September 1980
Final Report
EVALUATION AND OPTIMIZATION
OF HYDROLYSIS SCREENING
PROTOCOLS
By T Mill, R. Bawol, I Partridge, and W.R. Mabey
Prepared for:
BATTELLE COLUMBUS LABORATORIES
505 King Avenue
Columbus, Ohio 43201
Attention: Dr Robert Coutant. Project Officer
SRI Project PYD 8982
Contract No. T-6417(7197)-031
Approved by
M E Hill, Laboratory Director
Chemistry Laboratory
Paul J Jorgensen
Senior Vice President
Science Group
-------
ABSTRACT
We have evaluated two protocols that provide hydrolysis rate constants
k^, kg, and k.^ for acid-catalyzed, base-catalyzed, and neutral hydrolysis
processes, respectively. The protocols have been performed at 25.0°C
using ethyl acetate, cyclohexene oxide, and isopropyl bromide as test
compounds. One major conclusion is that rate constant data obtained from
experiments of short duration generally have higher precision than data
from longer experiments. Other factors related to obtaining reliable
hydrolysis data are discussed.
We have developed a collaborative test design for evaluating the
precision and accuracy of the test protocol among several laboratories.
We discuss the several factors including the number of laboratories,
replication and use of regression analysis and have developed appropriate
statistical methods for analyzing the test data. We also developed the
detailed methodology, including initial planning, evaluation of chemicals,
preparation of the collaborative test and evaluation of the reported
results.
-------
CONTENTS
ABSTRACT v L
LIST OF ILLUSTRATIONS iv
LIST OF TABLES iv
SUMMARY AND CONCLUSIONS 1
INTRODUCTION 4
OBJECTIVES 6
DESIGN OF PROTOCOLS 7
Criteria for Selecting Test Methods 7
Hydrolysis Processes and Kinetic Relations 8
Hydrolysis Protocols 10
Screening Tests 13
Data Treatment and Reporting 14
Scope Limitations of the Hydrolysis Protocol 14
EVALUATION OF SRI AND EPA PROTOCOLS 16
Laboratory Studies 16
Hydrolysis of Ethyl Acetate 17
Hydrolysis of Cyclohexene Oxide (CHO) 23
Hydrolysis of Isopropyl Bromide 31
Experimental Methods 35
Chemicals 35
Constant Temperature Bath 35
Preparation of Reaction Solutions 37
Buffer Solutions 37
Kinetic Measurements 38
Sampling Regimen 39
Analytical Method 39
Data Treatment 42
Optimized Screening Protocol. A3
ESTIMATED COST FOR OPTIMIZED SCREENING PROTOCOL 44
COLLABORATIVE TEST DESIGN FOR HYDROLYSIS 4 7
li
-------
Background 47
Hydrolysis Testing Protocols 50
Statistical Approach 51
Number of Laboratories 51
Replication . 52
Least Squares Regression 53
%
Statistical Methods 54
Comparison of Laboratories 57
Evaluation of Precision and Accuracy 63
Operational Steps of the Collaborative Test Program 69
Initial Planning 69
Preliminary Evaluation 69
Collaborative Testing Protocol 70
Collaborative Testing 70
Data Analyses and Interpretation 71
Reports 72
REFERENCES 74
APPENDICES 75
A A GENERAL SOLUTION OF k , kg, AND k^ FROM THE OVERALL RATE CONSTANT
B DATA COLLECTION FORMS
C KINETICS OF HYDROLYSIS IN SOLUTIONS OF INADEQUATE BUFFERING CAPACITY
D ADDITIONAL ERROR ANALYSES FOR ETHYL ACETATE HYDROLYSIS EXPERIMENTS
in
-------
ILLUSTRATIONS
1. pH Dependence of k, for Hydrolysis by (a) Acid-,
(b) Water-, and (c) Base-Promoted Processes 11
2. Flow Diagram of Collaborative Test Program 73
TABLES
1. Hydrolysis of Ethyl Acetate at 25°C 19
2. Summary of Measured Values of Acid, Base, and Neutral Rate
Constants for Hydrolysis of Ethyl Acetate in Water at
25°C 20
3. Rate Constants k^ (s-1) Calculated for Hydrolysis of Ethyl
Acetate at 25°C as a Function of pH 22
4. Hydrolysis of Cyclohexene Oxide at 25°C Using Standard
Buffer Concentrations 25
5. Hydrolysis of Cyclohexene Oxide at 25°C Using Several Buffer
Concentrations 26
6. Best Values of k for Hydrolysis of Cyclohexene Oxide at
25°C at Selected pHs 27
7. Acid, Neutral, and Base Rate Constants k^, kg, and k^ for
Cyclohexene Oxide at 25°C 28
8. Composite Rate Constants, k^ (s~l) x 106, for Cyclohexene
Oxide at 25°C and pH Values 3 Through 11 30
9. Hydrolysis of Isopropyl Bromide at 25°C Monitored by the
Loss of Isopropyl Bromide 33
10. Effect of Buffer and Ionic Strength (u) on Hydrolysis of IPB
at 25°C 34
11. Comparison of Hydrolysis Rate Constants for IPB at 25°C
Obtained from Analysis for IPB and for IPA or Br~ 36
12. Sampling Regimens for EA, CHO, and IPB at 25°C 40
IV
-------
13. Instrument Settings and Columns Used for Chemical
Analysis 41
• 4
V
14. Similarities and Differences in SRI and EPA Protocols 43
15. Estimating Costs for Hydrolysis Screening Protocols 45
-------
SUMMARY AND CONCLUSIONS
This report describes a two part study to evaluate and- optimize
screening tests for hydrolysis kinetics and to design a collaborative
test program for interlaboratory comparison of screening test results
using standard chemicals.
In part one we selected three chemicals for the laboratory study,
to provide a variety of physical properties and different absolute rates
and rate dependence on pH:
(1) ethyl acetate (EA), a moderately soluble and volatile ester,
hydrolyzes to give ethanol and acetic acid by acid and base catalyzed and
neutral processes. First-order rate constants were measured at pH values
of 3, 5, 7, 9, and 11 in buffered solutions at 25°C (Table 1); the half-
lives of these reactions varied from 1.7 hours (pH 11) to 114 days (pH 5
and 7). The very slow reactions at pH 5 and 7 caused problems in using
the EPA protocol to obtain reliable estimates of k^, k^, k^, and k^; the
use of the SRI protocol which requires measurements at pH values of ^ 7
and 11 led to more reliable estimates of all rate constants including
those for k^ at pH 5 and 7. The rate measurements for k^ and kg are in
good agreement with published values but k^ is about 400 times larger
(Table 2) .
(2) Cyclohexene oxide (CHO) has lower solubility and vapor pressure
than EA but we estimate its volatility from water is similar. CHO hy-
drolyzes tro give the corresponding diol (with no change in pH) and exhibits
only acid catalyzed and neutral processes. We measured rate constants
at pH 3, 5, 7, 9, and 11 at 25°C. At pH 3 the half-life is only six
minutes, increasing to about 75 hours at pH 7-11 (Table 4); small effects
of both buffer salts and ionic strength were noted (Table 5). Values of
k and k agreed well when estimated from the SRI and EPA protocols but
A N
k was estimated much more reLiablv from the SRI protocol because of its
B
sma
11 contributions to k^ at pH values lower than 11. In general estimates
1
-------
of k, based on the SRI protocols were in better agreement with measured
h
values at all pH values than were those based on the EPA protocol but at
pH values below 11 the EPA procedure gave satisfactory agreement between
calculated and measured values of k^ (Table 8).
-\
(3) Isopropyl bromide (IPB) is a quite volatile, insoluble chemical,
which hydrolyzes to the alcohol and bromide ion by base-catalyzed and
neutral processes only. At 25°C the half-life is close to 55 hours at
all pH values up to 11 where the half-life decreases to 47 hours (Table 9).
In addition to measuring k^ by loss of IPB, we also performed
experiments to estimate k^ from formation of isopropyl alcohol and bromide
ion (Table 11). Although several rate measurements done this way gave
good agreement with rate measurements performed on loss of IPB, significant
discrepancies (factors of two or three) were observed at pH 7 and 9 for
formation of bromide ion. Both SRI and EPA protocols gave satisfactory
results with IPB for pH values of 3 to 9; only the SRI protocol would be
used to estimate k satisfactorily owing to the small contributions made
B
by this process. Our measurements showed small buffer salt and ionic
strength effects on the hydrolysis rate constant (Table 10).
We propose an optimized protocol for hydrolysis using pH values of 3,
7, and 11 with a minimum of 6 time points at each pH and replicate analysis
at each time point. We recommend that both EA and CHO be used as standard
chemicals for calibrations of the testing methodology. Additional work
is necessary to decide whether IPB is suitable as a standard or whether
some other alkyl halide or other chemical might be a better choice. We
estimate the cost of performing the optimized protocol at about $4,000.
In part 2 we. describe a collaborative test design that provides
statistical and operational methods for evaluating the precision and
accuracy of the hydrolysis laboratory protocol. Definitions of terms
used in the literature on collaborative testing serve as background in-
formation. A review of the h\drolvsis testing protocols shows that the
fundamental statistical problem is to estimate the rate coefficient for
a first-order chemical reaction. Our statistical approach to designing
2
-------
a collaborative study is based on a linear model of the natural logarithm
(In) of concentration-versus time.
. 1 -N
V
We discuss this approach in terms of the required number of labora-
tories, experimental replication, and the appropriateness of least squares
regression analysis. Statistical methods are then presente'd for analyzing
collaborative test data for a kinetic chemical process such as hydrolysis.
Computational formulas estimate rate coefficients from data for individual
laboratories and from collective data for all laboratories and determine
whether differences among laboratories are explained by random error or
are systematic.
Within-laboratory precision and repeatability are evaluated from the
residual variation of data from the regression line that represents a
first-order kinetic process. Between-laboratory precision and repro-
ducibility are evaluated by subtracting the within-laboratory variance
from the total variance of rate coefficients for laboratories in a
collaborative study.
Finally, a discussion of operational elements of a collaborative
study provides general information about initial planning, preliminary
evaluation of chemicals, preparing a collaborative test protocol, conductin
interlaboratory testing, analyzing data, and reporting results.
-------
INTRODUCTION
The Toxic Substances Control Act of 1976 (P.L. 94-469) requires
chat 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 constitute 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.
Laboratory test methods or protocols have now been developed by
*
SRI for EPA/ORD and by OPTS for a variety of kinetic and equilibrium
fate processes believed to be important in aquatic, atmospheric, and
soil systems; other protocols are still being developed. These protocols
describe in detail screening and detailed laboratory tests, from which
the investigator can determine first an approximate rate constant for
a process and, if needed, a set of detailed rate constants to cover a
wider range of environmental conditions.
The screening protocols for hydrolysis proposed by EPA and SRI
are designed to provide approximate rate constants for hydrolysis over
a range of pH commonly found in aquatic systems, at one temperature.
Althouen the procedures described in the protocol are standard practices
in environmental research laboratories and most of the procedures have
been performed satisfactorily at SRI, the complete procedure has not
A set of interim test prococols for transformation and transport
processes has been prepared bv the Office of Pesticides and Toxic Sub-
stances (OPTS); SRI has prepared another set of protocols under the EPA
contract 68-03-2227 for th<_ Office of Research and Development. These
two sets of protocols are verv similar in most respects, and we have
examined both sets of prococols during this study.
4
-------
been optimized and systematically evaluated with several chemicals
having widely different physical properties and chemical reactivities.
Nor have any standard chemicals suitable for calibration and checking
procedures been recommended or tested. We seek to remedy these deficiencies
in the existing EPA and SRI protocols and to develop a care£*lly
designed collaborative test to be performed by several laboratories.
The results of this study will be broadly applicable to environmental
fate testing programs in industry and government in the United States.
5
-------
OBJECTIVES
The objectives of this study are
(1) Evaluate and opcimize the accuracy and efficiency of proposed EPA
and SRI screening test protocols for hydrolysis
by performing screening tests using selected chemicals to
examine the effect of pH, volatility, reactivity, and solubility
on the accuracy of the procedure.
(2) Recommend and test standard chemicals for calibration of
laboratory procedures for hydrolysis.
(3) Design but not implement a collaborative test program to be
performed in several different laboratories to objectively
evaluate the optimized protocol.
6
-------
DESIGN OF TEST PROTOCOLS
The foundation for use of laboratory data for environmental assess-
ment 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 condi-
tions using simple or computer models.
The 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 environmental descriptors, not
the laboratory data.
Criteria for Selecting 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 developing 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.
7
-------
Another reason is faulty design of the experimental procedure, which
prevents control of some important variables and hence gives data that
V
are affected by some other, unsuspected and more rapid process. An
example of this situation is found in measurements of loss of a highly
insoluble chemical from water at elevated temperature, where the loss
is thought to be caused by hydrolysis but actually is caused hy
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.
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 extrapolation procedures.
Apart from the purely scientific validity of specific laboratory
tests, the generality and complexity or sophistication of tests must
also be considered in evaluating available methodologies, especially
if such tests are intended as protocols for regulatory use. Preferred
test methods are those generally performed by experienced laboratory
personnel with instruments commonly found in well-equipped analytical
and physical chemistry laboratories. Each procedure must be evaluated
and optimized for the balance between speed, accuracy, and cost.
A
Hvdrolvsis Processes and Kinetic Relations
Hydrolysis refers to a reaction of a compound with water, usually
resulting in Che net exchange of some leaving group (-X) with OH at a
reaction center:
RX + HjO ^ ROH + HX
A detailed discussion of environmental hydrolysis processes is found
in the review by Mabey and 'Iill (1978).
8
-------
I
The mechanism of the reaction may involve a cationic or anionic
intermediate, and the hydrolysis tate. may be promoted or catalyzed by
V
acidic or basic species, including hydroxide (0H~) and hydronium (H30+
or tl+) ions . The promotion of the reaction by H30+ or OH is referred
to as specific acid or specific base catalysis, as contracted to general
acid or base catalysis encountered with other cationic or anionic
species.
For the hydrolysis 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, 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 not expected to
contribute to the overall rate (Mabey and Mill, 1978).
The rate law for hydrolysis of chemical RX usually can be put in
the form
- = kB [ 0H~ ] [ RX ] + kA[H+][RX] + k^' [Ha0][RX], (2)
where kg, k^, and k^' are the second-order rate constants forbase-
and acid-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 (k^) . The pseudo-first-order rate
constant k^ is the observed or estimated rate constant for hydrolysis
-ir. a specific and constant pH and temperature. Equation (2) 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
kh = kB[OH~] + kAtH+] + k,, • H)
9
-------
From che autoprotolysis water equilibrium [equation (4)], equation (3)
may be rewritten as equation (5).
[H+](0H~] = K
w
(4)
r + kA[H+1 +kN
(5)
From equation (5), it is evident how pH affects the overall rate:
at high or low pH (high 0H~ or H+) one of the first two terms is usually
dominant, whereas at pH 7 the last term can often be most important.
However, the detailed relationship of pH and rate depends on the specific
is pseudo first order, and the half-life of the substrate is independent
of its concentration:
Figure 1 shows how the log of the rate constant for hydrolysis varies
as a function of pH following equation (5).
Screening test protocols for hydrolysis of chemicals in water have
been prepared to enable an investigator to estimate hydrolysis rate
constants and half-lives nor chemicals at any environmental pH between
dHs 3 and 11 (SRI) or 5 and 9 (EPA).
The test protocol for nvdroivsis is based on a large body of experi-
mental data together with a detailed kinetic analysis of the process.
In most natural waters, on'- iH and temperature affect rates of hydrolysis,
"The SRI and EPA protocols ,.r>. similar; where they differ, we note the
differences and designate aource (EP-\ or SRI).
values of , k^, and k^. At any fixed pH, the overall rate process
tt = 0.693/k^
(6)
Hvdrolvsis Protocols
10
-------
PH
log k|
(bl log kh = log kN
y
T A -327522-29R2
FIGURE 1 pH DEPENDENCE OF kh FOR HYDROLYSIS BY ACID. WATER AND BASE PROMOTED PROCESSES
-------
and all investigations to date show that hydrolysis rates at the same
pH in buffered and natural waters are closely similar. Many classes of
chemicals exhibit rate dependence "on pH because of acid- or base-catalyzed
hydrolysis. The EPA protocol recommends using pH 5, 7, and 9 to estimate
the pH effect, whereas the SRI protocol recommends the wider range of
pH 3, 7, and 11. Both protocols have sound rationales for they: re-
commended pH ranges. One trade-off may be one of accuracy versus time:
at pH 3 or 11 the rates are faster by a factor of 100 than at pH 5 or 9
for the acid- or base-promoted reactions, respectively, and thus are more
quickly measured at useful conversions of chemical. However, the rate
constants measured at pH 5 and 9 are more useful for environmental assess-
ment purposes if accurately measured; the relative accuracy of the methods
depends on several factors including the contribution of the neutral
process to the total rate. If k = 0, the accuracy of the two methods
is the same. Measuring k^ at pH values of 3 and 11 increases the con-
tribution of the acid- or base-catalyzed process to the value of k^,
thereby making estimates of k or k_ more accurate. However, the data
A o
must be extrapolated to the more environmentally relevant region of pH 5
to 9.
Conditions under which hydrolysis experiments are conducted in the
laboratory differ from those in the aquatic environment. In the environ-
ment, natural processes maintain the pH of a water body relatively constant
(C02 absorption from air, metabolism, natural buffers); low concentrations
of a chemical usually will not significantly affect the pH of the water.
In laboratory measurements, however, the pH of the solution is usually
kept constant by mixtures of acids or bases and their salts (buffers),
which can also act as general acids or bases to catalyze the reaction
under study and increase iomc strength. Therefore the challenge to the
investigator is to select buffer concentrations high enough to maintain
constant pH and yet avoid significant buffer catalvsis or ionic strength
ef fec ts.
Below we summarize the hydrolysis protocols recommended bv SRI and
EPA.
12
-------
Screening Tests
The proposed screening protocols provide an estimate of the half-
life of a chemical at pHs 3, 7, and 11 (SRI) or 5, 7, and 9 (EPA).
Solutions should be prepared using sterile, pure water and reagent
grade (or purer) chemicals. Buffer solutions hsould be prepared according
to the recommended procedure for pHs 3, 7, and 11 or 5, 7, and 9.
For each chemical being tested reaction mixtures should be prepared
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 necessary, l-vol% acetonitrile may be added
to facilitate solubilization if the chemical is too insoluble in pure
water to permit rapid dissolution.
Sealed ampoules or stoppered (no grease or polymers) volumetric
flasks containing the reaction mixtures should be placed in a constant
temperature bath at 25° ± 1°C. Chemicals that exhibit sensitivity to
visible light should be placed in foil-covered flasks.
In the SRI test,solutions are analyzed for the concentration of
chemical at t = 0, 44, and 88 hr. 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
1 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.
The EPA protocol recommends using detailed measurement regimens
at pHs 5, 7, and 9: one for chemicals that hydrolyze rapidly, one for
chemicals of moderate reactivity, and another for unreactive chemicals.
Data Treatment and Reporting
The EPA protocol uses the analytical data to calculate the rate
constant and half-life at the pH of the measurements. The first order
kinetic relation is
Ln(C /C ) = -k, t,
co n
(7)
-------
where C arid C are concentrations of chemical at times zero and t,
o t
and k, is the first order rate constant in hr~l. A least squares fit
n
of the values of and t to the regression equation (7) gives the
;lope k . The half-life (in hr) is
= 0.69/k^ . (8)
The EPA protocol specifies that the following data be reported: k^
and its correlation coefficient for each experiment, the mean
value of k, and its standard deviation for replicate experiments at
h
the same pH, and t^ from equation (8) using the mean value at pHs 5, 7,
and 9. The SRI protocol uses the concentrations at 44 or 88 hr to
estimate limits for thus giving approximate values of k^.
Scope and Limitations of the Hydrolysis Protocol
Although many chemicals exhibit limited rate dependence on pH because
of the relative unimportance of one or more of the hydrolysis processes
in the pH region of prime interest, kinetic studies should always be
performed at three pH values near 3, 7, and 11 or 5, 7, and 9 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 be important for some chemical
structures.
Another limitation on the scope of this protocol is in the measure-
ments of the hydrolysis races of chemicals that reversiblv ionize or
protonate in the pH range ot~ interest. The hydrolysis rates of these
compounds will often have unusual pH-rate profiles because of competition
between the reactions of the inarged and uncharged forms:
14
-------
HjO + HAY + H30+
V
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 concerning the possible importance of this effect
in hydrolysis of an ionic chemical having a pK& or p!^ in the pH region
of 3 to 11, additional measurements should be made to define the pH-rate
profile.
15
-------
EVALUATION OF SRI AND EPA PROTOCOLS
Laboratory Studies
We selected three simple commercially available chemicals to evaluate
the SRI and EPA protocols: ethyl acetate, CH3C(0)0C2H3, (EA); cyclohexene
oxide, C6Hlo0, (CHO); isopropyl bromide, (CH3)2CHBr, (IPB). Each compound
was selected because we believe it represents a class of chemicals that
exhibit specific hydrolytic properties common to many organic structures,
e.g., only acid and neutral hydrolysis or only acid and base hydrolysis.
Each chemical also has specific physical properties, such as solubility
and volatility, that can lead to special problems that occur in testing
many chemicals. Thus we chose these chemicals to provide a limited but
reasonable cross section of hydrolysis kinetic systems expected to be
encountered among many potential chemicals that might be tested in the
future.
We specifically avoided chemical structures that we believed would
hydrolyze by more than one chemical pathway to minimize kinetic com-
plications in testing the screening protocols; complications may be
introduced at a later time when the basic screening test is optimized.
We also tried to exclude all other loss processes by using foil wrap
to avoid photolysis, sterile water and containers to avoid microorganisms,
and sealed containers to avoid volatilization. Controls help check for
the presence of these adventitious processes, but, despite our best efforts,
some experiments were confounded by other processes and had to be repeated.
In at least one case with IPB, at the lowest concentrations we could use
in nearly pure water, insolubility may have been a contributing problem.
Buffer catalysis and ionic strength effects, which were also encountered,
are potentially serious pri'iiU'n that are discussed in the context of
specific experiments.
16
-------
Hydrolysis of Ethyl Acetate
The reaction for hydrolysis q|l EA is as follows:
CH3C(0)0C2Hs + H20 —~ CH3C(0)0H + C2Hs0H
Ethyl acetate was chosen as a representative of a class of chemicals that
exhibit both acid-, and base-catalyzed and neutral hydrolysis in the
environmental pH region 4 to 9. In our earlier review of hydrolysis
(Mabey and Mill, 1978) we found that aromatic and aliphatic esters had
no important neutral (pH independent) hydrolysis process unless a strongly
electron-withdrawing group(s) was present on the a-carbon of the carboxvl
or alcohol group.
The Henry's law constant for EA was calculated to be 118 torr M~1
at about 25°C, using a solubility of 7.44 g EA per 100 ml water (0.85 M)
(The Merck Index, 1976) and a vapor pressure of 100 torr (or 0.13 atm)
at 27°C (CRC Handbook, 1975). Therefore EA would not volatilize rapidly
from water. The high water solubility of EA also showed that sorption
to glass would not be a problem in experimental work.
Our earlier review of hydrolysis data (Mabey and Mill, 1978) reported
the following rate constants for hydrolysis of EA at 25°C:
k = 1.1 x 10-" M-1 s"1
A
k = 0.11 M_1 s"1
D
= 1.5 x lO"10 s"1
These data were reported b\ Skrabel and Ruckert (1928'), and the k^ value
has been confirmed bv Haloncn c 1956). Mo other data were found to cor-
roborate the value of k, or k. . Furtner evaluation of these data has
A <•
shown that the value ot k^ i quest Lonaole because at pH 5.5, where the
acid- and base-catalyzed proti'-.,-. rates are equal, the neutral hydrolysis
17
-------
process contributes only 18% of the total value of k^ and might not be
detectable.
. V •>
Using the values of k , k , and k listed above and using equations
Ad N
(5) and (6), we calculated the half-lives of EA at 25°C and at pH values
used in the EPA and SRI protocols. These values, listed below, were used
in planning the hydrolysis experiments: *
pH 4
3 73 days
5 16 yr
5.5 26 yr (minimum)
7 720 days
9 7.3 days
11 1.8 hr
The analytical method of choice was gas chromatography; detectability
by direct analysis from water solution (the preferred method) limited
initial concentrations of EA to about 1 x 10-3 M. The very slow rate of
hydrolysis expected at pH 5.5 also suggested that bringing each reaction
mixture to pH 5.5 was an effective quencher for hydrolysis and was used
throughout the study. Initial studies on EA found that adventitious
process(es) (probably blodegradation or volatilization) complicated the
experiments, and some hydrolysis data did not agree with literature data.
Results of well-controlled experiments at pH values of 3, 5, 7, 9, and
11 are given in Table 1.
From these data, the acid, base, and neutral rate constants, k , kg,
and k,,, for EA were calculated using sets of simultaneous equations given
in Appendix A. These second-order rate constants were obtained in accord-
ance with the EPA and the SRI protocols (see Background). In addition,
acid, base, and neutral rate constants were calculated using the overall
rate constants at all four pHs. These constants are summarized in Table 2.
The k and k values from the literature and those calculated
A B
according to the SRI protocol, agree exceptionally well. However, the
value of k obtained from tin.' EPA protocol is more than a factor of ten
A
larger than the literature and the SRI values for k . The values of kg
from the literature and the EPA experiments agree more closely than the
18
-------
Table 1
HYDROLYSIS OF ETHYL ACETATE AT 25°C
Elapsed ,, Number
Concentration
Time in^rrAi of Time /* , b
ua /i\ 10 EA M 0 _ ,, k, (s~ )
pH (hr) o* Points Convers ion h
3 864 0.998 L0 38 (1.73 i 0.15) x 10"? 0.97
5 234 1.05 1 5.7 7.0 x 10"8 c
7 1008 1.03 2 25 6.98 x 10"8 c
9 552 0.998 k 99 (1.69 t 0.18) x 10"6 0.96
lld 3.8 1.04 7 78 (1.08 ± 0.01) x 10"* 0.999
aStandard pH buffer concentrations were used for all five solutions (CRC Handbook,
bl9?5)'
These estimates of k^ are obtained from the regression of ln(fC0]/[Ct]) versus time where
^<"7 is the average concentration obtained from triplicate analyses.
R is not calculated for one or two points.
^See Append lx C and footnote in Table 2 for discussion of the effect of inadequate buffering
during this experiment. Appendix D discusses analytical error and systems error.
-------
Table 2
SUMMARY OF MEASURED VALUES OF ACID, BASE, AND NEUTRAL RATE CONSTANTS FOR HYDROLYSIS OF ETHYL ACETATE IN
WATER AT 25°C
(M-1 s"1) k_ ( M-1 s-1)* kKI(s-1)*
Experiment A_ ' Bj ' N
Literature 1.1 x 10 u 1.1 x 10 1 1.5 x 10 10
SRIa'* (1.14+ 0.15) x 10-" (1.08 i 0.01) x 10"1 (5.90 ± 0.01) x 10"
EPAb 1.66 x 10" 3 1.64 x 10" 5.33 x 10-B
ALLC (-7.55 x 10-5) 1.08 x 10"1 2.47 x 10-7
aSRl denotes the set of EA experiments performed at pHs 3, 7, and 11.
^EPA denotes the set of EA experiments performed at pHs 5, 7, and 9; no error can be calculated since
pH 5 and pH 7 rate constants are based on one data point.
aALL denotes the set of EA experiments performed at pH values of 3, 5, 7, 9, and 11.
Appendix C discusses the effect of inadequate buffering of pH during the pH 11 experinent; allowing for
the drop in pH during the experiment, is (1.26 ± 0.01) x 10-2 M-1 s-1, or an error of ^ 14%. Using
a value of ^ = 1.26 x 10-J (= kB[10-3], kN is calculated to be 5.72 x 10-8 s~1 from the data at pH
values of 3, and 11; the error in k^ is then ^ 3%. Further error analyses for the EA experiments is
presented in Appendix D.
-------
values of k^. Still, the EPA value of kg is about 50% larger than the
SRI value. Finally, the k^ values for the EPA and the SRI experiments
agree within 12%; however, the EPA^nd SRI values differ from the literature
value by a factor of 400. As noted previously, the literature k value
is highly suspect and we believe the present value to be mor^ correct.
When the data from all five pH value experiments were used to cal-
culate k , kD, and k (bv multiple linear regression, HP-97 program
Ad IN
ST1-13A), kg was identical to the SRI value. The k^ value was about a
factor of five larger than either the SRI or EPA k^ value; k^ was negative
and therefore invalid. The statistical section of this report discusses
the difficulties associated with the multiple linear regression procedure.
As a check on the values of k,, k„, and k., calculated by the several
A B N J
methods, the values of k^ were calculated for pH values other than those
used to originally calculate the respective k^, kg, and k^ values (that
is, the rate constants k, at pHs 5, 7, and 9 were calculated from k., k„,
h Ad
and k obtained according to the SRI protocol using data from experiments
at pHs 3, 7, and 11). These k^ values are given in Table 3 and are com-
pared with the measured values.
The rate constants calculated according to the SRI protocol agree
fairly well with the measured values at pHs 5 and 9; the measured and the
calculated rate constants are identical at pH 7. Comparison of the
measured rate constants and those obtained using the EPA protocol shows
that the kh values at pH 3 are in poor agreement, whereas the cal-
culated value at pH 11 is only in fair agreement with the measured
rate constant . Finally, the rate constants calculated from the acid,
base, and neutral rate constants obtained by multiple linear regression
were compared with the measured rate constants for all five pHs. The
measured and calculated rate constants at pHs 3 and 11 are identical;
the rate constants at pH 9 agree fairly well; the calculated rate constants
at pHs 5 and 7 are, however, much larger than the measured values.
Product analyses for echanol and acetic acid were performed by gas
chromatography (GC) but no good material balances were obtained. The
reasons for this failure are not clear because ethanol appears to be well-
behaved on GC analysis even though acetic acid is not.
-------
RATE CONSTANTS k. (s_1)
n
Source pH 3
Measurou U-73 i 0 15) x 10"7
Calculated'5 from pli 3,
7, 1L data/SRl
Calculated'1 from pH 5,
7, 9 dal.i/i:PA (1.711 0.18) x 10-6
( .,1. ,,l iiiii'' l i • mi pll 3, 1.72 x 10-'
'> , 7 , •) , II .1 i [ i
Table 3
CALCULATED FOR HYDROLYSIS OF ETHYL ACETATE AT
FUNCTION OF pH
pH 5 pH 7
7.0 x 10"Ba 6.98 x 10"sa
(6.02 i 0.02) x 10"a (6.98 ± 0.14) x 10"®
(6 98 ± 0.19) x 10"B
2.46 x 10-7 2.58 x 10"'
25°C AS A
pH 9 pH 11
(1.6^ i 0.18) x 10-6 (1.08 t 0.01) x lO"
(1.14 ± 0.01) x 10"6
(1.64 ± 0.18) x 10^
1.32 x 10"6 1.08 x lO-"
Si.iiKliivl ill v i .11 mils lou I d nor bu calculated for these reactions where only one data point exists. .
ro ''a, ul |, ,,,id neuLral r.iLe constants obtained from the rate constants at these pH values are used in the calculations of'-the rate
N> ' ' * , , J
i. «»ns t .Ul L Kivcit on t',ls ' ll,L-
-------
Hydrolysis of Cyclohexene Oxide
The reaction for hydrolysis oft i^yclohexene is shown below:
The reaction is acid catalyzed via protonation of the oxygen to give the
intermediate C6Hl00H , which is followed by reaction with water. Since
alcohols are not very acidic (pK^ > 14), hydrolysis does not change the
pH of the solution.
Cyclohexene oxide was chosen as a representative of a class of
chemicals that exhibit neutral (pH independent) and acid-catalyzed hy-
drolysis processes in the environmental pH region 4 to 9. Our earlier
reivew of hydrolysis (Mabey and Mill, 1978) found that base-catalyzed
hydrolysis of epoxides was not important below pH 11, but that acid
catalysis was important and competitive with neutral hydrolysis at pH
values ranging from 4 to 8, depending on the structure of the epoxide.
CHO was chosen as a model compound because it is structurally similar
to 2-butene oxide [ whose half-life at pH 7 and 25°C was estimated to
be 4.4 days (Mabey and Mill, 1978)] but less soluble and more volatile.
No data on the physical properties of CHO were found other than the
boiling point of 129° to 130°C at 760 torr. Another compound with the
same molecular formula C6Hlo0, mesityl oxide (boiling point of 130°C),
is reported to have a vapor pressure of 10 torr at- 26°C, (CRC Handbook,
1975) and CHO probably has a similar vapor pressure. Although no water
solubility data were found for CHO, a value of 9.4 x 10~2 M was calculated
from a log K value of 1.60 (Johnson, 1980) and the water solubility-log
ow
Kqw correlation equation of Yalkowsky and Valvani (1980). From these data
the Henry's law constant was calculated as 106 torr M~1. This value
indicates that CHO has onl'. noderate volatility from water at 25°C.
Sampling times for n\drol>sis studies of CHO were initially selected
using data for 2-butene o\ido. Because initial time points showed that
23
-------
CHO was hydrolyzing more rapidly than expected, samples were taken more
frequently.
The results of these experiments to measure the hydrolysis rate of
CHO at 25°C and at several pH values are tabulated in Table 4. In all
-\
experiments, samples were taken according to the SRI and EPA protocols.
Standard buffer concentrations were used in this initial set of .experiments
(CRC Handbook, 1975).
The results of the initial set of experiments at pH values 7, 9,
and 11 show that the rate constant k, varied from 1.96 x 10-s s-1 to
n
2.76 x 10-6 s~l in this pH range and was not independent of pH over the
pH range 7 to 11, as expected. Epoxides are known to undergo buffer
catalysis (Whalen, 1973), and therefore another set of experiments at
pHs 7 and 11 were performed using one-tenth the standard buffer concen-
trations (SBC) as well as with added sodium perchlorate (NaCIO,.) to
determine the importance of buffer catalysis on the hydrolysis of CHO.
The results of these experiments are given in Table 5.
The rate constants at 0.1 SBC-pH 7.11 (Table 5), 0.1 SBC-pH 11
(Table 5), and SBC-pH 9 (Table 4) agree more closely (1.83 to 2.02) x
10-6 s~l, as expected. The rate constant at 0.1 SBC-pH 7.11 (1.83 x 10-6
s~l), however, is smaller than the rate constant at SBC-pH 9 (Table 4).
Another experiment was then performed at pH 9 in minimally buffered
pH 9 borate solution to determine the extent of buffer catalysis on the
hydrolysis of CHO. The measured rate constant in this minimally buffered
(0.01 SBC) pH 9 solution is 1.81 x 10~6 s~1. As shown in Table 5, this
rate constant is in excellent agreement with the result from 0.1 SBC-pH
7.11 solution (1.83 x 10~6 s"1) and in good agreement with the rate constant
at 0.1 SBC-pH 11 (2.02 x 10-6 s_l).
In earlier experiments at 0.L SBC-pH 7, the measured pH was 7.11.
Although the rate constant from these experiments (0.1 SBC-pH 7.11) should
be unaffected by a small change.' m pH in this region, another experiment
was performed to measure the rate of hydrolysis (at pH 7.00) in a minimally
buffered system. The rate uMistant in this minimally buffered system
(0.4 SBC) is 2.10 x 10-6 s~ . Tins rate constant agrees much better with
24
-------
Table 4
HYDROLYSfS OF CYCLOHEXENE OXIDE AT 25°C USING STANDARD BUFFER CONCENTRATIONS
Hydrolysis Rate
, , , „ Constant, 106 „ . ^
Total TLine % No. of Time Initial Cone. (s->) Correlation
pH,d Buffer Condi t ions*1 Elapsed (days) Conversion Points x 103 (M) n Coef., Ra
J, S14L 14 mm 80 6 1.01 1950 ± 9 0.999
sue 1 03 90 9 1.01 25.5 i 1 2 0.983
7, sue 8 9 84 7 1 08 2.76 t 0.11 0.992
y> siiC 9.8 80 7 1.02 1.96 i 0.04 0.998
ro i| siSC 8 8 85 7 1.03 2.46 i 0.08 0.995
^pll values are accurate Lo I 0.02 pH.
Buffer solutions made of standard buffer concentrations (SBC) listed in CRC Handbook (1975).
-------
Table 5
HYDROLYSIS OF CYCLOHEXENE OXIDE AT 25°C USING SEVERAL BUFFER CONCENTRATIONS
Total Time %
pH,a Buffer Conditions Elapsed (days) Conversion
ho
o>
7, 0 4 SBC
7 11,01 SBL
9 , l) 01 SUC
9, 0 01 SBC
0.L M NaC10„
6.9
8 0
7 8
3 7
73
76
74
46
No. of Time Initial Cone.
Points x I03(M)
0 995
1.04
0.998
0.986
Hydrolysis Rate
Constant, 106
kh(8-)
2.10 l 0.09
1 83 i 0.12
1 81 i 0.08
1 88 i 0.13
Correlation
Coef.. R2
0.994
0.988
0.992
0.991
11, 0. I SBC
8.0
75
1.05
2.02 ± 0.10
0.990
j^pll values are accurate to 1 0 02 pH units.
Buffer solutions mailt; of standard buffer concentrdtioiib (SBC) lxsted in the CRC Handbook (1975).
-------
the other rate constants in the pH-independent region than the rate
constant in the SBC-pH 7 experiments, although some buffer catalysis may
have occurred. "
To check for the effects of ionic strength on the rate of hydrolysis,
we conducted experiments with CHO solutions in a minimally goffered 0.01
SBC-pH 9 solution with added 0.1 M NaClOt. The measured rate constant
k^ for this experiment was (1.88 ± 0.13) x 10-6 s-1, compared with (1.81 r
0.08) x 10-s s~1 for the 0.01 SBC-pH 9 CHO solution without any added
NaClOi.. These results are also in excellent agreement with the value of
k^ from the experiment with 0.1 SBC-pH 7.11.
These experiments show that the hydrolysis rate constant is inde-
pendent of ionic strength, but subject to moderate buffer catalysis.
Examination of the data in Table 6 shows that the value of k^ in the pH-
mdependent region (pH ^ 7 to less than 11) is about 1.8 x 10-6 s~1 and
corresponds to k^.
Based on the foregoing discussion, we believe the vaJLues of k^ shown
in Table 6 are the best values of these hydrolysis rate constants.
Table 6
BEST VALUES OF kL FOR HYDROLYSIS OF CYLCOHEXENE OXIDE AT 25°C AT SELECTED pHs
h
Vfc-^yin6 r
pH, Buffer Conditions h h
pH 3, SBC 1950 r 9 5.92 min
pH 5, SBC 25.5 ± 1.2 7.55 hr
pH 7, 0.1 SBC 1.83 ± 0.12 105 hr
pH 9, 0.01 SBC 1.81 r 0.08 106 hr
pH 11, 0.1 SBC 2.02 r 0.10 95.3 hr
The acid, base, and neutral rate constants, kA, k„ , and kM calculated
Ad iN
from these values of k, aro in Table 7. The rate constants were
h
calculated according to the SiU and EPA protocols and from multiple linear
regression fit of selected values (see Appendix A for equations).
27
-------
Table 7
ACID, NEUTRAL AND- BASE RATE CONSTANTS kA, kB, and k^ FOR
CYCLOHEXENE^>XTDE AT 25°C
kA (N-1 s-1) 10 kg (M-1 s"1) 10s ^ (s"1)
Calculated from
pHs 3, 7, 11/SRI 1.95 r 0.01 0.335 r 0.156 1.63 r 0.12
Calculated from
pHs 5, 7, 9/EPA 2.38 r 0.02 21.7 ; 14.6 1.59 ; 0.12
Calculated'3 from
pHs 3, 5, 7, 9,
11 1.95 : 0.00 -1.15 ± 2.58 3.15 : 1.45
Calculated'3 from
pHs 3, 7, 9, 11 1.95 _ 0.00 0.301 : 0.148 1.72 : 0.09
aThese standard deviations represent estimation errors due to
.imperfect fitting of experimental "time points".
These standard deviations represent estimation errors due to
imperfect fitting of the k^ "data points" and should not be
compared with those above.
The k^. values calculated using the SRI and EPA protocols agree very
well, the k^ values agree only moderately, and the kg values differ by
two orders of magnitude. When all the values of k^ were used to calculate
k , k.., and kD (by multiple linear regression, HP-97 program ST1-13A),
AN o
k^ was identical to the value calculated using only pH 3, 7, and 11 data
(SRI), k was a factor of two larger than either the SRI or EPA value
and kD was negative and therefore not valid. The rate constants were
tnen recalculated with the HP-97 program using the four k^ values from
pH values 3, 7, 9, and 11; the pH 5 rate constant was excluded on the
basis of its low correlation coefficient and suspected contribution re-
sulting from buffer catalvsia.
These calculated value-, of k_ kD, and kv are in much better agree-
A D IN
ment with the values calculated using the SRI and EPA data sets: k
28
-------
agrees extremely well with the SRI value, k^ is in good agreement with
both the SRI and EPA-values, and k^ is of the same magnitude as the SRI
value. Since the contribution froth the base-catalyzed process to the
overall value of k^ is small at these pH values and therefore difficult
to measure, the agreement of kg with the SRI value is accep'tkble.
One method of verifying the accuracy of k^, kg, and k^ is .to use
them in calculating k^ and comparing the results with the measured values.
Values of k^ for CHO were therefore calculated from the various sets of
acid, base, and neutral rate constants according to equation (3),
kh = kA[H+1 + kN + kB[0H"] • (3)
and the results are summarized in Table 8.
Values of k, at pHs 5, 7, and 9 were calculated from values of k ,
h a
k and k. derived from data at pHs 3, 7, and 11 according to the SRI
B N
protocol (Table 6). These k^ values compare well with the measured values
of k^ at pHs 5, 7, and 9. The values of kA, kfi, and k^ estimated using
the EPA protocol give a value of k^ at pH 7 that agrees well with the
measured value of k, at pH 7. The calculated rate constants at pHs 3
and 11, however, differ by 22% and a factor of ten, respectively, from
the measured values. In addition to these calculated values of k^, rate
constant values were calculated from the acid, base, and neutral constants
obtained from using all five k^ data points. While good agreement was
obtained between these calculated values and the measured values at pHs 3,
5, and 11, the rate constants at pHs 7 and 9 are a factor of two larger
than their corresponding measured values.
Finally, the acid, base, and neutral rate constants obtained from
the rate constants at pHs 3, 7, 9, and 11 were used to calculate kh values
at all five pH values. The values at pHs 3 and 11 are identical to
the measured values. The race constants at pHs 7 and 9 are in excellent
agreement with the correct' i>iing measured values, whereas the rate constant
29
-------
Table 8
OJ
O
COMPOSITE RATE CONSTANTS, kh (&"') x 106 , FOR CYCLOHEXENE OXIDE AT 25°C AND pH VALUES 3 THROUGH U
Source pH 3 pH 5 pH 7 pH 9 pH I]
Measured3 1950 i 9 25.5 t 1.2 1.83 > 0.12 1.81 >. 0.08 2.02 ± 0.10
Calculated'3 from
plls 3, 7, 11
daLa/SRl — 21.1 t 0.12 1.82 1 0.12 1.64 i 0.12
C.ilc u I a t ed'5 f rum
plls 5, 7, 9 data/
EPA 2387 I 15 -- 1-83 i 0.12 — 23.3 J. 14.6
Ca 1 c ul ated*3 Crom
pHb, 3, 5, 7, 9,
11 datac 1950 22.6 3.35 3.14 2.01
Calculated'5 from
pHs 3, 7, 9, 11
d a t a L 1950 21.2 1.91 1.72 2.02
fSee Table 6.
At id, neutral and base rate constants obtained from the rate constants at these pH values are
used in the calculation of the raLc constants given on this line. ' y
CSLandard deviations have noL been calculated for these k. 's because a valid stjListual formula
h
is not available. '
-------
at pH 5 agrees well with the measured pH 5 rate constant. In addition,
all the rate constancs derived from the SRI protocol agree well with
those calculated from the data obtained at pH 3, 7, 9, and 11.
Hydrolysis of Isopropyl Bromide
-\
The equation for the hydrolysis of isopropyl bromide is as follows:
(CH3)2CHBr + H20 (CH3)2CH0H + HBr
Isopropyl bromide (IPB) was chosen as a representative of a class of
chemicals that hydrolyze at rates independent of pH in the environmental
pH region 4 to 9. Our critical review of hydrolysis (Mabey and Mill,
1978) found that hydrolysis rates of monohalogenated alkanes were not
acid- or base-catalyzed in the region pH 3 to 11; although the base-
catalyzed process is important for these alkyl halides above pH 11, there
is no evidence that a specific acid-catalyzed mechanism for alkyl halide
exists (i.e., reaction with protonated water H30+).
The hydrolysis of isopropyl bromide produces bromide ion, hydroniun
ion (H30+), and isopropyl alcohol (IPA) as products. Since acid is formed
during hydrolysis, buffering of reaction solutions is necessary to main-
tain constant pH.
Isopropyl bromide has a boiling point of 59.4°C and a Henry's law
constant of approximately 5700 torr M~l at 25°C making IPB a highly
volatile chemical. The Henry's law constant was calculated from water
solubility for IPB of 3.5 x 10~2 M estimated using a logarithmic octanol/
water partition coefficient (log K ) of 2.0 (Johnson, 1980) and the cor-
r ow
relation of Yalkowsky and Valvani (1980) for water solubility and log
K. ; the vapor pressure of IPB used in the Henry's law constant estima-
ow
tion was 200 torr at about 20°C. [The CRC Handbook (1975) lists a IPB
vapor pressure of 400 torr at 41°C and 100 torr at 8.0°C.]
»The calculated value at pH 5 ls slightly lower than the measured value
as a result of buffer cataUsLS in the experiment at pH 5.
31
-------
The use of isopropyl bromide as a model compound also allowed us Co
evaluate the IPB hydrolysis rate using the rate of product formation as
an independent check on the IPB lo'ss rate. IPA concentrations were de-
termined concurrently with the IPB analyses using gas chromatography,
and bromide ion was measured using an ion-selective electrode.
The initial set of IPB hydrolysis experiments were performed in
solutions containing standard buffer concentrations (CRC Handbook, 1975).
The results of these experiments based on IPB loss at several pHs are
given in Table 9. The rate constants at pHs 3 to 11 appear to be inde-
pendent of pH, and the averaged observed value of 3.79 x 10"6 s"1 (t, =
H
50.8 hours) in this pH-independent region agrees very well with the
literature value of 3.77 x 1CT6 s-1 (Koskikallio, 1967). The hydrolysis
rate constant at pH 7, however, is low compared with the r«#te constants
at other pH values in the neutral range. For this reason, a new set of
experiments at pH 7 were performed to check this value of the rate constant
and the effects of buffers and ionic strength on the rate constant. The
results of these experiments showed that our earlier estimate of the rate
constant probably was too high, but both buffer salts and ionic strength
seem to influence the rate. These data are summarized in Table 10.
We cannot explain the apparent increase in rate with a decrease in buffer
concentration but the increase in rate constant on addition of NaClOi. is
consistent with Koskikallio1s (1967) earlier results with IPB. It should
be noted that ionic strengths of the standard buffers vary by less than
a factor of 2 over the pH range of 3 - 11 as listed below
pH 102 Ionic Strength ( u)M
3 7.23
5 7.26
7 7.91
9 4.21
11 A.78
In addition to determining the rate constant k^ by loss of IPB, we
also measured the rate constants for the appearance of IPA and bromide
ion (Br ). Rate constants cor the production of IPA were obtained by
linear regression of ln[IPA] versus time and are listed in Table 11 for
various pH values. The rate constants for IPB loss and for IPA formation
32
-------
Table 9
IIYDKOI Yb IS Ol ISOHKOPYI UKOMIDE AT 25°C MUNlTUKtO BY fill: LOSS OK ISOPKOl'YL HKOMIOE
L-' i '1 ' f iiiul 11 i ons
i. SH(
> , -)ttl
I , SU»
•J. SB(
I1, SMC
lot.il Tlroe
fc.Iapst-d (lu )
I Oil 8
98 o
yb 8
98.b
95 i
louversi on
78
77
72
77
74
Number of
Time I'nnitt.
6
5
6
6
8
Initial
Concent rat. Ion
10"|1PB| (H)
o
8 79
9 46
9 52
9 06
10.80
Hydrolysis Hate
Constant," 10* k (s_l)
li
J 90 1 0 09
J 75 ! 0 11
J 28 '. 0.2i
3.96 I 0.1J
4.08 t 0 70
Correlat ion
Coef ficlent, KJ
0.998
0 999
0 980
0 996
0.871
^BoHt-r solutions made u|> to standard buffer eoiieeutrat 1 ons (SBC) listed In [lie CRC Handbook (1975).
lliese estimates of ja obtained f i on the regression of ln|lPB| versus t uhere |IPB) is tlie content rat Ion of 1PB at
1 I EL l 1 t
-------
Table 10
EFFECT OF BUFFER AND IONIC STRENGTH (u) ON HYDROLYSIS OF IPB AT 25°C
Conditions th - 10' ^ <"> .^f0"cs
pH 7 SBC3 3.28 ± 0.23 9.52 ,6
pH 7 SBCb 2.13 ± 0.54 9.66 6
pH 7 MBC° 2.82 ± 0.33 9.35 6
pH 7 MBC/c,d 3.38 ± 0.35 9.A3
0.1 M NaClOi
a
^Original measurement shown in Table 9 y = 7.91 x 10~2 M.
cRepeat experiment y = 7.91 x 10" 2 M.
Minimally buffered solution y = 3.16 x 10"2 M.
y = 0.131 M.
6
agree well for pHs 5, 7, and 11. In addition, these rate constants for
IPA formation agree extremely well with the average measured value of k
h
(3.79 x 10 6 s l) based on IPB loss and with the literature value of k
h
(3.77 x 10-6 s-1) (Koskikallio, 1967). The rate constants for IPA ap-
pearance at pHs 3 and 9, however, are both much larger than the corresponding
rate constants for IPB loss.
Hydrolysis experiments were performed at pHs 3, 5, 7, and 9 to measure
the rate of Br ion appearance. We sampled these solutions in accordance
with the SRI and EPA protocols. A linear regression of ln[Br ] versus
time was used to obtain a rate constant for the production of bromide at
pHs 3, 5, 7, and 9. Rate constants for these experiments are given in
Table 11; they agree well with the corresponding rate constants for IPB
loss at pH value of 3, 5, and 9. The rate constant for Br formation at
pH 7 differs from the corresponding value of k, for IPB loss by a factor
h
of three. The rate of bromide formation at pH 11 was not monitored.
The data in Table 11 show tiiat the rate constants for loss of IPB and for
production of Br and IPA do not always agree closely. At pH 3 the rate
34
-------
Table 11
COMPARISON OF HYDROLYSIS RATE CONSTANTS FOR IPB AT_25°C OBTAINED FROM ANALYSIS FOR
IPB AND FOR IPA OR Br
[kh (s-1) x 106]
Estimation
Method pH 3 pH 5 pH 7 pH 9 pH 11
From LPBa 3.90 t 0.09 3.75 I 0.22 3.28 ± 0.23 3.96 ± 0.13 4.08 ± 0.70
I OSS
From lPAb 5.58 i 1.28 3.67 i 0.94 3.83 t 0.82 5.77 i 1.21 3.51 ± 0.52
production
From Br~b 3.68 ± 1.42 3.90 ± 0.55 10.69 ± 3.82 4.68 ± 1.43
produr tion
aRate constant obtained from regression analysis of ln( [ IPB1q/[ IPB ] t) versus t where
^[IPB]C is tliq concentration of IPB at time t.
Rate constant obtained from regression analysis of ln[C]t versus t where [C]t is
the concentration of IPA or Br at time t.
-------
constant for IPA appearance is about 40% higher than for Br" appearance
or for loss of IPB. At pHs 5 and 7 the rate constants for IPA formation
agree well with those for loss of both have large statistical errors,
but this is probably due to the way in which the data were treated. Rate
constants for appearance of Br at pHs 7 and 9 and appearance of IPA at
pH 9 have significant errors and differ markedly from the value of k
n
for loss of IPB.
Experimental Methods
Chemicals
Ethyl acetate, cyclohexene oxide, and isopropyl bromide were purchased
from Mallinckrodt, Aldnch Chemical Company, and Matheson, Coleman, and
Bell, respectively. According to infrared and gas chromatographic analyses,
EA and CHO were better than 98% pure and were used without additional
purification. IPB was analyzed only by GC and used as received.
Constant Temperature Bath
The constant temperature bath used in these experiments consisted
of an 8-gallon glass container contained in a large wooden box and sur-
rounded with 1 to 3 inches of vermiculite as insulation. A Plexiglass
top covering the water bath had holes for the heater, stirrer, and
temperature control probe ; the cover was hinged at the diameter for easy
access to the samples. The shaft speed of the stirrer was set at about
2500 rpm. The 250-watt ceramic heater was controlled by a YSI Model 72
thermoregulator that maintained the temperature to within ± 0.02°C. To
further ensure that the temperature in the bath remained at 25 r 0.02°C,
a heat exchanger coil of 1 m by 6.4 mm diameter copper tubing was placed
into the bath. Water was pumped through the coil in a closed loop from
a reservoir; this circulated water was cooled by passage through the inner
loop of a 50-cm-long Allan condenser whose outer jacket was connected to
the water tap. Direct circulation of tap water through the coil was un-
satisfactory because of dLurnal fluctuations in flow rate. The heat ex-
changer was essential to ensure proper temperature control when the ambient
temperature exceeded 25°C, d-> Lt sometimes did in this laboratory.
36
-------
Preparation of Reaction Solutions
All glassware used in these experiments was thoroughly washed and
placed in an oven (560°C) overnight.
Reaction solutions were prepared according to the procedure outlined
below. Reagent grade chemicals and sterile, pure water were used for all
sample preparation. The concentration of chemical in the final"buffered
solution used in kinetic measurements was about 1 x 10-3 M or lower.
Enough chemical to make a 0.1-M solution was weighed into a 100-ml
volumetric flask that already contained some buffer solution or
acetonitrile; acetonitrile was used to assist in the dissolution, if the
chemical was not readily soluble in water. The flask was filled to the
mark with either buffer solution or acetonitrile and a 1.00-ml aliquot
was diluted 1:100 with buffer solution to the final concentration. Heat
was not used in any stage of the preparation.
The solutions were placed in the bath according to the procedure
outlined below. In addition, an aliquot was immediately quenched; this
quenched mixture serves as a t = 0 sample.
Because hydrolysis of CHO at pH 3 is fast C% 6 minutes), a special
procedure was used to prepare this test solution. A known volume of pH 3
buffer in a round-bottomed flask was allowed to thermally equilibrate in
a 25°C constant temperature bath. A known amount of CHO dissolved in
acetonitrile was introduced into the flask; aliquots were withdrawn from
the flask at known times and quenched to pH 9. After sampling for two
half-lives, we analyzed the samples randomly to minimize systematic errors.
Buffer Solutions
The buffer solutions used in these experiments were prepared in the
following manner, using the composition and proportions of the standard
buffer concentration (denoted SBC) given below and described in the CRC
Handbook (19 75):
pH 3: 250 ml of 0.100 M kllC6H„C20,.
111.5 ml of 0.Lon M HC1
pH 5: 250 ml of 0 100 '! nHC6Hi.C20<.
113 ml of 0.100 M ViOH
37
-------
pH 7: 250 ml of 0.100 M KH2P0<.
145.5 ml of 0.100 M NaOH
. < -•
pH 9: 250 ml of 0.025 M Na2B-'C07 »/0H20
23 ml of 0.100 M HC1
pH 11: 250 ml of 0.0500 M NaHCOj
113.5 ml of 0.100 M NaOH
All final volumes were 500 ml.
Minimally buffered aqueous systems were prepared by adding enough
standard buffer to a known volume of sterile water to adjust the pH to
that of the standard buffer. For pH 9, for example, 1 ml of SBC pH 9 was
diluted to 100 ml with water to obtain a pH of 9.00 ± 0.02; this solution
was labeled 0.01 SBC-pH 9. A minimally buffered pH 7 solution was pre-
pared by diluting 40 ml SBC pH 7 to 100 ml with sterile water.
Minimally buffered solutions of high ionic strength were prepared
by replacing half the volume of water called for in the preparation of
the minimally buffered solution with 0.2 M sodium perchlorate. For example,
1 ml of SBC pH 9 was mixed with 49 ml of water and 50 ml of 0.2 M NaClO^
to make a minimally buffered pH 9 solution of high ionic strength.
Kinetic Measurements
Aliquots of the reaction mixture were transferred with a pipette to
13 mm OD by 100 mm test tubes (approximately 8 ml capacity). Each tube
was filled to overflowing and immediately covered with a watertight Teflon-
coated Mimnert valve. A test tube was filled for each time point. Each
tube was covered with aluminium foil to exclude light and labeled. The
tubes were suspended from wires stretched across the bath so that each
tube was submerged in the bath.
At selected time points, a tube containing reaction solution was
removed from the bath and quenched by either cooling in ice or adding a
known volume of the reaction mixture to a known volume of acid or base
solution, which had been precooled to ^ 5°C. The acid or base solution
was adjusted so that at the final solution pH, the hydrolysis rate was
minimized. For the chemicals studied in our laboratory, the reaction
solutions were quenched by adjusting the pH as well as by cooling:
38
-------
EA - The pH of all solutions was adjusted to pH 5.5.
CHO - pH 3 solutions were adjusted to pH 9.
IPB - pH 11 solutions were adjusted to ^ pH 6.
All other samples were cooled to further quench the hydrol^is reaction.
Sampling Regimen
%
Sampling of the reaction mixture was performed according to EPA and
SRI protocols. The EPA protocol recommends using one of three measure-
ment regimens at pHs 5, 7, and 9:
(1) For chemicals that hydrolyze rapidly, 6 analyses should be taken
between t = 0 and t = 672 hours at which time 60% to 99% of the
chemical will have hydrolyzed.
(2) For chemicals with moderate reactivity, 15 to 20 analyses should
be taken between t = 0 and t = 672 hours at which time 20% to
60% of the chemical will have hydrolyzed.
(3) For unreactive chemicals one analysis should be taken at t =
672 hours at which time less than 20% of the chemical will have
hydrolyzed.
The SRI protocol requires that the rates of hydrolysis be measured
at pHs 3, 7, and 11, according to the following regimen:
(1) For chemicals that hydrolyze rapidly, i.e., 60% to 70% of the chemical
hydrolyzes in several weeks, a minimum of 6 analyses should be
taken.
(2) For chemicals that hydrolyze more slowly, i.e., 20% to 30% of
the chemical hydrolyzes in several weeks, 15 to 20 analyses
should be made with most of the points taken between 10% and
30% conversion.
The SRI protocol also requires that a control solution be analyzed.
Table 12 shows the sampling regimens for the chemicals tested in our
laboratory.
Analytical Method
All analyses for EA, IPB, and CHO were performed by directly injecting
aqueous solutions onto a HP-)700 gas chromatograph coupled with a Sepctra-
Physics integrator. The instrument settings and columns used for these
analyses are summarized in fable 13.
39
-------
Table 12
SAMPLING REGIMENS FO^'EA, CHO, AND IPB AT 25°C
_pH_
EA
7 9 It -
. -\
No. of Points 13 1 14 6
% Conversion 10-30 5.7 25 95 80
CHO
No. of Points 6 9 6 6 6
% Conversion 80 90 ^30 ^30 ^ 80
IPB
No. of Points 6 5 6 6 8
% Conversion 78 77 72 77 74
For all chemicals, GC analyses were performed in triplicate at each
time point; injection sizes were usually 2.5 gl. Peak areas were deter-
mined by electronic integration. Calibration runs were performed before
the reaction mixtures were analyzed. The calibration mixture was prepared
at a pH where the hydrolysis rate was the slowest. The mixture was pre-
pared according to the general procedure outlined previously. Immediately
after the calibration solution was prepared, it was quenched and analyzed.
The average areas from three analyses for the chemical and the internal
standard were then used to estimate concentration of the chemical.
The concentration of chemical, C, m a sample was measured by comparing
the ratio of the .peak areas of C and the internal standard, IS, in the
sample with the ratio of the IS and C peaks in the calibration solutions.
The concentration of C<, was then obtained using the following relationship:
Peak Area IS Peak Area C
frl = -< x rci
1 's Peak \t"c a IS Peak Area C 1 Jc
s c
40
-------
Table 13
INSTRUMENT SETTINGS AND COLUMNS USED FOR CHEMICAL ANALYSES
EA
CHO
IPB
2.75 in x 0.2 cm I.D. glass 2.75 m x 0.2 cm I.D. glass 2.75 m x 0.2 cm I.D. glass
Porapak Q Mesh 80/100;
Porapak QS Mesh 80/100
Co Iumn
Pac klng
Support —
S i 11 11 ni.i r y phase —
So I veil I —
liiLernal standard Acetone with Porapak Q;
methyl ethyl ketone with
Porapak QS
Detection meLhod
TemperaLure
FJow rates
N2
h2
Ai r
Flame ionization
160°C (isothermal)
JO nil/mm
30 ml/min
240 ml/min
Chromosorb 750 Mesh 80/100
Carbowax 20M
Chloroform
Methyl ethyl ketone
Flame ionization
75°C at 4°C/min to 110°C
30 ml/min
30 ml/min
240 ml/min
Chromosorb 750 Mesh 80/100
Carbowax 20M
Chloroform
^-Butanol
/
Flame ionization
80°C for 4 min; then 4°C/n
to 100°C
30 ml/min
30 ml/min
240 ml/min
-------
where s denotes the sample and c the calibration standard where the con-
centrations of IS in' the sample ancj .in the calibration solutions are
V-
identical.
Data Treatment
First-order rate constants were estimated from the regression of
lnCC^/C^) versus time using standard linear regression programs available
in many hand calculators, including the HP-97 Stat Pac. The special case
of C = C was not used. The slope of the regression is k, .
to h
C was measured thrice by GC at each time point; the ratio C /C was
t o t
calculated, transformed to In (C^/C^), and averaged for the three values
of In (C /C ) for use as one data set with time t in the regression
o t
analysis. Values of the standard error(s) and R2 were given for k^ or
k by the regression program.
U2
-------
Optimized Screening Protocols
The similarities and differences between the screening protocols
proposed by EPA and SRI are summarized in Table 14. We evaluated both
hydrolysis screening protocols for precision, accuracy, simplicity, and
economy. A new screening test protocol should incorporate the best features
of the existing screening tests with any changes that would improve the
test without undue complications or loss of economy. Perhaps one of the
most striking results of this investigation is the finding that at least
for EA, rate measurements at low and high pH (3 and 11) provide a more
reliable basis for estimating k, at pHs 5 and 9 than do the direct but
h
very slow measurements at those pH values. This paradox is explained by
the relative reliability of measurements of fast versus slow reactions.
Very slow reactions with half-lives of two or more weeks are much more
subject to intrusion by unwanted processes, especially biodegradation,
to failure of control equipment, and to intermittent power failures.
Because of the long intervals between analyses in very slow reactions,
discovery of these problems can lead to significant losses of time.
Table 14
SIMILARITIES AND DIFFERENCES IN SRI AND EPA PROTOCOLS
Differences
Similarities
pH Hydrolysis rate
measured at 3 pHs
Samples Sample prepared in
sterile H20 with-
out heat; final
conc. < 1 x 10"3
and < h solubility
SRI
Rates measured at pHs
3, 7, and 11
L sampling procedure:
at t = 0, 44, and 88
lir plus 8 optional
^amp1ings
EPA
Rates measured at
pHs 5, 7, and 9
sampling procedure
varies according
to chemical's
reactivity
43
-------
Another perhaps less important factor, which may diminish the
reliability of rate measurements at pHs 5 and 7, is the occurrence
of buffer catalysis that results from using phosphate buffer. The im-
portance of this effect, generally, in confounding accurate measurements
is not readily assessible, but our data demonstrate the occurrence of
this effect in the hydrolysis of both CHO and IPB. We believe that
measurements at pH values within the range of environmental relevance and
interest, e.g., pHs 5, 7, and 9, will constitute the preferred method of
screening for hydrolysis; however, our results show that when half-lives
exceed one to two weeks, measurements at pHs 3, 7, and 11 are preferred.
We therefore recommend that wherever possible zero-level screening
by structure-activity relationships be used first to help select optimum
pH values to minimize measurement times needed for reliable measurements.
In the absence of clear indications of life-times we again recommend
measurements at pHs 3, 7, and 11, but with a minimum of six to eight time
points over AO to 70% conversion to define more accurately- the rate constant
k. . In this respect the recommended protocol is really a synthesis of
h
the SRI and EPA methods—the SRI pH values and the EPA measurement regimen.
Estimated Cost for Optimized Screening Protocol
We used our experience in performing hydrolysis experiments in the
laboratory as a basis for estimating the cost for performing such experiments
for an optimized protocol in a modern, well-equipped laboratory by trained
personnel. The costs used for the estimation are listed in Table 15; note
that no capital costs are included for instruments such as chromatographs,
electronic integrators, or temperature controllers. No cost for analytical
method development is included; that would add another 25% to labor cost.
In our estimate we assume that each screening protocol requires
88 hours (Table 15) plus 25% additional time for unexpected problems, for
a total of 110 hours per screening experiment. The prorated cost per
protocol is estimated to '¦>(• ?_0 for chemicals and solvent and S100 for
materials, including some hro.i\age and replacement costs. The combined
cost of chemists and supervi-.or\ time is estimated to be $35 per hour.
44
-------
Thus the tocal cost for time, materials, and chemicals would be about
$3970 per protocol in 1980 dollars.
-------
COLLABORATIVE TEST DESIGN FOR HYDROLYSIS
Background
A collaborative test program involves applying a test method at
multiple, independent laboratories. Such testing provides data for
evaluating the precision and accuracy of the method. Also, problems
with the method may be discovered that were not apparent at the origin-
ating laboratory. Since the participating laboratories represent a
diversity of environments, equipment, instrumentation, reagents, and
technicians, a collaborative study provides an evaluation under circum-
stances that are similar to those that will occur when the test method
is put into practice.
Another use of a collaborative test program is to obtain the
best estimate of the property being measured. Such an estimate is based
on the results from independent laboratories and is possibly more re-
liable. By and large, the design of a collaborative test program is the
same whether the primary interest is in the test method or the test
result.
There is a well-established literature on collaborative testing.
This literature is concerned with measuring nonkinetic entities, such
as in analytical chemistry. Collaborative testing for hydrolysis dif-
fers in that the property being measured is a kinetic rate coefficient
or half-life. However, since the principles and definitions given in
the collaborative testing literature are still relevant, we review them
here. Two authoritative sources for information on collaborative test
ing are the American Society for Testing and Materials (ASTM) and the
Association of Official Analytical Chemists (AOAC).
* See, for example, the ASTM publication "Suggested Recommended Prac-
tice for Conducting an Interlaboratory Test Program to Determine the
Precision of Test Methods" or Statistical Manual of the AOAC which
includes "Statistical Techniques for Collaborative Tests" by W. J. ^
Youden and "Planning and Analysis of Results of Collaborative Tests
by E. H. Steiner. 47
-------
Intralaboratory study: A principle often emphasized in the litera-
ture is that a test method should be thoroughly evaluated within a
single laboratory before submitting it to a collaborative.,, _ lhterlabora-
tory study. In practice, this usually means that the originating
laboratory trys the method with various materials and under various
conditions. Most of the literature on intralaboratory testing is devo-
ted to formal experimental designs that allow the effects of several
factors to be evaluated simultaneously. The most prominent design
is one suggested by Youden (1950). In this design, test conditions are
varied by an amount similar to the range encountered when several labor-
atories are presumably following the procedure. Youden calls this type
of intralaboratory study a test of ruggedness.
Precision: The ASTM defines the precision of a test method as the
degree of agreement among individual test results obtained under pre-
scribed similar conditions when the number of individual observations
in a single test result is specified in the method of the test. Precis-
ion may be inversely characterized by the imprecision of the test
results as measured by their standard deviation.
Systematic error or bias: A systematic error or bias is the dif-
ference between the average test result and a reference value. Whether
or not a reference value actually exists, it is often conceptually help-
ful to think of the reference value as being the idealized true value.
Accuracy: The ASTM defines accuracy as the degree of agreement of
the individual test results with an accepted reference value when the
number of individual observations in a single test result is specified
by the test protocol. So defined, accuracy includes both the random
error of precision and an\ accompanying systematic error or bias.
* These definitions of pr<.i L=.Lon, systematic error or bias, accuracy,
repeatability, and repri'Jiu Lbility are taken in part from Duncan
(1978).
48
-------
Repeatability: Repeatability'"refers to the variability of test re-
sults within a single typical laboratory under conditions that have been
carefully prescribed. It is often described by a 95% confi^nce inter-
val for the difference between two test results from the same laboratory.
Reproducibility: Reproducibility refers to the variability of test
results between laboratories under conditions that have been carefully
prescribed. It is often described by a 95% confidence interval for the
difference between two test results from different laboratories.
Outliers: The analysis of laboratory data will sometimes reveal
results that are way out of line and suggest that something went wrong.
Statistical methods are available to assess the likelihood that such
deviations are due to chance, and graphical methods are available to
provide a more descriptive impression. The ASTM position is that,
while such techniques are useful for "flagging" suspicious data, the
decision to reject such data should be the prerogative and responsibili-
ty of the committee running the study. Such decisions
should be based on general scientific as well as statistical considera-
tions .
Replication: Statements about the precision of a test method re-
quire information about random variability within a laboratory. The
usual approach, and the ASTM recommendation, is to perform replicate
determinations on each material in each laboratory to estimate the
within-laboratory variation. The conditions of the repeat determina-
tions need to be specified, e.g., whether replicate tests are done by
the same personnel using the same reagents, equipment, and instrumen-
tation on the same day. Another approach, suggested by Youden (1975),
is to estimate the within-laboratory variability from the difference
between single measurements on pairs of samples with slightly different
levels of content. The advantage of this "Youden pairs" approach is
that individual measurements are more likely to be independent of one
another and that the paired results plotted for all laboratories pro-
provide an informative graph for interpreting results.
49
-------
Hydrolysis Testing Protocols
The SRI screening and detailed test methods for hydrolysis in water
were reviewed in the Background section and discussed in th"e subsection
Optimized Screening Protocol; we repeat that information here t® high-
light data collection and data analysis specifications and to describe
the scope of this development of collaborative testing methodology.
The screening protocol for hydrolysis is intended to identify
chemicals with half-lives of less than one year and more than one hour
at 25°C. Each chemical being tested is hydrolysed in pH 3, 7, and 11
buffer solutions. The pH 7 solution is analyzed after 2 hr and 88 hr;
if more than 75% of the chemical has hydrolyzed after 2 hr, the hydroly-
sis half-life will be less than 1 hr; if no loss of chemical occurs in
88 hr, any loss in the pH 3 and pH 11 solutions is probably due to hy-
drolysis. The pH 3 and pH 11 solutions are analyzed at 44 hr and 88 hr;
if more than half the initial concentration of chemical has hydrolyzed
in 88 hr at either pH 3 or pH 11, then the chemical is expected to have
a half-life of less than 1 year at pH 5 or pH 9; the loss at 44 hr
should be more than 29% if the half-life is less than 1 year.
The detailed protocol for hydrolysis is designed to estimate hydro-
lysis rate constants and half-lives for most chemicals at any pH and
temperature. Like the screening method,- each chemical being tested is
hydrolysed at pH 3, 7, and 11 at a fixed temperature, preferably 25°C.
However, the detailed protocol requires that solutions be sampled and
analyzed more frequently: at least six times if 60% to 70% conversion
occurs within several weeks and even more frequently for slower reac-
tions. The hydrolysis rate constant, k^, is estimated from the
concentration-time data for each pH experiment by (1) plotting concen-
tration versus time on senuloi; graph paper or (2) calculating a linear
regression analysis of In , ,mu , ncrat ion versus time. The estimates of
kh at the three experimenc.il pH levels are used to estimate the hydro-
lysis rate coefficients tor the acLd, neutral, and base process,
50
-------
meeting the assumptions required for regression analysis and on the ap-
propriateness of the least squares criterion. ^
Linearity: Applying the natural log transformation to the expon-
* \
ential decay function results in
In C = In C - kt
t o
or In C /C = kt ,
o t
where C denotes the concentration at time t. Regression analysis based
on either of these linear functions will lead to the same estimate of
the rate coefficient k. The SRI kinetic testing protocols do not force
the latter form of the regression function through the origin. Instead,
the regression function used is
In C /C = a + kt
o t
The intercept a is interpreted as a systematic error of analytical mea-
surements that should not affect the estimation of the rate coefficient.
Whether the kinetic process being studied is, in fact, a first-order
reaction can best be judged by inspecting a plot of or versus
time on semilog graph paper. A formal statistical test of this assump-
tion would require multiple observations of independent experiments at
synchronized time points, which is probably not technically feasible in
a laboratory.
Independence: The independence assumption is that the random error
associated with the concentration at each time point is statistically
independent from the random error for other time points. This is quite
plausible for the error from the analytical method and possibly also for
technical error deriving from the sampling procedure. However, the in-
dependence assumption may not be met for experimental error due to
physical or chemical conditions or competing processes. Such experimen-
tal effects are likely to cause random errors to be serially correlated
over time.
54
-------
important implications for the subsequent data analysis and interpreta-
tion of results.
There are two basic types of collaborative test designs for' selecting
the number of laboratories:
(1) A few carefully chosen laboratories may participate in the
collaborative tests, leading to a comparison of results for
a fixed selection of laboratories with any number of labora-
tories down to two providing a meaningful comparison.
(2) Randomly chosen laboratories may represent a population of
laboratories, leading to more general conclusions about the
precision and accuracy of the test method as revealed by the
random selection of laboratories; note that ten or more lab-
oratories are needed to represent a large population of
laboratories (Youden,1975).
In this report, we consider both types of collaborative test designs and
the subsequent data analysis based on fixed or random effects statisti-
cal models. However, considering the status of hydrolysis testing,
near-term needs for collaborative testing, and probable constraints on
the number of participating laboratories, more attention is given to
collaborative testing that involves relatively few (3 to 6) carefully
selected laboratories.
Replication
Another key design parameter is the number of experimental repli-
cates within each laboratory. In nonkinetic collaborative testing, such
as in testing an analytical method, within-laboratory variability is
ascertained from either replicate measurements on the same sample or
single measurements on pairs of samples, i.e., Youden pairs. For kine-
tic process testing, the standard error of a rate coefficient estimate
is obtained from the regression analysis of sample measurements at mul-
tiple time points. This standard error may be interpreted as the
within-laboratory error for estimating a rate coefficient. In this way
experimental error analvsLs is based on the residual variability within
a single experiment without needing to replicate experiments within each
laboratory.
52
-------
There are advantages arid limitations to basing the error analysis
for a kinetic test method on residual variability, i.e., deviations
-A
from a first-order rate law. Of course, laboratory work Is- held to a
minimum if there is no need to replicate experiments, and resources may
be used to test other chemicals or to test under alternative controlled
conditions. Furthermore, studying residual variability within an ex-
periment leads to a detailed understanding of error sources and sampling
regimens, which would not be possible if the test results were simply
the rate coefficient or half-life estimates for replicate experiments.
The primary limitation of our approach is that there are probably impor-
tant sources of experimental variability within a laboratory that are
not represented by residual variability within a single experiment.
Within a kinetic experiment, the "random error" of the reaction cor-
responds to "chance events" that occur between sampling times, leading
to deviations from a deterministic process and hence estimation error.
Within a laboratory, there are probably additional chance events that
would occur if the experiment is replicated at a different time or a
different initial concentration, which may lead to results outside the
confidence interval derived from a single experiment.
The statistical methods described in this report do not consider
experimental replication within each laboratory. Within-laboratory
variability is estimated from regression analysis techniques applied to
single experiments. This approach was also used in the intralaboratory
study of this project and is an extension of the statistical method and
error analysis provided in the original test methods protocol (Mill and
Mabey, 1980).
Least Squares Regression
It is common practice to linearize the exponential decay function
that describes a first-order process by a natural log transformation,
then to use least squares regression analysis to estimate the first-
order rate coefficient. The validity of this approach depends on
53
-------
meecing the assumptions required for regression analysis and on the ap-
propriateness of the least squares criterion.
Linearity: Applying the natural log transformation to the expon-
ential decay function results in
In C = In C - kt
t o
or In C /C = kt ,
o t
where Ct denotes the concentration at time t. Regression analysis based
on either of these linear functions will lead to the same estimate of
the rate coefficient k. The SRI kinetic testing protocols do not force
the latter form of the regression function through the origin. Instead,
the regression function used is
In C /C = a + kt
o t
The intercept a is interpreted as a systematic error of analytical mea-
surements that should not affect the estimation of the rate coefficient.
Whether the kinetic process being studied is, in fact, a first-order
reaction can best be judged by inspecting a plot of C or versus
time on semilog graph paper. A formal statistical test of this assump-
tion would require multiple observations of independent experiments at
synchronized time points, which is probably not technically feasible in
a laboratory.
Independence: The independence assumption is that the random error
associated with the concentration at each time point is statistically
independent from the random error for other time points. This is quite
plausible for the error from the analytical method and possibly also for
technical error deriving from the sampling procedure. However, the in-
dependence assumption mav ,-vt be met for experimental error due to
physical or chemical condLtiini-. or competing processes. Such experimen-
tal effects are likely to cai'se random errors to be serially correlated
over time.
54
-------
Equal variance: Because of the lri transformation, the assumption
of equal error variance for all data points is in terms of the relative
concentration rather than the absolute concentration. Constant relative
variability is a reasonable assumption for chemical data since experi-
mental error rates are often stated in relative terms for such data, e.g.
s.d. = + 5% of true value. For kinetic testing, this assumption can be
checked by the plot of C or C /C versus time on semilog paper; the
tot
variability of points about the fitted line should be constant across
time.
Normality: The assumption of normally distributed relative error
is needed for the statistical tests presented in the next section.
(This assumption is not needed to merely fit a least squares regression
line.) The required distribution is more specifically a lognormal dis-
tribution because the log of the error in concentration is assumed to
be normally distributed. The following graph illustrates a typical
lognormal distribution.
Distribution of error
A skewed distribution of this type is reasonable for chemical data.
Least squares: Applying the least squares criterion to estimate
a logarithmic relationship ls sometimes advocated (Hoel, 1962) and
sometimes criticized (Cvetanovic and Singleton, 1977).
-------
Let denote the observed concentration at time t and denote the
concentration predicted at time t txy--estimates of a and k. Then the
least squares estimates of a and k are those that minimize the sum of
squared deviations between observed and predicted concentrations accord-
ing to the following equation:
%
SS = I (in(Co/Ct) - ln(Co/Cc))2 = £ (lnCC^C^)2 (6.5)
This amounts to minimizing the sum of squares of the In of the relative
deviations about the regression line. The appropriateness of this ap-
proach depends on whether relative deviations are more relevant than
absolute deviations, and if so, whether minimizing SS is a meaningful
estimation criterion. The relevance of relative deviations for chemical
data has been discussed. Minimizing SS provides a meaningful criterion,
as can be seen by sample calculations, in that (lnC/C^)* = 0 when C = C^,
and (lnC/C^)2 increases as the error cf prediction increases, e.g. it
the prediction error is ± 5%, then (lnCt/Cc)2 = (In 1.05/1) = .0024 or
(lnC^/C^)2 = (In .95/1)2 = .0026; if the prediction error is i 10%, then
(InC/C )2 = (In L 10/1)2 = (In 1.10/1) 2 = .0091 or (lnC^)2 = (In - 9/1)2
.0111. Therefore, the following statistical methods are based on gen-
eralizations of least squares regression techniques.
56
I
-------
Statistical Methods
Statistical methods for analyzing the data from coliattcfratlve test-
ing apply to two types of questions. The first type involves the
comparison of results among laboratories. Are the rate coefficients
the same? If not, which laboratories are different? Are the standard
errors of rate estimates the same9 The second type involves statements
about the precision and accuracy of the test method. What is the within-
laboratory variabilitv and what are its components'' How can the
precision be described in terms of the repeatability of results Is
there evidence of systematic bias7 What is the between-laboratory
variability and how does it effect the reproducibility of results?
Comparison of Laboratories
The rate coefficient is first estimated by simple regression analy-
sis in each laboratory. Let the subscript 2, index the N laboratories
in the collaborative study and the subscript i index the n^ data time
points for the Uh laboratory. Employing the In transformation, the
regression function for the £th laboratory is
The rate coefficient (k ) and intercept (a.) for each laboratory
K * K
are estimated in the usual way:
ln(Clo/CU) = + Vu
(6.6)
k
I
(6.7)
- I ln(C- /C, .) - k i I t
L ¦ o >.i l n? v.i
(6.8)
* All I denote E unless indicated otherwise.
l
57
-------
The standard errors (se) of the estimates of the rate coefficient
and intercept are a function of the variance of concentrations about
•A
the regression line in each laboratory. This variance is estimated in
each laboratory by using the following equations:
s? . 1
1 V2
I [ln(Cto'CU>)2
'£(Cto/Cti» ,2
— i i ¦¦¦¦¦-- i. i — \r
n„
n
(6.9)
The standard error of the estimate of the rate coefficient is
1/2
nf.
Se(kn) = Sf
(6.10)
The standard error of the estimate of the intercept is
Se(ad) = Sd
- iWi' J
1/2
(6.11)
A statistical test is first described for comparing the rate coef-
ficients for two laboratories. The difference in their coefficient
estimates is statistically significant if it is unlikely that a differ-
ence of this magnitude would occur by chance if their true coefficients
are equal. A pooled estimate of the variance of concentrations about
the regression line is calculated as
2 (n^-2)S7 + (n^-2)
Sp nL+ n, - 4
(6.12)
The standard error of the Ji i rence* oetween the rate coefficients is
given by
55
-------
2 2
= s
d p
nl
"2
-nl
2
Cli "
[Z cii]
2
"2 J
2
t0 . -
2i
\l V 1
L 2i
2
(6.13)
The t statistic for testing the hypothesis that the rate coefficients
are equal is given by
59
-------
t =
--'ki " k2
(6.14)
The hypochesis is rejected if the absolute value of t is greater than
the value in a statistical "t" table for the selected a level and
(n^ + - 4) degrees of freedom.
The test given above assumes that the variance about the regression
line is the same for both laboratories. This assumption may be tested
by the F statistic
s2
F = —L_ (0.15)
s2
2
The variances are significantly different if this statistic is greater
than Che cabled "F" value for the selected a level, df^ = (n^ - 1) and
df^ = (n^ - 1). (The reciorocal also needs to be checked.)
A more general statistical comparison for any number (N) of labora-
tories involves the collective estimates of the rate coefficients (k )
c
and intercept (ac) based on the data points from all the laboratories.
These estimates are calculated from the formulas for k, and a, by re-
£ «*»
placing n,, by En. and by taking all summations over both i and i; i.e.,
^ Jv
I denotes II. The collective estimate of the variance about the regres-
li i
sion line (S~) is calculated similarly, as are the standard errors tor
c
the estimates of k and a .
c c
The idea behind the comparison of N laboratories is that if their
true rate coefficients are equal, then the collective regression line
based on all data will be nearlv as good as when regression lines are
fit for each laboratory individually.
A statistical test of the hypothesis that the regression functions
(slope and intercept) are fie same for all laboratories is based on the
60
-------
difference between Che sum of squared- residuals for the collective re-
gression and the sum of squared residuals for the individual regressions
for all laboratories. The F statistic for this test is
-\
F =
(I no - 2> $1 - I (n - 2) S2 £(n - 2) S2
JI I .1
I n - 2 - I (n? - 2)
I I
l(n, - 2)
(6.16)
The hypothesis is rejected if F is greater than the tabled "F" value for
the selected a level, df^ = En„ - 2 - ^(n,i ~ 2) and df^ = ~ •
It is preferable to test whether the rate coefficients for labora-
tories are equal while allowing their intercepts to be different. This
way, different systematic errors in analytical methods do not affect the
comparison of rate coefficients. The t-test for comparing laboratories
does this; however, the preceding F-test for comparing any number of
laboratories tests whether the rate coefficients and intercepts are the
samp for all laboratories.
For testing the equality of rate coefficients only, a modified
version of the collective rate coefficient is calculated.
kc' =
I cln(C)lo/C£i) Lq I"? \ ln ^eo^J-i*]
I i I Li i J
I i U .li 'J
(6.17)
(For simplicity, it is assumed that each laboratory, has the same number
(n) of data points.) Next, k is used to calculate the associated
residual variance.
S2 = i
c' nN - N - 1
y i
l i
ln(C_o/Cfi)
[! I in
U i
(CW]
nM
k2,
c
nN
1
(6.18)
61
-------
The hyposthesis is rejected if S is greater than
S > \/ (N - 1) Fd; N - 1, I - 2N (6.23)
where F , r- <¦,», the table "F" value for the selected c*
a; N - 1, - 2N
level, df. = N - 1 and df0 = En, - 2N.
1 2 y X,
If N = 2, this test reduces to the t-test for comparing the rate coeffi-
cients for two laboratories.
A more common wa> to present the result of applying the S-method is
by a confidence interval. Let d^. denote the true difference between the
rate coefficients and k,' for any two laboratories. Then the (1 - a)
confidence interval for is given by
-S/(B"1) f«;»-lfn.-2» £ dTS kl " +Sdy
-------
2 ' 2
The residual variance a is estimated by S? for the £th laboratory or
2 2 8
bv S when the S„ are pooled across all laboratories.
p Z r -*\
In theory, var (k.) can be reduced by sampling more frequently at
the beginning and end of an experiment since this will increase
_ 2
T.( t - t)". However, this practice is not recommended because it is
i 1
more important to have a better check, on whether the reaction is first-
order by spacing sampling times evenly.
2
The residual variance o has two components: one due to the analv-
e
tical method and the other due to the experimental reaction. The
2
analytical component 0 can be estimated by a preliminary test of the
3
analytical method. Its contribution to the residual variance can be re-
duced by basing the regression analysis on the average of ln(C /C ) for
0 c *
multiple chemical analyses of the concentration for each time point.
2
The contribution of the experimental reaction component cannot
be reduced by multiple samples at each time point, since the solution
being tested is assumed to be homogenous. (There would be reason for
multiple samples at each time point if the sampling procedure itself
contributes substantially to the residual variance.)
The variance of the estimate of the rate coefficient reflects the
error components due to tne analytical method and the experimental reac-
tion. For a single chemical analvsis of concentration at each time
point,
+ a2 (6.26)
ear
For the average of the In of (C for m chemical analvses at each
time point,
The average of the InfC /C ), rather than the In of the average
& o t
(C /C ), should be used ip the regression analysis. These two
o t
quantities are nearly the same when analytical measurement are
within 5% of one another.
')4
-------
0. = CJ2/m + o2 (6.27)
e a r
The number of chemical analyses for each time point should be the same
to satisfv the regression analysis assumption of equal error variance.
Then, for the regression analysis of the average of lnCC^/C^) versus t,
a2/m a2
var(k) = — - ~ (6.28)
I ~ t)Z I (ti - O
i i
The first term is the imprecision due to the analytical method, while
the second term is the imprecision due to the experimental reaction.
A repeatability statement for a kinetic test method can be made in
the same manner as for a nonkinetic test method. The 95% repeatability
interval for estimating a rate coefficient is
a
2 1/2
I - i.96yr( ^-ry' <6,29)
I (ti - 0
i
The difference between estimates of the rate coefficient for two repli-
cate experiments conducted within the same laboratory has a 95%
probability of being less than the size of this interval. As before,
C2 is estimated by S2 or S2. The repeatability interval depends on the
sampling times {t } and tne number of chemical analyses per time point,
which wil-1 be reflected m the estimate of the residual variance.
The svstematic error and accuracv of a kinetic test method can only
be implied bv comparing results among laboratories, since the true value
of a rate coefficient is unknown. This was the purpose for the preced-
ing presentation of statist'.al methods for comparing estimates of rate
coefficients among laborer Rejecting the hypothesis that the
rate coefficients for di- u laboratories are equal implies that
laboratories have differed -oscematic errors that are large compared
-------
to wichin-laboratory imprecision. In this case, the reproducibility of
the test method is poor. Conversely, accepting the hypothesis that the
rate coefficients are equal would lead one to believe that tfie system-
atic error is small relative to the within-laboratory imprecision.
However, the accuracy could still be poor if all the laboratories have
the same systematic error, even though the reproducibility from labora-
tory to laboratory is good.
The between-laboratory variability of a kinetic test method can be
studied by regarding the participating laboratories as a random selec-
tion each of which has a random effect on the rate coefficient.
Employing the In transformation for a first-order reaction and allowing
a non-zero intercept, the random-effects model is
ln(C /Ct) = a + a^ + (k + • (6.30)
In this model, a and k are the overall intercept and rate coefficient,
where and k0 are the random effects of the 1th laboratory.
In terms of statistical theory and methodology, this random-effects
model is fundamentally different than the fixed-effects model that is
the basis of the methods for comparing a fixed selection of laboratories
and that is implicit in the preceding discussion of within-laboratory
precision. Unfortunatelv, random-effects models are more difficult to
deal with than fixed-effects models, and no well-established statistical
methods are available for treating the current problem. However, one
statistical formulation is derived here to estimate the between-labora-
tory variability.
For the random-effects model, the between-laboratory variability of
the kinetic test method corresponds to the variance of the random effect
k The within-laboratorv variability for the tth laboratorv corre-
jL*
sponds to the variance ot the estimate of k„ conditional on the random
effect k^. The withm-laberator. regression estimate is denoted by k,,
66
-------
to distinguish it from the random effect k^. Let varfi(k^) and varw(k^),
denote the between- and within-laboratory variances. It can be shown
that the total variance of k across all laboratories, var (kf), is the
*
sum of the between- and within-laboratory variance components,
•-\
varT(k^) = varg(k^) + var^k^) (6.31)
Provided there are enough randomly selected laboratories, prefer-
ably ten or more, then the total variance across all laboratories of
the within-laboratory regression estimates of the rate coefficients can
be estimated bv the standard formula for calculating a sample variance,
- *> <6'32)
Tne within-laboratory variance component is again estimated by the pool-
ed estimate of the residual variance about the regression line for each
laborator\,
, I (ni " 2)s*
var (k?) = S = (6.33)
" 1 P l n. - 2N
I
e,
*Proof: For two random vairables x and z,
2
x i x i i E(x | z)
a2 = e[oJ|z] + (Rao, 1973)
Let x = and z = k^ .
2
a
2 f ^ 2; 1 _ e
Then Or 11,= EKk^— k ) ik, - _ 2
L - '• J I (t.. - t)£
. l-i
2 (
and aE(ktiM =
K(k ki ) - E(E(kJk^)
¦]'!
-------
The between-
traction,
laboratory variance component can then be estimated by sub-
= varT(V " varw(^}
I (n- - 2)S2
1 ^ ^ 9 /
= n~=~T ^ (ki " k) r (6'34)
N 1 l I n - 2N
i
68
-------
Operational Steps of the Collaborative Test Program
A collaborative test program consists of six steps, as shown in
Figure 2; each step is described bejlow.
Initial Planning
The initial planning serves to define the scope of a collaborative
test program. The objectives of a particular collaborative study should
be stated at the outset to establish a basis for planning decisions.
Testing may be based on screening or detailed methods, or some combination
of the two. The chemicals selected for testing may be familiar and
well-behaved, may have special properties of interest, or may be of
environmental concern. The number of laboratories participating in a
study may be limited to a "fixed" selection of three to six laboratories
or may involve a larger number of "randomly" selected laboratories
that represent the population of all laboratories that might use the
test method. There may or may not be a plan to replicate experiments
within each laboratory. These and other planning decisions should be
based on scientific principles as well as practical considerations.
Preliminary Evaluation
A preliminary evaluation of the chemicals is made by the coordinating
laboratory to obtian information and data that will be used to plan
and conduct the collaborative testing. A "zero-level" evaluation is
based on theoretical and empirical literature and possibly ancillary
laboratory work. Physical and chemical properties are studied in this
way to aid in selecting an analytical measurement technique and to
anticipate difficulties that might occur in conducting the screening
or detailed test. It na\ be desirable to run the screening or detailed
test on t~he selected chemicals at the coordinating laboratorv. The
advantage of such a preliminary evaluation is that problems can be
identified and resolved in a more cost-effective and consistent manner
than if left up to each Dartlcipating laboratory. Alternatively, the
selected chemicals may be ^ubmt ted for collaborative testing with a
minimum preliminary evaluation to determine how well the independent
laboratories handle diffivi 1 f .¦-? on their own.
-------
COORDINATING LABORATORY
PARTICIPATING LABORATORIES
Subcontracting negotiations
Special instructions
Protocols
Data
Data
REPORT COLLABORATIVE
TESTING RESULTS
PRELIMINARY EVALUATION
OF CHEMICALS
Theory, literature,
experimentation
DATA ANALYSIS AND
INTERPRETATION
For analytical method
For photolysis testing
INITIAL PLANNING
Objectives
Chemicals
Number of laboratories
Replications
CONDUCT COLLABORATIVE
TESTING
Demonstrate analytical
capabalities
Photolysis testing
PREPARE COLLABORATIVE
TEST PROTOCOLS
To validate analytical
method
To conduct photolysis
testing
OPERATIONAL ELEMENTS OF A COLLABORATIVE TESTING PROGRAM
Figure 2
70
-------
Collaborative Testing Prococol
The collaborative test protocol consists of various instructions
. I *>
and forms for analytical measurements and photolysis testing. General
instructions will relate various portions of the program protocol,
which will be assembled to meet the needs of a particular collaborative
study. The collaborative test protocol will usually provide advice or
requirements for analytical procedures, including forms to record
calibration data. However, on some occasions the choice of an analytical
technique may be left to the discretion of each participating laboratory.
The screening or detailed test method for photolysis will be summarized
in the collaborative test protocol, with reference to the original
document (Mill and Mabey, 1980) and other reports for elaboration re-
garding the test apparatus and procedure. Supplementary information
about the chemicals being tested will be provided e.g., physical
properties, toxicity, and handling precautions , including results of
the preliminary evaluation. Data collection forms will be provided to
(1) record quality control information that will ensure satisfactory
control of experimental conditions and that will be used for monitoring
test problems and (2) record test data that will be the raw data for
the statistical analysis of single and multiple laboratory test results.
Data analysis procedures will be provided for each laboratory to analyze
its own results. The coordinating laboratory will also develop a plan
co apply statistical methods to analyze collective results.
Collaborative Testing
Collaborative testing will be conducted under the guidance and
monitoring of the coordinating laboratory. The collaborative testing
protocol will be distributed to participating laboratories and meetings
will be arranged according to the travel budget. Each participating
laboratory will be required to demonstrate its analytical capability
for the selected chemicals by providing test results for a set of
unknown concentrations. On the basis of these chemicals analyses, the
coordinating laboratory will decide whether the participating labora-
tory's procedures are accepcable. After this approval, each participating
laboratory will conduct photolvsis testing as specified in the collaborative
71
-------
testing protocol. Each participating laboratory will be asked to follow
the protocol as closely as possible1 and report any deviations. Laboratory
data will be recorded on data collection forms, and each
laboratory will analyze its own data as instructed by the collaborative
testing protocol. All data will be submitted to the coordinating
laboratory for further analysis.
Data Analyses and Interpretation
Test data received from participating laboratories will be analyzed
and interpreted by the coordinating laboratory. Statistical analyses
will be performed to (1) evaluate the precision and accuracy of each
laboratory's analytical method, (2) compare photolysis test results
between laboratories and evaluate error components, and (3) calculate
the best overall estimates of rate coefficients, half-lives, within-
laboratory precision, and between-laboratory reproducibility. Analytical
methods will be evaluated by standard statistical techniques for
collaborative testing based on replicate measurements or differences
between paired samples. Photolysis testing methods will be evaluated
by the statistical methods discussed earlier in this report. Rate
coefficients will be estimated for each laboratory and for all
laboratories to determine whether differences between laboratories are
statistically significant. Within-laboratory precision will be
evaluated by analyzing departures from a first-order rate law. If the
number of laboratories in the study is adequate, the between-laboratory
error variance of the rate coefficient will be estimated to evaluate the
reproducibility of the hydrolysis test method. Graphs of rate coefficients
or half-lives for pairs of chemicals plotted for each laboratory will
show anv tendency for systematic bias between laboratories. Additional
statistical methods will be developed and applied if each experiment
is replicated within each laboratory at the same or different initial
concentrations. Such replication would provide another perspective on
within-laboratory precision.
72
-------
Reports Results
The coordinating laboratory will prepare and issue a final report
• l -X
of collaborative test results. This-report will include a description
of the study, test results, conclusions regarding the precision and
accuracy of the test method, and recommendations for changes -*n the
test method and for further collaborative testing.
73
-------
REFERENCES
CRC Handbook. 1975. Handbook of Chemistry and Physics, We'ftt, R. C.,
editor, CRC Press, Inc., 55th edition, p. D114.
Cvetanovic, R. J., and D. L. Singleton. 1977. Comment on the Evaluation
of the Arrhenius Parameters by the Least Squares Method. Int. J.
Chem. Linet. 9^: 481-438.
Duncan, A. J. December 1978. Views of the E-ll Task Group on Statements
of the Precision and Accuracy of a Test Method. Standardization Mews,
18 (12): 16-18.
Halonen, E. 1956. Activation Energies of Alkaline Hydrolysis of Saturated
Aliphatic Esters. Acta Scand., 10: 485-486.
Johnson, H. 1980. SRI. Private communication.
Koskikallio, J. 1967. Acta Chem. Scand., 21:397-407.
Mabey, W. R., and T. Mill. 1978. Critical Review of Hydrolysis of Organic
Chemicals in Water. J. Phys. Chem. Ref. Data, 7: 383-413.
The Merck Index. 1976. An Encyclopedia of Chemicals and Drugs, 9th Ed.,
Merck & Co., Inc. Rahway, UJ. p. MISC-66.
Mill, T., and W. R. Mabey, ed. 1980. Laboratory Protocols for Evaluating
the Fate of Organic Chemicals in Air and Water. Final report sub-
mitted to EPA, EPA Contract No. 68-03-2227.
Rao, C. R. 1973. Linear Statistical Inference and Its Applications,
Wiley, New York.
Scheff£, II. 1959. The Analysis of Variance, Wiley, New York.
Whalen, D. L. 1973. Buffer Catalysis in Epoxide Hydrolysis. J. Am. Chem.
Soc. 95: 3432-3434.
Yalkowsky, S. H., and S. C. Valvani. 1980. Solubility and Partitioning
for L>Jon-Electrolytes in Water. Submitted for publication to J. Pharm.
Sci.
Youden, W. J. May 1950. Comparative Tests in a Single Laboratory, ASTM
Bulletin, No. 166, pp. 48-51.
Youden, W. J. 1975. Statistical Techniques for Collaborative Tests,
Association of Official Analytical Chemists, Washington, D.C., pp. 29-32.
74
-------
Appendix A
A GENERAL SOLUTION FOE k , k , AND k FROM THE OVERALL RATE CONSTANT
A B N
Three measurements of the rate constant, k , at a fixed temperature
hi
and at any three pHs can be used to solve for the values of the acid, base,
and neutral rate constants, k , k , and k , respectively,
A B N
k = k [H+l + k + k [OH ]
hi Al -i N ji
where 1 = 1, 2, 3
k = k ([OH"], - [0h"]3) - k ([OH~]j - [0h"]3)
h!
+ k
h3 - [OH"l2)
/J
k =
([H+]2 - [H+]3) + k ([H+l1 - [H+]3)
I hl 2 \
- kh ([h+]j - [H+]2)| /J
¦{
!< ([H+] 2 • [OH'n3 - [H+13[0h"12)
hl
- k ([h+^[oh"]3 - [h+i3[oh
+ k ([h+\[oh"]2 - [h+_i2[oh~i
/J
J = ([H + ]2[OH -3 - [H+^[0H~12) - ([H + l^OH-^ - [h'M&h'U
+ ([h+ii[oh"]2 - [H+12[0H"^)
75
-------
The standard deviations of k . k , and k may be calculated from
A B N
the above equations. Let y = k.-k;, or k ; the above equations can
A B N
then be written in the general form:
y = ak + bk + ck
h j h2 hj
where a, b, and c are the coefficients associated with k , k , and
hi 2
k , respectively. Since k , k , and k are independent, the
h3 hj h2 h3
variance of y, g2y, and hence the standard deviation of y, oy> can be
readily obtained from
2y = *2
-------
Appendix B
DATA COLLECTION FORMS
This appendix consists of sample data collection forms for the
hydrolysis screening and detailed tests.
77
-------
Appendix B
Data Collection Form
Chemical
pH
Time/Concentration Data:
Date/Time
Elapsed Time
(minutes)
78
-------
Data Analysis Form
Chemical Experiment I. D.
pH
•-r
Is there any reason why you believe the experiment at this "pH
is invalid?
If yes, explain:
Are any particular data points invalid?
Data Pt. No. Reason invalid
Calculate the average concentration from the chemical analyses for each
time and enter the results on the data collection form. For each data
point (1), record below the time (tt) and the ratio of the average con-
centration (Cj^) to the initial concentration (CQ) :
Ci/Co
Ci/Co
0,/C.
0
1
2
3
4
5
6
1.000
79
-------
Plot Ct/C versus t on the attached semilog graph paper. Fit a straight
t o
. < ^
line through these points (by eye)^. Can you think of any reasons that
might explain noticeable departures from linearity (if any)''
-\
If yes, explain: -
80
-------
APPENDIX C
KINETICS OF HYDROLYSIS IN SOLUTIONS OF INADEQUATE BUFFERING CAPACITY
Hydrolysis reactions in solutions which are inadequately buffered
against generation of acidic or basic products can lead to small changes
in pH. These systematic changes introduce errors in the estimates of k^
based on simple first order kinetics because the usual calculation assumes
a constant pH value. We have evaluated the error introduced into rate
constants by such changes, and applied the error evaluation to the hy-
drolysis experiment at pH 11 for ethyl acetate.
From the data m Table 2 it can be shown that for ethyl acetate the
rate of the base-catalyzed process is equal to the neutral process at pH
values of 7.7 or 7.5, depending on whether the data from the SRI or EPA
•k
protocols, respectively, are used. The hydrolysis rate constant k^ for
ethyl acetate at pH 11 is then dominated by the base-catalyzed process.
The acetic acid produced from hydrolysis of ethyl acetate neutralizes
some hydroxide ion, and thereby lowers the pH of the solution. Under the
experimental conditions described on pages 37 and 38 for the pH 11
experiment, the hydroxide ion concentration would drop approximately 32%
if all the initial 10-3 M ethyl acetate were hydrolyzed to acetic acid
and ethanol. The error analysis presented below has been applied to the
estimation of k_, which is the dominant term in the value of k, at pH 11.
B
Since neutral hydrolyses are not pH dependent, the error in kfi is the
maximum error that will occur in k^ at pH values where acid-catalyzed
processes do not occur.
The loss of ethyl acetate (C) due to hydrolysis at pH 11 is given
by the equation
*This condition occurs when (OH kB = kN; after solving for [OH ], the
[H"1"] value used to calculate cue pH is [H+] = K /[0H~].
81
-------
(C-l)
If the pH is constant throughout the experiment, the hydrolysis rate ex-
pression reduces to a simple first order kinetic relation .-\
^ = k_[0H ][C -x].
dt B o o
(C— 2)
Integrating equation (C— 2) gives
1 . o
B = [OH ] [C -x]
C C— 3)
where [0Hq] and [Cq] are the initial concentrations of [OH] and ethyl
acetate, respectively, and x is the amount of C reacted at time t. In
the inadequately buffered solution the (0H~) term is not constant; how-
ever some buffering does still occur and a simple second order kinetic
expression does not apply (i.e. [C^-x] does not have a simple corresponding
[OH -x] relationship). From the buffering expression, however, it can
o
be shown that
- ^
[OH ] = —
ka
_A_
HA
(C-A)
where A and HA are the C03~ and HC03~ buffering components, respectively;
K is the autoprotolysis constant and is the acid dissociation constan
for HA. The loss of ethyl acetate can then be expressed as
^ = k [C -x'
dt BL o
K
w
A -x "
0
K
. a.
HA + x
0
(C-5)
where A and HA are the mLCLal concentrations of C03 and HC03
o o
solution to this differential equation is
The
82
-------
K
tkB =
C + HA
o o
.C -A
o o
1 Co"X + KA
1 -
C + HA
O 0
C -A
o o
lit
A -x
o
(C—6)
Rearranging and substituting appropriate terms with Cq-x = Ct, A -x = A
Kt
c
1 . o A
-ln-r- +
B |0H1o Ct ^
HA + A
o o
A C C
In—^ lrr-^
a ^cT
0 o o
(C— 7)
"first
order term"
correction term
The "correction term" above is then the part of the equation which is
neglected when the [OH] concentration is assumed constant; the "first
order term" is the part which is used in the regression analysis to cal-
culate k assuming constant pH.
D
Table C-l shows a comparison of the rate constants calculated from
equations (C-3) and (3-7) using the pH 11 experimental data. The first
three columns show the time t, the concentration of ethyl acetate at time
t (C^) , and the calculated pH of the solution at time t (the change in
pH was verified in experiments where appropriate amounts of acetic acid
were added to the pH 11 buffer solutions). Columns 4 and 5 list rate
constants calculated from equations (C-3) (kg) and (C-l) (^g')i respec-
tively. The rate constants k_ or k ' listed in the rows for each time
J D D
point were calculated using C , Cc and t values directly, and represent
a rate constant averaged over the time period (i.e., AC vs. At for two
points.) The rate constants kg or kg' calculated regressing the right
hand terms in equations (C-3) or (C-7) vs. t are given below the double
lines in columns 4 and 5, respectively. The sixth column shows the in-
creasing error in the "averaged" kg values resulting from the use of
equation (C-3) rather than the "true value" k 1 calculated using equation (C-7).
The acetic acid produced in the pH 3 hydrolysis experiment has an
insignificant effect on the pH, and therefore the value for pH 3 is
correct as shown in Table 1. the effect of acetic acid production on the
pH 7 data is also minor. It the values of an<^ kh(7) are ta^en as
shown in Table 1, and k taken as 1.26 x 10 2 M s (- kg(10 ]),
83
-------
Values of k and k. are 5.72 x 10-8 s~1 and 1.16 x 10"'* M~1 s l,
N A
respectively, are calculated according to regression analyses used for
Table 2 data.
From the data in Table C-l and comparison of equations.-^ C-3) and
(C-7) , two relationships need be emphasized. The first is tnat the
error in k_ resulting from a slight change in pH is not directly assessable
from the pH change itself but rather is dependent on the initial concen-
trations of ethyl acetate and buffer salts. The second relationship
evident from column six is that the error in kg increases with the extent
of the reaction, making it time dependent. Therefore a decision to use
equation (C-3) or (C-7) will depend on the extent of conversion in the
experiment: for the data in Table C-l, the error incurred up to 35% con-
version is comparable to the error of analyses, and therefore the use of
equation (C-3) may be acceptable.
84
-------
Table C-l
COMPARISON OF RATE CONSTANTS kg CALCULATED FROM pH 11 ETHYL ACETATE
EXPERIMENT USINC EQUATIONS C-3 AND C-7a
103 Ct 10* kB 10J kgd ZError
(sec)1 'Et0Ac1(M) pH (IT' sec-') (M- sec-') 10 "b*
0
1.04
11.05
—
—
—
310.8
1.01
—
9.42
9.46
0.45
2273. A
0.81
11.024
10.99
11.39
3 5
4571 4
0.645
10 999
10. 79
11 51
6 3
70 JO.2
0.475
10.978
11. 15
12.24
8.9
94 13.0
0. 365
10.964
11.04
12. 39
10.9
LI,722.2
0.290
10.955
10.90
12.42
12.3
14,255.4
0.225
10.948^
10.74
12.43
13.6
Elate constants calculated from
10.8 ± 0.1
12.6 ± 0.1
142
regression
analyses
aSee text for discussion and equations.
kpH change during experimuiil is equivalent co a 22% change in [OH]
at 772 reaction of ethyl acetate.
^Calculated using equation (C-3).
Calculated using equatipn (C-7).
e[(kB' - kB)/kB*] x 100X.
-------
APPENDIX D
ADDITIONAL ERROR ANALYSES FOR ETHYL ACETATE HYDROLYSIS EXPERIMENTS
Additional error analysis of the ethyl acetate experiments has been
performed to evaluate the contribution of analytical error to overall
error in the measured rate constants. The standard errors for k^ in Table 1
range from 0.9% at pH 11 to 10.7% at pH 9. For pHs 3, 9, and 11, the
precision of the chemical analysis has been calculated from multiple
determinations at each time point. The proportions of variance (the
square of the standard error) of estimates of k^ due to analytical error
are 10.5% at pH 3, 18.5% at pH 9, and 68.9% at pH 11. There was not suf-
ficient data to perform an error analysis for k^ at pHs 5 and 7. These
results suggest that for experiments of short duration analytical error
will be dominant, whereas in the longer experiments systems errors will
become more important (i.e. temperature variations, volatilization, other
adventitious processes).
These estimation errors in the k^ contribute to the errors for k^,
kg, and k^ through the equations given in Appendix A. The standard error
given in Table 2 for EA are based on the standard errors for kh at pHs 3,
9, and 11. For the SRI experiment, the standard error for kA is dominated
by the standard error for k^ at pH 3; the standard errors of kg and k^
are dominated by the standard errors for k^ at pH 11. For the EPA ex-
periment, the standard errors for k^, kfi, and k^ only reflect the standard
error for k^ at pH. 9. In general, standard errors for k^, kg depend on
both the standard error for k, at the three pH levels and the pH-hydrolysis
n
profile for a particular chemical.
86
------- |