compound studied. Liu et al. (1970) studied the pH dependency
of ametryne and diuron sorption and found that as pH decreased, sorption
increased. At a pH approximately equal to the pKa, the sorption increased
much more rapidly. Bailey et al. (1968) sorbed S-triazines, substituted
ureas, and phenylalkanoic acid on montmorillonite clay and found that sorption
began to increase at a surface pH about 1-2 pH units above the pKa and
continued to increase as the pH further decreased.

The pH of a sediment-water system is difficult to determine because
the pH of the solution can be different from the pH of the sediment surface.
Bailey et al. (1968) observed that the pH of the sediment surface can often
be 3-4 pH units lower than the solution pH. This conclusion was made by

319
-------
noting that very little atrazine should have been sorbed on the montmorillonite
clay at the measured solution pH (due to little dissociation). Sorption, how-
ever, was almost complete, indicating that the pH of the clay surface must be
about 3 pH units lower than the solution pH.

From the work done by Bailey et al. (1968), it would appear that the
dependence of sorption on pH of the bulk solution or on pH of the sediment
surface varies with different organic chemicals. They found that sorption
of the basic S-triazines and substituted ureas depends on the surface acidity
of the montmorillonite clay rather than on the pH of the bulk solution. For
acidic compounds, (2,4-D), however, it was found that sorption was dependent
on the pH of the solution. Unfortunately, very little other work has been
done in this field, and any generalizations are made rather tenuously.

8.8.8 Effect of Other Dissolved Organics on Sorption

It is important to understand the effect of dissolved, indigenous
organics on sorption of a particular organic chemical. Unfortunately, little
work has been done in this area of research. It has been found, however,
that organic chemicals are generally sorbed less when other dissolved organic
chemicals are present. Meyers and Quinn (1973) performed experiments that
involved removing various amounts of the indigenous organics from natural
waters by sorption on filters. They used a Whatman-54 filter, which sorbs
almost no organics, and a Gelman A filter, which removed almost all the organ-
ics. The treated natural water was then used for sorption isotherm experi-
ments with heptadecanoic acid on bentonite. About 95% of the heptadecanoic
acid was sorbed on the bentonite when the indigenous organics had been removed,
and only about 85% was sorbed from the water still containing the indigenous
organics.

The second experiment simulated sorptions onto marine sediments and
involved equilibrating various organic chemicals in a saline solution before
adding the fatty acids to be tested for sorption. After the fatty acids were
mixed in, the clay was added. The organic chemicals used were glucose, amino
acids, fatty acid methyl esters, fatty acids, soil fulvic acid, a synthetic
mixture, and dissolved marine organic matter. They found that the presence
of individual organics at naturally occurring levels did not significantly
affect the fatty acid sorption. When combinations of organic chemicals were
dissolved in the water, however, an appreciable decrease in sorption did occur.
The significant decrease in sorption is due partly to the greater concentra-
tion of organics in the water for a mixture than for an individual organic
chemical. Also studied in this experiment was the effect of allowing the
fatty acids to "age" with the dissolved organics, before adding the sediment.
An aging time of 24 hours resulted in a reduction in sorption 3 to 4 times
greater than for an aging time of 15 minutes.

Decrease in sorption of organic chemicals when in the; presence of other
organic chemicals is apparently due to two mechanisms. The primary mechanism
involves a change in solubility of the organic chemical when it is present
with other organic chemicals. The water solubility of an organic chemical
often increases when other dissolved organics are present, and sorption has
been found to correlate inversely with solubility of an organic chemical in
water (see Section 8.8.6).
320
-------
The second mechanism that results in decreased sorption of an organic
chemical when in the presence of other dissolved organics is competition for
sorption sites. Indigenous organics will also be sorbed on the sediment
particles and any sorption by them will decrease the number of sorption sites
available to the organic chemical of interest. A decrease in sorption sites
will result in decreased sorption.

8.8.9 Comparison of Using Wet and Dried Sediments for
Isotherm Measurements

A factor affecting determination of sorption characteristics that has
been largely ignored is the question of whether to use natural wet sediment
suspensions or previously dried sediments. The character of the sediment is
changed when it is dried. Some clays, such as montmorillonite have a lamellar
structure, which when naturally wet holds a considerable amount of interstitial
water. This interstitial water can affect sorption by altering access mech-
anisms to sorption sites.

Fulk (1975) has worked on determining if there are differences in
pesticide concentration between the bulk solution and the interstitial water.
No description was given for how the interstitial water was separated from
the bulk solution. However, pesticide concentrations were much greater in
the interstitial water than in the bulk solution. If this interstitial water
were removed, the structure would collapse and access to sorption sites would
be affected. Rewetting dried clay can be a difficult process. It may take
several weeks for the system to equilibrate and the interstitial spaces to be
filled with water so that they are once again in natural wet state.

Another important change that can occur in sediment when it is dried
is the greater adhesion of any sorbed organics. If a sediment is dried, any
organic chemical .that has been sorbed on its surface will become more tightly
bound. This is apparently due to the presence of water between the sediment
and sorbed organic material when the system is in the naturally wet state.
In dried sediment, the water layer is no longer present and the sediment-
sorbate bond is strengthened. Graham and Bryce (1967), using disulfoton
sorbed on soil, found that it was considerably harder to remove disulfoton
from a dried and rewet sample than from a naturally wet sample.

A problem with storing wet samples is that biological degradation is
likely to occur. Therefore, we recommend that the sediments be stored wet
at 4°C to minimize biological activity and that they be used promptly.

8.8.10 Derivation of Equations

Equations (8.6). (8.7), (8.15). (8.25). and (8.27)

C V = Weight of chemical added to flask (yg)

C V = Weight of sediment added to flask (g)
ss s
F * Fraction of chemical sorbed
s

321
-------
C V F = Weight of chemical sorbed
o c s

C V (1-F ) = Weight of chemical in supernatant after

equilibration with the sediment

C = C V F /C V (8.25)
s ocssss

C = C V (1 - F )/V_
w o c s t
then
C = (K F )C = K C (8.5)
s oc oc w p w

C V F (K F )C V (1 - F )
PCS OC OC O C _ S ,0 ,^
_____ _ (8<6)

ss s t

FsVt

Vs = (K F )(1 - F )C (8>7)
oc oc s ss

Solving equation (8.6) for F , gives
S

(K F )C V

F oc oc ss
s V + (K F )C V
t oc oc ss s
To satisfy the relationship that V < (V - V ) , and

solving equation (8.6) for C ,
SS
FsVt
s c (8.25)
'ss (K F )(1 - F )V
oc oc s' s
Equations for Centrifugation Time

The reader is referred to Ambler and Keith (1956) for a more general

discussion of centrifuging. The force on a particle, expressed in grams, in

a circle of rotation is
where
nuo2R/g (8.46)
F = centrifugal force (g)

m = mass of the particle (g)

co = rotational velocity (radius sec )

R = radial distance from the particle to the axis of rotation (cm)

g - gravitational constant - 980.7 cm sec

322
-------
Substituting the values of g

CD = 2TTN/60 (8.47)

where
N = revolutions (min )

into equation (8.46) gives

F = m (2irN/60) 2R/980.1

= 1.117 x 10~5m R N2 (8.48)

For convenience, the relative centrifugal force, RCF, is defined as

RCF = cA/g (8.49)

which is the force acting on a particle in terms of multiples of its weight
in the earth's gravitational field. Substitution of equation (8.46) into
equation (8.49) gives

RCF = 1.117 x 10~5 R N2 (8.50)

The problem with using RCF is that it is directly proportional to R and the
gravitational force on a particle increases as the particle moves to the end
of the centrifuge tube. Therefore, the settling velocity will increase, and
it is difficult to define the centrifugation conditions using equation (8.50)

Stokes law states that the viscous resistance to the motion of a
small particle in a fluid is

F = 3irnDv (8.51)
s

where n is the viscosity of the fluid (in poise) and D is the diameter of
the particle (cm). The mass of the particle in equation (8.46) must be
corrected for the weight of the fluid displaced. Thus, for spherical
particles, equation (8.46) becomes

F = (ir/6) D3 Ap w2R (8.52)

where D is the diameter of the particle and Ap is the difference of the
density of the particle and the fluid (Ap = p - p ).
P *•
Combining equations (8.51) and (8.52)
HR 9
v = -^ = Ap D uR/18n (8.53)
s dt

323
-------
For nonspherical particles,

v = ^| = Ap D2 w2RK/4n (8.54)
S Q c

where K is a shape factor and equals 2/9 = 0.222 for spherical particles.

For nonspherical sediment particles, we used a value of K = 0.15.

Separating variables and integrating equation (8.54)

-R2
L A r
ID A«r> ,, v I

dt (8.55)
/dR ApD2co2K /*

«, E * 4n y
•'
In ^2 • c. (g>56)

and t , the identification time, in sec, is

4n ln(R7/!L)

tc -- 22 (S6C) (8'57)
u D ApK

Since ID = 2irN/60, equation (8.57) can be written

4n(602)2.303 log(R2/R1)

fcc - - 2~2 - (sec^
(27r N) D ApK

840ri log(R9/R1)
D ApK
(sec) (8.58)
If
n = 0.0100 poise at 20°C

K = 0.15

Ap = p - p = 2.65 - 1.00 - 1.65

D = 2 x 10 cm
324
-------
then 840(0.01) log(R2/R1)
C (2 x 10~5)2(1.65)(0.15)N2

10 2
= 8.48 x 10iU log(R2/R1)/N (sec)

= 1.41 x 109 log (R2/R1)/N2 (min) (8.20)

Equation (8.21)

If only C is measured, then C V = weight of chemical in
1 w ' w t &
supernatant,

C = K C
s p w

- (C V - C VJ/C V (8.59)
ocwtsss '

K = (C V - C VJ/C V C (8.21)
pocwtsssw
8.8.11 Theory of Nonlinear Least Squares Estimates of

Isotherm Parameters

Parameter estimates for the regression model described in Section

8.7.3 may be found using a Gauss-Newton algorithm to minimize the residual

sum of squares. The BMDP3R program uses a modified version of the standard

Gauss-Newton method, developed by Jennrich and Sampson (1977).

In the least-squares approach, the structural relation y = f(z; 0)

is fit to observations Y., z., j = 1,..., n, by finding 8 such that: ~ ~

S =^] (Y.. - f(z ;9))2 (8.60)

J-l

is minimized. Here, z* is the vector of independent variables, and 9

is the vector of m(m