[PA-600/3-77-110
ctober 1977
Ecological Research Series
INSWOG
US,
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RESEARCH REPORTING SERIES
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This document is available to the public through the National Technical Informa-
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EPA-600/3-77-110
October 1977
MEASUREMENT OF RATE CONSTANTS
OF IMPORTANCE IN SMOG
by
John R. Barker, Sidney W. Benson,
G. David Mendenhall, and David M. Golden
SRI International
(formerly Stanford Research Institute)
Menlo Park, California 94025
Grant No. R802288
Project Officer
Marcia C. Dodge
Atmospheric Chemistry and Physics Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
Tj =; O7 V ,\ "O"'*7
JUf.il..;>A v'^J-Jri' J.
U. S. £!:V;:.;.,t ..;.';,;L FRGTECIiON
EpissK & L
-------
DISCLAIMER
This report has been reviewed by the Chemistry and Physics Laboratory,
U.S. Environmental Protection Agency, Research Triangle Park, North
Carolina, and approved for publication. Approval does not signify that
the contents necessarily reflect the views and policies of the U.S.
Environmental Protection Agency, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.
ii
-------
PREFACE
For some time, considerable effort has been devoted to understanding
and characterizing the complex phenomenon of photochemical smog. This
effort has encompassed several different areas of study so as to take
full advantage of the wide range of expertise in the scientific
community. The extensive experience accumulated using smog chambers to
simulate smog conditions, and the results of field observation indicate
that a complete understanding of smog depends on the development and
validation of reliable chemical mechanisms consisting of elementary
reactions.
Since the polluted atmosphere is highly complex and depends sensi-
tively on parameters such as solar irradiance, temperature, pollutant
concentration, and transport phenomena, any errors in the reaction
mechanisms are likely to be magnified at the extremes of the parameter
ranges. A general approach to formulating general reaction mechanisms
is to include all elementary reactions thought to be important, and then
test them using smog chamber simulations. Although smog chamber simu-
lations are designed to be simplified versions of the polluted atmosphere,
the gas mixtures are so complex and spurious chamber effects often are
so important that the technique cannot be used to ascertain elementary
rate processes and can only be used for validation purposes.
To develop a reliable chemical mechanism describing smog, elementary
reaction rate constants are needed. Such rate constants preferably can
be obtained by direct experimentation, but estimates can sometimes be
made if sufficient experimental data on related reactions are available.
Such rate constants, once obtained, are often useful, not only for
iii
-------
understanding smog chemistry, but also for understanding pollutant
formation in combustion processes, and the like. As rate constant
measurements of higher quality are performed, inaccurate rate constants
are superceded and the general understanding of photochemical smog is
improved.
In the absence of good elementary reaction rate studies, one must
resort to estimation techniques to formulate an overall reaction scheme.
Such estimation techniques draw upon data available for reactions
analogous to the one of interest. If no analogous reactions have been
studied, the estimated rate parameters must be considered highly
uncertain. A-factors can be estimated much more reliably and readily
than activation energies, but even A-factors can be in error if the true
chemical nature of a reaction is misunderstood. Hence, it is desirable
to observe the products of elementary reactions in order to guarantee
that the chemistry is correct. Until more complete data of higher
quality become available, estimation techniques, like those illustrated
in this report, will be valuable adjuncts to experiments.
No satisfactory substitute for experimental determinations for
elementary reaction rate constants is available, however. All estimates
are subject to errors that can distort the results of computer simulations
of photochemical smog. The experiments described in this report were
intended to help refine estimates of unmeasured reaction rate constants.
IV
-------
ABSTRACT
In an effort to understand elementary reactions of importance in
smog, we have carried out a three-part investigation: (1) experimental
determinations of certain elementary reaction rate constants, (2) develop-
ment of general techniques for estimating elementary reaction rate
constants, and (3) estimation of rate parameters for many reactions
important in smog.
The experimental studies determined rate constants for the following
reactions:
CH3CH2CH2ON02 1± CH3CH2CH20 + N02
-a
b
t-BuONO ;» t-BuO + NO
-b
CH3OOCH3 £ 2CH30
-c
CH3 + CH3OOCH3 ^ CH3OH + CH2OOCH3
CH30 + N02 5 CH3ONO2
(M)
CH3O + N02 £ CH2O + HONO
CH30 + 02 * CH20 + H02
Specific estimated rate constants included the following reactions:
(1) Decomposition of alkoxy radicals
(2) Isomerization of alkoxy radicals
(3) Reactions of alkoxy radicals with oxygen
(M)
(4) The reaction H02 + NO2 ^ HO2NO2
-------
CONTENTS
Preface i i i
Abstract V
Figures IX
Tables .x
XT.1
Abbreviations and Symbols '
Acknowledgments XI11
1. Introduction 1
2. Conclusions and Recommendations 3
3. Experimental Studies 5
A. The Very Low-Pressure Pyrolysis (VLPP) of
n-Propyl Nitrate, tert-Butyl Nitrite, and
Methyl Nitrite. Rate Constants for Some
Alkoxy Radical Reactions 5
Experimental 6
Results—n-Propyl Nitrate 8
Results—tert-Butyl Nitrite 10
Results—Methyl Nitrite 11
Results—Methyl Peroxide and N02 11
Discussion 12
Thermochemistry 19
B. The Decomposition of Dimethyl Peroxide and
the Rate Constant for CH3O + 02 -* CH20 + HO2 ... 20
Experimental 23
Results and Discussion 26
Dimethyl Peroxide Decomposition .... 26
Dimethyl Peroxide with Added N02 .... 32
Dimethyl Peroxide with Added NOg and 02 . 42
Summary 50
4. Estimation Methods 51
A. Methods for the Estimation of Rate Parameters . . 51
Transition State Theory 52
A-Factors and Entropies of Activation .... 54
A-Factors for Metathesis Reactions 60
Addition Reactions 68
Recombination Reactions Involving Atoms ... 71
Activation Energies 77
Vll
-------
B. Rate Parameter Evaluation and Estimates 80
Alkoxyl Radical Decomposition Reactions ... 81
Alkoxyl Radical Reactions with Oxygen .... 89
Alkoxyl Radical Isomerization Reactions ... 92
Reaction of NO2 with HO2 96
Simulations of Smog Chamber Experiments . . . 102
Reactions of n-Butane 104
Reactions of Propene Ill
Conclusions 113
References and Footnotes 116
Appendix A: VLPP Unimolecular Rate Theory 123
vm
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FIGURES
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
nPrON02 Pyrolysis
tBuONO Pyrolysis
Schematic Diagram of Apparatus
Decomposition of Initially Pure DMP
Arrhenius Plot Summarizing Data for DMP Decomposition. .
Decomposition of DMP with Added NO2
Gas Chromatography Results Demonstrating Mass Balance. .
-kjj"1 (dP/dt) vs. [DMP]0 for Four Temperatures
Decomposition of DMP with Added NO2 and 02
Arrhenius Plot of Data for k17
t-BuO1 H Me + Acetone
EtO' H Me + CH20
i-PrO- M, Me + MeCHO
s-BuO- 51 Et + MeCHO
Correlation Between Activation Energy E and
Enthalpy of Reaction ^HR
Falloff Calculated by RRKM Theory as a Function
of Activation Energy for the Reaction HO2NO2 -• HO2 + NO2
(a) Simulation of Run EC-41 in Reference 90
(b) Simulation of Run EC-41 as in (a)
Simulation of Run EC-41 in Reference 90
Reactions of Propene
Simulation of Run EC-121 in Reference 90
Appendix: VLPP Unimolecular Weight Theory
Page
9
9
24
28
30
34
36
38
43
48
83
83
84
84
86
101
105
108
108
109
112
114
123
IX
-------
TABLES
Number Page
I Reactor Parameters 7
II Decomposition of Dimethyl Peroxide in the
Presence of Nitrogen Dioxide 13
III Molecular Parameters Used for RRKM Calculations;
Molecular Parameters for n-PrON02 and tert-BuONO . . 14
IV Thermochemical Quantities 15
V Rate Constants 15
VI Rate Constants for Computer Calculation 31
VII Dimethyl Peroxide Rate Constants 31
VIII Data Summary for MeO + O2 - H02 + CH2O 46
IX Standard Entropies and Heat Capacities at 300°K
of Some Structurally Similar Molecules 57
X Standard Entropies and Heat Capacities of Some Complex
but Structurally Similar Molecules 58
XI Standard Entropies and Heat Capacities of Some Complex
but Structurally Similar Molecules 58
XII Arrhenius Parameters for Some Metathesis Reactions
Involving H-Atoms 62
XIII Arrhenius Parameters for Metathesis Reactions
Involving Atoms 63
XIV Arrhenius Parameters for Some Metathesis
Reactions of Radicals 66
XV Arrhenius Parameters for Some Addition Reactions
of Atoms and Radicals to Pi Bonds 69
XVI Experimental Values for RO' Decomposition Rates ... 82
XVII Estimated RO' Decomposition Rates 87
XVIII Estimates: RO' + O2 Reactions 91
x
-------
Number
XIX RO' Isomerization Reactions—Estimation
Procedure 94
XX Estimated RO' Isomerization Reaction Rates 95
XXI Frequency Assignment for H02N02 98
XXII RRKM Calculated k/koo for H02NO2 Decomposition 99
xi
-------
LIST OF ABBREVIATIONS AND SYMBOLS
BuO - Butoxy Free Radical
BMP - Dimethyl Peroxide (CH3OOCH3)
EtO - Ethoxy Free Radical
Me - Methyl Free Radical or Substituent Group
MeO - Methoxy Free Radical
Omega (cu) - Collision Frequency
PrO - Propoxy Free Radical
RO - Alkoxy (Alkoxyl) Free Radical
RRKM - Rice, Ramsperger, Kassell, and Marcus Theory of
Unimolecular Reaction Rate
VLPP - Very Low-Pressure Pyrolysis Experimental Technique
xii
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ACKNOWLEDGMENTS
Thanks go to Karan Lewis for preparing many batches of dimethyl
peroxide and to Dr. L. Batt, H. Niki, and J. G. Calvert for permission
to use some of their respective results prior to publication.
xm"
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SECTION 1
INTRODUCTION
To develop an explicit mechanism for photochemical smog formation,
it is desirable to have experimental determinations of elementary reaction
rate constants. In the absence of such experimental data, estimation
techniques must be developed and utilized for estimating appropriate rate
parameters. This report summarizes efforts made in both these areas.
The experimental studies reported below were conducted to elucidate
the chemical reactions of alkoxyl radicals in the polluted atmosphere.1
These radicals are present, not only in the atmosphere, but also in flames
and combustion processes where they are potential chain carriers and
propagators.
Alkoxy radical rates with the free radical traps, nitric oxide and
nitrogen dioxide, had been reported2a to be about two orders of magnitude
slower than for other similar reactions.2*5 An investigation was under-
taken to test this unexpected result, and it is described in Section 3.A
of this report.
Another reaction of particular importance is that of alkoxyl radicals
with molecular oxygen. The prototype alkoxy radical —CH3O— was used to
determine the rate constant in a study described in Section 3.B. This
reaction is important in the oxidation of nitric oxide to form NO
according to the following sequence:
RH + OH -» R + H20
R + 02 $i R02
RO2 + NO - RO + N02
-------
RO + O2 -* HO2 + carbonyl
HO2 + NO - OH + NO2
Other reactions of alkoxyl radicals can compete under certain
circumstances, and their rates must be estimated to achieve formulation
of a proper chemical mechanism. General procedures for estimating rate
constants are described in Section 4.A, and specific applications are
presented in the remaining sections.
Alkoxyl radicals larger than methoxy can undergo ^-cleavage, and
the rates for such processes were estimated on the basis of data in the
literature, as described in Section 4.B. For still larger alkoxy free
radicals, isomerization reactions are possible, leading to the sequential
oxidation and degradation of hydrocarbons (Section 4.B). The relative
rates of these competing processes are important in developing an explicit
reaction mechanism, and the resulting mechanism appears to be a relatively
good representation of reality.
M
A reaction for which virtually no data exists is H02 + N02 ^ HOON02 .
The technique described in Section 4.A was used to estimate the forward
and back rates of this reaction, and the sensitivity of the reaction
mechanism to variations of these rates are presented in Section 4 .B .
Each section of this report contains a detailed discussion of the
background behind each rate, along with a thorough description of the
experimental technique or estimation procedure used and a discussion of
the result.
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SECTION 2
CONCLUSIONS AND RECOMMENDATIONS
In the course of this work, a number of elementary reaction rate
parameters have been measured :
(a) CH3CH2CH2ON02 CH3CH2CH2O + N02
log ka(sec-1) = 16.5 - 40.0 kcal mole'1 /2. 3 RT
log k_a(M-J s-1) = 9.5
b
(b) t-BuONO & t-BuO + NO
~b
log kb (sec"1) = 15.8 - 39.3 kcal mole-1 /2 . 3 RT
log k (M-1 s-1) = 9.8
b
(c) CH3OOCH3 £ 2CH30
~c
log k_ (sec-1) = (15.7 ±0.5) - (37.1 ± 0.9) kcal mole-V2.3 RT
c
-c
log k_c(M-1 s-1) = 9.7 ±.0.5
(d) CH3 + CH3OOCH3 - CH3OH + CH2OOCH3
kd(400 K) w 5 x 104 M-1 s~l
(e) CH0 + N0 " CHON0
(f) CH30 + N02 - CH2O + HONO
k./k = 0.30 + 0.05
i e ~~
If log ke(M~1 s-1) = 9.8 ± 0.5, then log kf(M~1 s-1) = 9.3 ± 0.5
(g) CH30 + 02 - CH20 + H02
log kg(M-1 s-1) = (8.5 ± 1.5) - (4.0 ± 2.8) kcal mole-1/2.3 RT
The rate parameters for reaction (g) are the most uncertain, and
further investigations are desirable.
-------
In addition to the experimental determination of rate constants, an
effort has been made to develop general techniques for estimating unknown
rate constants by using data from analogous reactions. Applications of
these techniques have been quite successful, and their utility has been
demonstrated for the following reactions:
(1) Decomposition of alkoxy radicals
(2) Isomerization of alkoxy radicals
(3) Reactions of alkoxy radicals with oxygen
M
(4) The reaction H02 + N02 & HOONO2
Application of the estimated rate constants to butane and propene
smog chamber experiments shows fair agreement and indicates sensitive
areas for further work:
(1) Experimental determination of the rate parameters
for HOON02 decomposition and association.
(2) Experimental determination of the photolysis rates
of aldehydes and ketones in oxygen gas.
(3) Experimental determination of the products of the
reaction of olefins with OH, 0, and 03 under
conditions of atmospheric interest.
Although a great effort has been expended to understand photochemical
smog formation, the phenomenon is so complex that much work remains to be
done. Until more experimental data become available, the estimation
technique described in this report will play an important role.
-------
SECTION 3
EXPERIMENTAL STUDIES
A. THE VERY LOW-PRESSURE PYROLYSIS (VLPP) OF n-PROPYL NITRATE,
tert-BUTYL NITRITE, AND METHYL NITRITE. RATE CONSTANTS FOR
SOME ALKOXY RADICAL REACTIONS
Although alkoxy radicals play a central role in the oxidative degrad-
ation of hydrocarbons, few absolute rate constants of reactions involving
these radicals have been reported in the literature. The reasons for this
situation include their lack of distinctive spectral features, high
reactivity, and complexities introduced into most systems due to multiple
pathways available for their decomposition and secondary reactions of
products. This situation has recently become more acute because of the
use of alkoxy rate constants in smog-modeling studies,1 and the assignment
of certain rates, e.g., that for the reaction leading to PAN, on the basis
of the former.
We initially had hoped to generate methoxy radicals in a VLPP reactor
and directly observe their reaction rate with oxygen. (Higher alkoxy
radicals undergo 3-cleavage under these conditions—see Section 4.1., this
report.) A variety of precursors, including dimethyl peroxide, methyl
nitrite, methyl hyponitrite, and methyl t-butyl peroxide, were decomposed
between 400°K and 800°K, and with quartz, carbon, Teflon, and boric acid
coated surfaces. A small signal at m/e = 31 (at low ionization voltage)
was observed when methyl t-butyl peroxide was decomposed in a boric acid
coated reactor, but the intensity was too low to be useful.
The rate constant for a reaction X + OR -» ROX can be calculated from
the rate of reverse reaction if the thermodynamic parameters are known.
-------
This method was used by Gray, Shaw, and Thynne2a to derive recombination
rates for CH3O + NO and CH3O + N02. These, however, were based on rates
for the reverse reactions which have been questioned.^
By pyrolysis of tert-butyl nitrite and n-propyl nitrate we have
derived recombination rates that are ~ 102 higher than the earlier values.
Recently Batt, McCulloch, and Milne3 in a paper on several nitrites
reported results for tert-butyl nitrite pyrolysis by a separate technique
that are in excellent agreement with ours.
In a separate study with a conventional static system, we determined
the yield of methyl nitrate from methyl peroxide and N02 as a function of
total pressure, in order to determine whether the reaction of methoxy
radicals with NO2 is in the high-pressure region at atmospheric pressure.
Experimental
n-Propyl nitrate (Eastman Kodak) and tert-butyl nitrite (Frinton
Laboratories) were fractionally distilled on a vacuum line. The center
1/3 was stored in a large bulb wrapped in Al foil. Methyl nitrate was
synthesized on 1/10 the scale reported by Delepine4 and fractionally dis-
tilled as above. Dimethyl peroxide was synthesized by the procedure of
Hanst and Calvert5 and fractionally distilled to remove dimethyl ether
(m/e 46). The gas detonated twice during handling and transfer, though at
low pressures in a seasoned vessel it was stable for weeks. Methyl nitrite
and methyl-d3 nitrite were synthesized by adding 200 p,l of 25% by volume
H2S04 in water to the requisite alcohols (1 cc) and excess NaNO2 at —78°
and distilling the product into a bulb on a vacuum line.6 Other reagents
and gases were commercial samples.
-------
The static system for the methoxy radical-NO2 work has been described.7
Product analysis was accomplished by glc (F and M Model 720, thermal conduc-
tivity detector, 10 ft. x 0.25 in. column of 20% di-(2-ethyl hexyl)sebacate
on 60-80 M chromasorb at 25°; detector at 100°). Seven percent of the reaction
mixture was removed with each aliquot, and 42% of the aliquot was swept onto
the glc column. The peak areas were related to concentrations in the reactor
with appropriate factors and a linear calibration curve made from peak areas
of various pressures of pure CH3ONO2.
The theory and practice of the VLPP technique have been described
previously.8 Essentially this involves the pyrolysis of a gas flowing through
a heated reactor with three different possible apertures (1-mm, 3-mm, and 10-mm)
diameters). The pressure of the gas in the reactor is very low (~ 0.1-1.0 JJL) ,
such that the flow is molecular, gas-gas collisions are few and most secondary
reactions are eliminated. The characteristics of the reactor are given in
Table I, and the exact VLPP unimolecular rate theory is presented in Appendix A,
where it is shown that ordinary RRKM theory is adequate.
TABLE I. Reactor Parameters
Volume, V = 130 cm3; Surface Area, A^, = 160 cm2; Collision Frequency, u> =
4.48 x 103 (T/M)1/2 sec-1
Aperture Diameter (cm) 0.115 0.305 0.995
kg/sec-1 0.4 (T/M)1/V! 1.8 (T/M)1/2 12 (T/M)1/2
Collision Number = Z 11,200 2,470 387
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Results—n-Propyl Nitrate
Rate constants for the unimolecular disappearance were obtained for
n-propyl nitrate over a 220° temperature range, and with a 100-fold vari-
ation in flow rates. The M-29 peak at 76 amu was monitored (see Figure 1).
The complete reaction is assumed to involve P-scission or isomerization:
n-CH2CH2ON02 - n-CH3CH2CH2O' + NO2 (1)
CH3CH2CH20' -* CH3CH2'+CH20
- 'CH2CH2CH2OH - C2H4 + tH2OH
of n-propoxy and subsequent reactions, perhaps on the walls, between N02 ,
formaldehyde and ethyl radicals. Due to the spectral similarity of the
products we did not analyze quantitatively for them in this case, although
intense signals were observed at the masses where they appear. We did show
quantitatively in two runs that propionaldehyde (yield < 10%) and propylene
(yield < 3.7%) were not significant products. This observation indicates
that neither of two anti-Markovnikov reactions were occurring:
n-CH3CH2CH2ON02 - CH3CH=CH2 + HON02
- CH3CH2CH=0 + HONO
That P-scission (or isomerization followed by scission) is the predom-
inant fate of n-propoxy can be determined from an RRKM calculation,9 Using
values of the Arrhenius parameters determined recently by Batt et al.,3 and
a value of s = (C°-4R)/R for the number of "effective oscillators," the
values for k(3-scission) are much greater than the escape rate constant.
B:iU :| et al. report log k ~ 16-17/6. For nPrO',10 Cp ~ 33; thus, s = 12.5,
B = E/RT = 12 at 700°K, and D = log A, log uu ~ 16 - 4 = 12 under VLPP condi-
tions, k/k^ ~ 8 x 10~8 , and thus k ~ 400 sec"1 , which is rapid compared to
escape from the reactor. The parameters for isomerization are not as well
known, but if we estimate log kisom ~ 12-12/9, this reaction followed by
scission would precede escape as well.
-------
>> O O f-
i-i o t- oo
O N 'J1 CO
O
cA
•H
03
rH O O t-
O O t* 00
fc N. « «
ft rH (M
O
s
%
o
II
-------
Results—tert-Butyl Nitrite
Rate constants for the unimolecular disappearance of t-BuONO were
obtained over a 240° temperature range and with a 100-fold variation in
Ilow rates. The peak at M-15 (88 amu) was monitored.
Above 650°K the data lie on a smooth curve of the type expected in
a unimolecular homogeneous process (Figure 2). Between 525 and 650°K
the rates are relatively too fast and exhibit considerable scatter.
At the higher temperature we observe fragments at m/e 58, 43, and
15, corresponding to the reactions:
tert-BuONO - tert-BuO + NO (2)
tert-BuO - CH3COCH3 + CH3
At the lower temperatures no methyl radicals were observed, and the
principal organic product is isobutylene:
tert-BuONO - HONO + (CH3)2C=CH2
Batt and coworkers3 have also reported this reaction. A significant
signal at m/e 59 in the product spectrum was ascribed to tert-butyl alcohol,
though the yield was measured as only 1.67o in one case. Under the reaction
conditions, tert-butanol decomposed to give isobutylene (kun^ =1.5 sec"1
at 672°K, Z = 20,000) .
RRKM curves were accordingly fitted to the data >650°K, and the presence
of small side reactions does not affect the result for the alkoxy forming
reaction.
10
-------
Results—Methyl Nitrite
The decomposition of methyl nitrite was studied briefly in a search
for methoxy radicals. At 650°K we observed intense signals at m/e 30 and 31
with low-ionizing voltage. Either of two reactions were considered possible;
CH3ONO - CH30 + NO
m/e 31 30
- CH20 + HNO
m/e 30 31
To resolve the question we prepared methyl-d3 nitrite and found under
these conditions product signals at m/e 30, and 32, with a smaller increase
at m/e 36 (CD3OD). A signal at m/e 34, corresponding to CD3O, did not
appear.
At 650°K methyl nitrite gave a 42% yield of methanol (Z = 200, 3 x 1016
uni
molec/sec). The value of k ± was 20 sec'1. From Batt's3 data, we predict
k«5o K = 93 sec"1 for the fission into RO and NO, and RRK calculations indi-
CO
cate kuni/k is about 10~5, so we cannot be observing a homogeneous process.
Results—Methyl Peroxide and NO9
At two temperatures, 121° and 163°K methoxy radicals, produced thermally
from dimethyl peroxide, give methyl nitrate by coupling with NO2 in the system,
An alternate reaction is disproportionation:
CH3OOCH3 .. 2CH30
CH30 + N02 —~*- CH3ON02
_— *. CH20 + HONO
11
-------
At the reaction temperatures NO2 reacts further with formaldehyde. There is
some scatter in the data in Table II, particularly at 163°, where the
reaction was carried to greater conversion, but a trend to higher yields
of CH3ON02 as the total pressure rises is indicated at both temperatures.
When we attempted to pressurize a mixture of peroxide and N02 at 163°
with air, the reaction vessel was destroyed in an explosion.
Discussion
The frequencies of the molecules and activated complexes are given
in Table III. These provide the input for a computer program based on
the RRKM theory, which computes values of the apparent first-order rate
constant as a function of pressure and temperature for various values
of the critical energy (activation energy at 0°K). Frequencies in the
molecule were selected to give total entropies at 300°K, in agreement
with experimental data or results obtained by group additivity. The
experimental rate constants (ky^) over a range of temperatures and the
predicted curves appear in the figures. The frequencies for the complex
found in Table III were actually selected to give a model transition
state which would, in turn, have a value of AS* (i.e., A-factor) which
would fit the VLPP data when the choice of critical energy was confined
to a value such that the activation energy at 298°K was identical with
the known value of AE(298°K) for the reaction (Table IV).
The Arrhenius parameters which best describe the VLPP data are
shown in Figures I and 2 and in Table V. These parameters combined with
the known entropy change for the reaction allow the calculation of the
rate constants for the reverse processes, the combination of the requisite
alkoxy radicals with NO and N02. These rate constants are also given in
Table V.
12
-------
TABLE II. Decomposition of dimethyl peroxide in the presence of nitrogen dioxide.
T°C
121
121
121
121
1^1
163
163
163
163
P°(torr)
Me,°2
30.5
10.0
10.5
10.0
10.0
7.0
1.6
4.8
13.5
N02
58
44.5
13.0
5.0
5.0
55.0
21.4
3.2
188.5
Other
i"*.-
—
740
torr
air
745
torr
N
1
745
torr
°z
"a
ka + kb
0.72
0.63
0.62
0.67
0.74
0.56
0.81
0.4
0.96
1.0
1.1
0.4
0.7
0.9
0.9
0.3
0.7
0.7
0.7
0.7
0.56
0.64
0.59
0.55
0.54
0.38
0.42
0.44
0.48
0.54
0.42
0.41
0.44
0.38
0.89
0.95
0.76
0.71
0.67
0.61
Time
(min.)
14
30
45
60
40
64
105
30
51
70
90
30
50
70
90
30
50
70
90
110
3.6
11.6
28
42
55
3
6.8
15
25
33
59
17
30
101
3.1
6.6
19
32
42
51
13
-------
TABLE III. Molecular parameters used for RRKM calculations; molecular parameters
for n-PrONO2 and fc
Frequencies, cm"1
with degeneracy
n-PrONO,
Molecule
30OO (7)
1600 (1)
1450 (4)
1350 (4)
1200 (1)
1000 (2)
1150 (4)
750 (3)
350 (4)
^50 (3)
100 (1)
50 (2)
Complex 1
3000 (7)
1600 (1)
1450 (4)
1350 (4)
1150 (5)
1000 (2)
720 (2)
125 (6)
50 (3)
Complex 2
260 (6)
tert-BuONO
Molecule
3000 (9)
16OO (1)
1400(15)
1200 (1)
1000 (3)
800 (1)
200 (3)
410 (5)
100 (4)
Complex 1
3000 (9)
1600 (1)
1400(15)
1200 (1)
1000 (2)
800 (1)
200 (3)
350 (3)
100 (6)
Complex 2
350 (2)
100 (7)
RO-NOX, A 1.46 2.46
1040 I /(gm cm") - - 6.10
red
log [A(300°K)/sec-1 ] - - 16.5
14.7
1.46 3.60
2.93 x 10T 1.53 x 108
1.00
- - 15.8 16.3
14
-------
TABLE IV. Thermochemical quantities.
Species
n-PrONO^
n-PrO
NO,
t-BuONO
t-BuO
NO
a
AH?
I ,2 98
- 41.6
- 9.0
7.9
- 41.0
- 22.7
21.6
Ref
c
h,e
f
g
d
f
b
oO
S298
91.1
74.0
57.3
89.6
75.0
50.3
Ref.
d
e
f
d
e
f
0 kcal/mole.
6 cal/mole • deg.
c Reference (11).
d See "Thermochemistry" section.
•Reference [10].
' Reference [12].
• Reference [3].
* We have chosen the value of —9.0 rather than the —9-7 listed in [103] because it is
more consistent with a large number of measurements of alkoxy compounds as well as with
a uniform RO-H bond strength of 104.0 ± 1.0 kcal/mole.
TABLE V. Rate constants.
n-PrONO,
I2 ~ n-PrO + NO2
t-BuONO - t-BuO + NO
^H°oo/kcal "ole-1
as500/cal mole-1 dec-1
log k* -/sec-1 [VLPP]
lnR*T)
2.3 R
log k+00/sec-1 [Ref. 3]
(1)
40.5
40.2
16.5 - 40.0/6
6.95
9.5
(2)
39.9
35.7
15.8 - 39.3/8
5.97
9.8
16.3 - 40.3/6
15
-------
The combination rates given in Table V are ~ 102 higher than values
currently accepted. The rate for t-BuO + NO is in good agreement with
the results by Batt et al.3 Phillips and Shaw,11 and Baker and Shaw12
reported relative rates for recombination of NO and N02 with RO (R = Me,
Et, t-Bu) between 1.7 and 2.7. The ratio k-^k^ = 10°'3 ^ 2 is in the
center of this range.
The results from the methyl peroxide-NO2 study are in good agreement
with those of Baker and Shaw12 who obtained ka/(k& + kb) = 0.90 at 130°C .
Extrapolation of the data shows that the combination at 760 torr is in
its high-pressure limit, and hence that combination of larger RO radicals
with NO2 will also be pressure independent.
The decomposition of n-propyl nitrate appears to be a uniform process
at various temperatures, collision numbers, and flow rates. The rate
constant reported here for nPrON02 decomposition was chosen so that the
activation energy at 298°K was Ea98 = AH298 —0.6. Thus we find a best fit
RRKM value of log k /sec'1 = 16.5 — 40.0/9. There is a value reported in
reference 2a of log k^/sec-1 =14.7 - 36.9/9. if we change frequencies in
the transition state to produce an A-factor of log A/sec-1 = 14.7, we find
that E = 37.7 kcal/mole (Figure 1). Thus we cannot really distinguish
between these values from the VLPP data alone, but require the values of
AHt from other sources, as well as the increasing evidence that the combin-
ation of alkoxy radical with NO2 would have to be higher than the value of
log k-j/M-1 sec-1 =7.7 which would follow from the lower A-f actor.
The rate constant for tBuONO decomposition was evaluated in the same
way as above. The data could be equally well fitted by the parameters of
reference 3 (Figure 2), and since the value of AH298 is uncertain by at
least ± 1 kcal/mole, no distinction is possible.
16
-------
The scattered points in the VLPP plot for tert-butyl nitrite at the low
temperature end, as well as the isobutene formation in that temperature range,
indicate that a surface-catalyzed process is operative that produces nitrous
acid and isobutene. In an earlier study of 1- and 2-nitropropane pyrolysis13
it was found that nitrous acid decomposed under VLPP conditions, even though
it could not have occurred in a homogeneous manner. We suggest that tert-butyl
nitrite decomposition is autocatalytic in the low-temperature range, in that
acid produced in the P-scission is absorbed onto the walls, where it both
decomposes and catalyzes elimination of more HONO. Surface effects for
RONO have been described by Batt et al.3 and the decomposition of tert-
butanol in our system to give isobutene must be a catalyzed process,
because the homogeneous rate is prohibitively slow. The origin of tert-
butanol from tert-butyl nitrite is not clear. It could arise from H-
abstraction from walls or HONO by tert-butoxy, or by a surface-catalyzed
hydrolysis of the nitrite by water in equilibrium with nitrous acid.
The decomposition of methyl nitrite was not studied extensively. The
NO and HNO may arise by homogeneous or multistep mechanisms; the falloff
for this small molecule [o.3, assuming log (k /sec'1) = 15.6 - 41.1/9],
r
CH3ONO - CH20 + HNO
^ CH30 + NO
t
CH30 + HNO - CH3OH + NO
CH30 + NO ^ CH2O + HNO
is much less than predicted (10~5) , and the process is probably wall catalyzed.
Methanol can arise by two mechanisms as discussed for t-BuONO above.
17
-------
In a relative rate study, Wiebe et al. 20 have concluded that for
the reactions:
3
CH30 + 02 - CH20 + H02 (3)
4
CH30 + NO -* CH3ONO (4)
k3/k4 = 5.5 x 10-5 at 25°C
If we take k4 to be the same as k_2 proposed in this work (i.e., k4 = 109 •8
M-1 sec-1) , then k3 = 1.7 x 10s M-1 sec"1 . Heicklen has estimated k3 as
1Q7.6-6/6 M_i sec-i _ io3>* at 25°C. The importance of measuring k3 is
underscored. Demerjian et al.x pointed out that a ratio of k3/k5 = 4.9 x 10~5
is compatible with CH3ONO2 formation in smog chamber studies:
5
CH30 + N02 - CH3ON02 (5)
If k5 is taken as ~ k_j of this study (i.e., k5 = 109*5 M'1 sec'1), this
would also make k3 ~ 105 M"1 sec-1 .
18
-------
Thermochemi stry
Entropy of nPrONO2;
The value used, 91.1 cal/mole-deg was computed from group additivity14
by assigning the value 72.3 cal/mole-deg to CH3ONO2, in agreement with Stull
et al.,15 and adding twice the value of the group C-(C).,(H)2 which is 9.42
cal/mole-deg [i.e., C-(C)(0)(H)2 = C-(C)2(H)2].
Entropy of tBuONO:
The entropy of tBuONO may be calculated from group additivity if a value
for the group 0-(C)(N=O) can be found. This, in turn, is found from the
entropy of CH3ONO whose value is in some dispute.15 The value16 S°98(CH3ONO) =
69.7 cal/mole-deg has been chosen. This leads to S°98(tBuONO) = 90.4
cal/mole-deg.
The entropy of tBuONO can also be calculated from the entropy of 2,2-
dimethylpentene-1 by correcting for the difference between CH3ONO and butene-1.
This yields a value of 88.7 cal/mole-deg, and we have chosen 89.6 cal/mole-deg
as the best choice.
Heat of Formation of tBuO:
The value AHf oo(tBuO) = 21.6 kcal/mole found in most recent references3'10
•*- 9 '^ ™ 8
comes from the activation energy of the decomposition of ditertiary butyl
peroxide,17 and the heat of formation of the same compound.16 The value in
Reference 18 of AHf (t-C4H90)^ = -81.5 kcal/mole is only correct if the
I 2 9 8
heat of vaporization used therein is also correct. Two values exist19 for
AHvap, and the second value gives AHf(t-C4H90)2 = -83.4 kcal/mole which yields
AHf(tDuO) =-22.7 kcal/mole.
19
-------
B . THE DECOMPOSITION OF DIMETHYL PEROXIDE AND THE RATE CONSTANT
FOR CH30 + 02 - CH20 + H02
The methoxy radical (MeO) is a ubiquitous species present in the
atmosphere as well as in flames and combustion processes where it is
potentially active as a chain-carrier and propagator. A reaction of
particular importance is that of methoxy radicals with molecular oxygen.
In the polluted troposphere that reaction plays an important role in
the oxidation of nitric oxide according to the following sequence of
reactions:21
CH4 + OH - CH3 + H20
CH3 + 02 CH302
CH302 + NO - CH30 + N02
CH30 + 02 -» H02 + CH20 (17)
H02 + NO -« OH + NO2
etc.
Not included in this sequence are two reactions which can compete
with reaction (l?) under certain circumstances:
CH30 + NO " CH3ONO (14a)
M
CH30 + N02 -• CH3ON02 (12a)
It is desirable that absolute rate constants for reactions (17), (14a),
and Cl2a)be obtained by direct observation. Unfortunately, the detection
of MeO is difficult, necessitating the use of indirect techniques which
can give the rate constants with as little attendant uncertainty as
possible. Since relative measurements are necessary it is advantageous
20
-------
to choose either reaction (14a) or (12a) as the reference reaction, since
these reactions are also of importance in the troposphere.
The reverse of reaction (14a) was the subject of a recent and
thorough study by Batt and coworkers3 who obtained Arrhenius parameters
for the unimolecular decomposition of methyl nitrite. Using the ex-
perimental parameters and the equilibrium constant for the reaction, they
then deduced the absolute rate constant for the forward direction of
reaction (14a) .
Reaction (12a) has been studied by a number of investigators3°>11> l*
who have obtained rate constant ratios kl2a/ki4a Although the experimental
values do not agree exactly, the net uncertainty in log k. is only
about ± 0.3. This point will be discussed in more detail later.
The rate constant for reaction (17) has never been measured di-
rectly, and the rate constant ratio k17/k14 has been obtained only at
room temperature.20 For our study, we decided to measure the ratio
k7/k14 as a function of temperature in order to obtain the Arrhenius
parameters for the reaction. We chose reaction (I2a)because N02 is
stable in an oxygen atmosphere, and because the activation energy of
reaction (I2a) is about zero.2 Since there can also be uncertainties due
to an assumed mechanism, we have made a considerable effort to understand
the reaction system as thoroughly as possible in order to reduce conse-
quent uncertainties in the resulting rate constant.
Dimethyl peroxide (DMP) was chosen as the precursor for producing
MeO since it decomposes cleanly and at relatively low temperatures
and it has been well studied before.22!23.5 To understand the chemistry
as thoroughly as possible, numerous experiments and analyses were carried
out in three stages: decomposition of pure DMP, decomposition of DMP
in the presence of N02, and decomposition of DMP in the presence
21
-------
of added NO2 and 02. The results we have obtained are entirely con-
sistent with those from earlier studies of DMP decomposition, and differ
only slightly from earlier investigations of DMP decomposing in the
presence of added N02.2a>11,12 As a result, we feel that the value we
obtain for k17 is relatively free of errors arising from an
erroneous reaction mechanism.
In the next section, the experimental techniques are described,
followed by a section on Results and Discussion that is divided into
three parts: 1) Pure DMP, 2) DMP + NO2, and 3) DMP + N02 + 02.
22
-------
Experimental
A schematic diagram of the experimental apparatus is shown in
Figure 3. The apparatus was changed from one configuration to another,
depending on the information needed. Thus, pressure measurements were
always made, but gas chromatography was carried out only for some ex-
periments with DMP + N02, and in situ spectrophotometric observations
of NO2 were made principally in the experiments with DMP + NO2 + O2.
The experimental apparatus consisted of a reaction vessel sur-
rounded by an oven whose temperature was regulated to within ± 0.2°C
by a ProportioNull temperature regulator. The reaction vessel was
connected to a Validyne (Model 7D) pressure transducer so that the
pressure of the reaction mixture could be recorded continuously on a
strip-chart recorder. Also connected to this reaction vessel was an
F & M (Model 720) gas chromatograph fitted with a 10 ft. by 0.25 in.
column of 20$ di-(2 ethyl hexyl)sebacate on 60-80 mesh chromasorb
at 40°C for product analysis. A standard vacuum line was used for mixture
preparation and gas handling.
For all experiments except for the In situ spectrophotometric runs,
the reaction vessel, RV, consisted of a double-walled pyrex vessel of
about 200 cc. The outer jacket of RV could be used as the reference
side of the pressure tranducer to reduce the effect of minor temperature
fluctuations, but this procedure was not really necessary and the gas-filled
outer jacket simply served to eliminate "hot spots" on the inner walls.
The temperature of RV was measured by either a copper-constantan or
Chromel-Alumel thermocouple.
For the in situ measurement of NO2, a conventional quartz cell
(~ 500 cc) fitted with windows and an optical path of ~ 15 cm was employed.
23
-------
VACUUM LINE
AND
CHROMATOGRAPH
- /
OVEN
M
:\
\
i\
i CELL 1
Os
*V
n
I
i
i
i
i
I
1
1
1
1
i
^
Qv
r
TRANSDUCER
J
/ 1
LIGHT BEAM
SPECTROPHOTOMETER
SA-2554-32
FIGURE 3 SCHEMATIC DIAGRAM OF APPARATUS
24
-------
A special oven, incorporating a window and a mirror, was used to house
the cell,24 and a Gary 15 spectrophotometer was employed to continuously
o
monitor the absorbance (at 4200 A) due to NO2.
Dimethyl peroxide was prepared according to Hanst and Calvert. 5
(One explosion occurred during preparation of DMP when the concentrated
base was added too rapidly to the hydrogen peroxide-dimethyl sulfate
mixture.) The DMP was conveniently purified by passage through a trap
cooled to —78°C. This procedure gave DMP with only a trace (< 1% by
gas chromatography) of a single unknown impurity. Occasionally, CH3ONO
was present in the apparatus after many runs had been performed. It
was found that the vapor pressure of DMP at —78°C (~ 2 torr) was a useful
indicator of higher-volatility impurities.
Nitrogen dioxide was obtained from Matheson Gas products, Inc.
and purified by bulb-to-bulb distillation. Oxygen gas was also
obtained from Matheson.
25
-------
Results and Discussion
In the next sections, we will discuss our results in the light of
other work on dimethyl peroxide decomposition. Since our primary ob-
jective was to evaluate rate constant k18, we have attempted to make
a self-consistent interpretation of our data, even though our inter-
pretation differs in small ways from those in the literature. In
some cases, the differences disappear when further considerations are
made, but in others, we feel that our results are the most consistent.
Dimethyl Peroxide Decomposition:
The decomposition of DMP has been studied by three different groups,
Takezaki and Takeuchi23(TT) pyrolyzed DMP in the presence of excess
methanol, which acted as a radical trap, and found that log k6/s-1 =
15.61 - (36.9 ± !.!)/» (9 = 2.3 RT in kcal/mole).
MeOOMe -» 2 MeO (6)
In a related study,25 Takezaki and coworkers concluded that the acti-
vation energy for reaction (7) is E? ^ 5.8 kcal/mole.
MeO + MeOOMe =* MeOH + MeOOCH2 (7a)
MeOOCH2 •* MeO + CH2O (7b)
Since the pre-exponential factor for many methoxy radical reactions is
log [A/M"1 s"1] ~ 8.5,2a reaction (7) is expected to lead to a chain
reaction, if no radical trap is present.
26
-------
Hanst and Calvert5 (HC) studied the decomposition of DMP without
a radical trap. They found that the stoichiometry was given by
2 DMP - 3 MeOH + CO, (A)
and reported log kg/s"1 = 15.2 - (35.3 ± 2.5)/9, giving a rate constant
about three times larger than that reported by TT. The larger rate
constant is consistent with a contribution from a chain reaction, but
HC concluded that there was no chain contribution. On the contrary,
our results (see below) explain the discrepancy as due to a chain
reaction.
In a recent study, Batt and McCullochB2(BM) studied the decomposition
of DMP using isobutane as a radical trap. They found log kg/s"1 =
(15.5 ± 0.5) — (37.0 ± 0.2)/9; in close agreement with the value reported
by TT. They also found that DMP is a "clean" thermal source of MeO
and wall reactions are not important.
Our own experiments are best described in terms of a mechanism
consisting of reactions (6) and (7) followed by a series of termination
reactions:
MeO + MeO -* MeOH + CH2O (8)
MeO + CH20 - CHO + MeOH (9)
MeO + CHO -* MeOH + CO (10)
CHO + CHO - CH2O + CO (11)
This mechanism is consistent with the stoichiometry found by HC and
is consistent with our results, as well.
In our experiments, we added pure DMP to the reaction vessel and
simply observed the pressure as a function of time as shown in Figure 4
-------
Tt
in
in
(N
00
{H CO CO
O -H
OT
d/dV
28
-------
for four runs. Typically, the rate of pressure increase, dP/dt,
is greater initially, and gradually decreases to a constant value as the
experiment progresses. In general terms, this is due to the chain reaction
being gradually inhibited by one or more of the reaction products, i.e.,
formaldehyde. Since the rate of reaction (9) is much greater than that
of reaction (7) , the MeO preferentially attacks the formaldehyde to
produce the relatively inactive CHO radicals, thus partially quenching
the chain.
We carried out a series of runs at different temperatures and
obtained data similar to that presented in Figure 4. From the data,
we deduced k = P * (dP/dt)at run times greater than about 180
obs DMP
seconds, when the rates approach a constant value. Despite some scatter
in the results, we found our data (Figure 5) to be very well fitted by
the expression obtained by HC: log k = 15.2 — 35.3/9. This good agreement
confirms the consistency between pressure measurements and the spectro-
photometric measurements of HC.
To test the proposed mechanism in detail, numerical calculations
were performed using the Gear computer program for integrating coupled
sets of stiff differential equations,2* Reasonable estimates for the
rate constants were made (Table VI) for all reactions except for ky, which
was used as an adjustable parameter. We experienced no difficulty in
fitting the experimental results, which indicates that the proposed
mechanism is consistent with the data. The particular rate constants
we chose may be somewhat in error, thus the rate constant k? can
also be slightly in error. Nonetheless, the best fits were obtained for
4 -i -i
k7^5xlO M s , which can be compared to that for similar reactions.
8.5 i 0.5
Typical A-factors for methoxy radical reactions are about 10
-i -i -i
M s , giving an activation energy E7 = 7 ± 1 Kcal mole ' in good agree-
-i
ment with the E, £ 5.8 Kcal mole deduced in Reference 25. These values
29
-------
(0
* §
d -P
rt x
o
.M -P
•P h
O
h (Q
30
-------
Table VI . Rate constants for computer calculation.
6
7
8
9
10
1 1
i2a
I2b
13
i4a
15
16
MeOOMe
MeO + OMP
MeO + MeO
MeO + CH,O
MeO + CHO
CHO + CHO
MeO + NO,
MeO + N02
HONO "
MeO + NO
MeO + NO
N02 + CHO
Reaction
•» 2 MeO
- MeO + CH4O + CH3OH
-• MeOH + CH,0
- MeOH + CHO
-• MeOH + CO
- CH20 + CO
" MeONO,
-• HONO + CH,0
mil * * '
i -; NO + f NO, + -J H20
- MeONO
- HNO + CH,0
•• HONO + CO
log ka
15.7 - 37.1/9
Adjusted
10
8 - 3/«
10
10
9.8
9.3
0.05
10.1
9.4
9
Ref
This Work
—
(b)
10
(b)
(b)
See Text
This Work
28, (b)
3
3 2O
(b)
' Units are as follows: unimolecular: sec-'; bimolecular: M-'-sec"1; wall reaction: sec ';
activation energies: kcal/mol.
6 Many of these rate constants are estimates, since the computer calculations are only
meant to be used as a test of the steady-state assumptions and not a definitive simulation of the
mechanism.
Table VII. Dimethyl peroxide rate constants."
T (°K)
391
404
411
414
432
log (kjj /a"1)
log (k, /s->)
*<•
8.99
3.52
8.90
1.06
7.39
= (15.6 ± 0.5)e -
= (15.7 ± 0.5)8 -
,-)"
(-6)d
(-5)
(-5)
(-^4)
(-4)
(37.1 ± 0.9)e/9
(37.1 db 0.9)6/*
kg (8""1)
1.06 <-5)d
4.15 (-5)
1.05 (-4)
1.25 (-4)
8.72 (-4)
• Uncertainties are estimated to be ± 10%.
6 See text for definition of kt/.
'k^= 1.18 kN.
d Notation: 1.00(-5) = 1.00 X 10-'.
• Uncertainties are one standard deviation.
31
-------
may be compared to log 1^ = 9.3 — 10/9 estimated by O'Neal and Richardson,27
which is about a factor of seven too low at 400°K. Thus, we have repro-
duced the results of HC and can explain them in terms of a reasonable
chain mechanism.
Dimethyl Peroxide with Added NO2:
Nitrogen dioxide is an effective radical trap and effectively
quenches the chain reaction in the pyrolysis of DMP. As long as suffi-
cient N02 is present, the mechanism for DMP decomposition consists of
reaction (6) followed by
M
MeO + N02 -• MeON02 (12a)
-• HONO + CH2O (12b)
HONO - 1 NO + i N02 + 1 H20 (13)
22 2
M
MeO + NO -• MeONO (14a)
- CH20 + HNO (14b)
HNO + NO2 -• HONO + NO (15)
MeO + CH20 -» CHO + MeOH ( 9)
NO2 + CHO -* HONO + CO (16)
This reaction mechanism is similar to those suggested by other
345
authors. ' ' Reaction (13) has been inferred to be wall-catalyzed and
to have rate constant ^3s* 0.01 sec"1 at room temperature; 28 at 400°K
it may well be somewhat faster. Rate constants for all of these reactions
are presented in Table VII. It should be pointed out that the following
32
-------
reactions have been omitted, even though they may be important when the
NO2 concentration is very low:
MeO + CH3OH - MeOH + CH2OH
MeO + CH3ONO2 •-• MeOH + CH2ON02
MeO + CH3ONO -• MeOH + CH2ONO
These reactions have been neglected since their rates are unknown, but
they are expected to be unimportant unless the NO2 concentration falls
to a very low value.
When the N02 has been consumed, the termination reactions mentioned
earlier as well as those listed above become important. Note that if
k12. « k12 the stoichiometry for the reaction would be
BMP + 2 N02 -* 2 MeON02 (B)
and a pressure decrease results. When all of the N02 has been consumed,
the stoichiometry reverts to equation (A) and a pressure increase results,
Thus the "titration endpoint" for N02 consumption is signaled by the
change in sign of dP/dt at time f as shown in Figure 6. Using this
simple picture, a rate constant k.^ can be defined:
(C)
This equation was written assuming stoichiometry equation (B) and
assuming all of the N02 has been consumed at time T.
Typical experimental data for a single run are shown in Figure 6
These data qualitatively resemble the simple picture described in the
preceding paragraph. The total pressure steadily decreases until nearly
33
1
. 1 ,-,
r
2 [DMP]O
2 [DMP]O -[N02]0
-------
in
in
CM
Ol
2
+» o
•P r-<
34
-------
all of the NO 2 has been consumed and then starts to increase. In most
runs, the titration endpoint at T is very sharp and easily recognized.
Typical uncertainties in T are of the order of a few seconds.
Gas chromatographic analyses for MeONO and MeON02 and spectropho-
tometric analyses for N02 were carried out to test the proposed mechanism
for consistency. The gas chromatography was slightly hampered by the
tendency of the DMP and MeON02 to decompose suddenly at the chromatograph
inlet. On several occasions, the DMP decomposed completely during gas
chromatography. The experimental data are presented in Figure 7. The
co-ordinates are reduced variables: the ordinate is the ratio of the
component concentration to the concentration of NO2 initially present,
and the abscissa is the reduced time, t/r. Despite the experimental
scatter, virtually all of the original N02 shows up later as MeON02 and
MeONO. Only small quantities of MeONO were observed (~0.1 - 0.3 times
[MeON02]), but the reproducibility was poor and that detected may have
been due to residual amounts in the inlet lines. In any event, the ob-
served products are consistent with the proposed mechanism. Note that
[NO2] /[NO2]0 » 0.06 for this series of runs; for another series of runs,
[N02] / N02]0 = 0.08 ± 0.03. The relative constancy of this value may
be due to the competition of reaction (k,0^) for MeO vs reactions of MeO
A A Si • ' —
with products such as those due to the reactions listed above that were
omitted from the mechanism.
According to the simple stoichiometry equation (B), one NO2 molecule
is consumed for each MeO radical generated. In actual fact, however,
k -is not greatly smaller than kl2a, and more than one methoxy radical
is necessary to consume each N02, implying k« > k6 by some amount due
to the effects of k^^. Moreover, in the simple picture, it was assumed
that [N02] = 0, an assumption not borne out by the data. Thus, less
N02 has been consumed by time T than was assumed, implying that k-, < k6
Since these effects tend to cancel, kjj ~ kg to a first approximation
35
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(below, we find kN = 0.85 kx ) . The data are presented in Table VI,
and log kj, is plotted vs. 1/T in Figure 5, along with data from the
literature. A more quantitative estimate of kG can be obtained if the
effects of k12b are taken into account.
The most obvious effect due to k12b is that the relative slope
[DMP]"1 (dP/dt) is not equal to unity (Figures), but is ~ 0.4. This de-
monstrates qualitatively that(l2b) is an important reaction. Baker and
Shaw12made measurements on the DMP + NO2 reaction system and came to the
conclusion that k12t)/k1 =0.1. This value, however, is not consistent
with our results.
We analyzed our data by carrying out a pseudo-steady state cal-
culation, assuming that the following species are in steady-state:
MeO, HONO, NO, and HNO. The formaldehyde was assumed to be immune from
attack in the early and intermediate stages of the reaction. Using these
assumptions, the rate of pressure change can be written
«p = _k [DMP]kl2a"3Xkl2b o»
dt
where X = k14a/(2k14a — k14^) . The ratio k14b/k14a has been measured
recently by two different groups to be 0.1729 and 0.18 ± 0.02.3 Using
k14b/k14c = 0.18 gives X = 0.55.
A series of in situ spectrophotometric runs was performed to determine
[N02] and it was found that [ N02] = (0.08 ± 0.03) [NO2]0. This finding,
along with the steady-state analysis allowed us to write k™ in terms
of k
where Cs is a ratio of rate constants that depends on the assumed steady
state conditions. Using this result and the expression for (dP/dt), the
37
-------
(JJOl) — —
s
s
in
CO
w
13
n a.
O
g
I
f
« us
• • o o •
« in m w
o • • o
r-i n m N
05 o IH n
oo ^ ^ •<#
O
00
38
-------
following expression can be written:
- — — = T DMPl (0-92) k*2a " ki2b (F)
dt k C k+~k
N s Ki2a r Ki2b
At early and intermediate times, [DMP] = [ DMP]0 and a plot of
— (dP/dt)/k vs. [DMP]0 is expected to give a straight line. The ex-
perimental data obtained at five different temperatures are plotted
this way in Figure 8 and the resulting straight line has a slope of
0.40 ± 0.05. With an appropriate value of C , the ratio k b/k
can be determined.
For the evaluation of C , three different sets of assumptions were
S
made:
1) Initial conditions: nothing except MeO is in steady-state
and no products have accumulated. This is unlikely to
be the case except for a very short period after an experiment
is begun.
2) Intermediate conditions: MeO, HONO, NO, and HNO are in
steady-state and formaldehyde is immune from attack.
This is a more likely case, since N02 greatly suppresses
the MeO concentration and thereby prevents its attack
on CH20. The rate of N02 attack on CH2O is very slow
at these temperatures. 30
3) Final conditions: MeO, HONO, NO, HNO, CH20, and CHO are
all at steady-state. This may be the case near the
titration point, but the respective concentrations
might not be the same as those calculated by the
steady-state expressions.
39
-------
The values of the constant C for these three cases are, respectively:
s
C1 = 1.0 (G)
ki2a + k X
kiaa
2ki4a
= 0.55 (I)
The corresponding values of k^^/k^ are 0.26, 0.30, and 0.29, respectively.
Since condition 1 is felt to be unlikely, we find that k12b/kl2a = 0 .30 ± 0.05
The result that k^ v/k, = 0.30 +. 0.05 may be compared to the value
1 2 O T- 2 9.
0.1 obtained by Baker and Shaw.12 Those authors depended on the assumption
that the attack of N02 on CH20 was very fast compared to the time scale
of their experiments ( ~ 3 hrs) carried out at 403°K. Literature values
for the rate constant,30 however, coupled with the pressures of NO2
used by Baker and Shaw give lifetimes for CH2O decomposition on the
order of ~ 1 .4 to ~ 2.8 hrs. Thus, for some of their runs, a substantial
amount of CH2O may have remained unreacted, possibly leading them to
underestimate the ratio k12b/ki2a* Thus, their results may represent a
lower limit to the actual ratio and are compatible with the ratio
obtained above .
Using ki2b//ki2a = ° *3 in e<5uation (H) and in equation (E) , the
expression for ke becomes
k6 = 1.18 kN (J)
A properly weighted least squares analysis of the data gives log
kjj/s"1 = (15.6 ± 0.5) - (37.1 ± 0.9)/0; thus log kg/s'1 =
(15.7 ± 0.5) - (37.1 ± G.9)/0, in good agreement with values obtained by TT
and BM. At 420°K, this rate constant is about 1.6 times that obtained by Batt
and McCulloch22and about 1.1 times that obtained by Takezaki and Takeuchi.23
40
-------
One possible source of discrepancies among these three sets of data
is thermal heating of the gas in the reaction vessel due to the exother-
micity of the reaction itself.31 Batt and McCulloch took special care
to avoid generating thermal gradients by using low pressures of DMP
(~ 0.5 — 5 torr) and high pressures of isobutane (-^ 700 torr). In the
present experiments and in those carried out by TT, considerably higher
pressures of DMP were employed (~ 10-50 torr and 23 torr, respectively)
and thermal gradients generated by the reaction could contribute to the
rate. In fact, shifts of only 2°K can account for all discrepancies
between the present results and those of TT and BM. In light of these
considerations, we feel that the data of BM are probably the best ob-
tained so far for DMP decomposition.
Aside from slight differences in A-factors, the present data and
those of TT agree well with those obtained by BM; the activation energies
are 37.1 ± 0.9, 36.8 ± 1.1, and 37.0 ± 0.2 Kcal mole"1, respectively.
The consistency of these results strongly supports the methoxy radical
heat of formation deduced by BM ( AH° (MeO) = 3.8 ± 0.2 Kcal mole"1),
and further supports their conclusion3 that values for the dissociation
energy D(RO — H) derived from ICR work and electron detachment32 are
consistently lower by ~ 2 Kcal mole"1.
To test the proposed mechanism and the rate constants deduced on
the basis of the pseudo steady state assumption, a calculation was
carried out using the Gear computer program26 to do the time-integration
of the coupled differential equations. The rate constants used are pre-
sented in Table VII, and the results of the calculation are presented
in Figure 6 along with data from one experiment. The calculated results
seem to be in good agreement with the experiment, essentially con-
firming the analysis. The computer calculation shows that the
41
-------
pseudo-steady-state concentration of MeO is attained very quickly; that
of HONO comes near the middle of the run, and those of NO, HNO, and
CH2O are attained only near t/j = 1. Thus, the "intermediate conditions"
assumed earlier are probably the closest to actual fact, but the other
sets of assumptions are not much in error.
Dimethyl Peroxide with Added N02 and O2 :
The experiments with DMP + N02 + 02 were carried out by placing
BMP — NO2 mixtures in the reaction vessel, then adding ~700 torr of O2.
The reaction was followed in situ by spectrophotometric observation of
NO2 and by measuring the total pressure as a function of time. Data
from a typical experiment is shown in Figure 9. The initial disturbance
due to gas mixing soon subsides and smooth curves of pressure and [N02]
are obtained. In all runs, the pressure curves were noticeably more
"rounded" and the amounts of N02 remaining at time T were larger than
when 02 was not present.
Only two more reactions need be added to the mechanism when O2 is
added to N02 — DMP mixtures:
MeO + O2 -» HO2 + CH2O (17)
H02 + NO2 -» HONO + O2 (18)
Reaction (17) is the reaction we have been trying to measure. Other
termination steps are not important as long as NO2 is present.
An "intermediate" steady-state treatment can be defined in which
pseudo-steady-states are assumed for MeO, HONO, NO, HNO, and H02;
42
-------
(JJOJ)
to
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43
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formaldehyde is again assumed to be immune to attack. The rate of
pressure change can be written
dP
dt - 6 ki2a[NOa] + 3 kl2b[No2] + k17 [02] X
where X = — - - — = 0.55, just as before. At the titration point
, (dP/dt) = 0 and equation (K) can be rearranged to give
T
pro.]
T
[02]
(L)
This expression is sensitive to the ratio kl2b/k12 , justifying the care
taken earlier to determine that quantity.
The expression for k 17 consists of three parts: 1) a stoichiometry
factor (in curly brackets), 2) rate constant ki2a and 3) experimental
values for the ratio [NO2] /[O2], The results obtained for the ratio
[NO2] /[O2] at several temperatures are presented in Table VII. These
T
ratios are subject to experimental uncertainties of about ± 15jb , as
noted in the table. The stoichiometry factor depends on the ratios
3
(= 0.18 ± 0.02) and k/k (= 0.30 ± 0.05) and is not subject
to a large uncertainty, barring gross errors in the reaction mechanism:
k k ^
- _ I4b 12M = 0.31 ± 0.05 (M)
3
Rate constant kiaa, on the other hand, suffers from a larger uncertainty.
Three indirect determinations of kl2a are reported in the literature,
Baker and Shaw12 measured the ratio k14a/kl2& =2.7 at 403°K and Phillips
and Sha* * 1 obtained k14a/k12b = 1.8 at 363°K. However, Baker and Shaw
44
-------
felt that their data was better since the pressure of NO2 was more
2 o
constant in their experiments. Wiebe, et al. measured k14/kl2 =1.3 at
room temperature, leading to k /k12a = 1 .1 . Jt is possible that this
ratio exhibits a temperature dependence, but that is not expected to
be the case.6 A likely explanation is that unrecognized systematic
errors influenced the experimental determinations. On the basis of
these data, a fair estimate seems to be k,4 /k, =2+1.
As mentioned earlier, Batt and coworkers3 measured the reverse of
reaction (14a) and on the basis of their data and thermochemical cal-
culations they concluded that log (k14a /M"1 s"1! = 10.1 ± 0.4 at 300°K;
at temperatures near 400°K, the rate constant should be about the same.
Combining their result with the ratio k14 /k12 = 2 +_ 1 , we find that
log fk12a/M-1 s"1 I = 9.8 ± 0.5, where the quoted uncertainty has been
derived by a propagation of errors analysis. Thus, the uncertainty
associated with k^ is far greater than that due to stoichiometry or
that due to random experimental errors in the ratio [N02 ] /[02].
T
The experimental values for [NO2] /[02] are presented in Table VIII.
T
A properly weighted least squares analysis of this data gives
log J[N02] /[02] = - (0.82 ± 1.46) - (4.0 ± 2.8)/9. When this value
is combined with the stoichiometry factor, we obtain the expression
[ . ] (4.0 ± 2.8)
log kl7 'k12J = — (1.33 ± 1.46) -- . The rate constant ratio
L T H
itself is not subject to as much uncertainty as the individual arrhenius
parameters. Combining the value log (k^g/M"1 s~1) = 9'8 - °*5 with tne
expression for log Ik17/k12a|, the final result is log Ik17/M~1 s"1^
The large uncertainty in the Arrhenius parameters mainly reflects
the relatively small temperature range of our experiments; the para-
meters themselves appear to be fairly reasonable. Our results are
45
-------
Table VIII
DATA SUMMARY FOR MeO + 02 -» HO2 + CH2O
T, °K 103 x [N02]r/{02]a ID'6 x k17 (NT1 s'1)
396
409
420
442
0
1
1
1
.71 J
.34 d
.26 d
.52 d
= 0
: 0
b 0
b 0
.10
.11
.10
.19
1
2
2
3
.4
.6
.5
.0
±
±
±
±
0
0
0
0
.2
.2
.2
.4
log k17 /M"1 s'1 = (8.5 ± 1.5)b - (4.0 + 2.8)b/9
a
Experimental uncertainties quoted are average error.
Uncertainties quoted are one standard deviation.
46
-------
presented in Figure 10 , along with a result (described below) obtained
by Wiebe et al»20as well as a line corresponding to log k17 = 8.5 — 4/9.
The extrapolated line clearly agrees well with the results of Wiebe et al,
at room temperature.
Wiebe et al. deduced k17/k14a= (5.5 ± 1.1) x 10~5 at 300°K. Using
k14a= 1010'1 * °'4 M"1 s"1 due to Batt and coworkers3 log
5.84 ± 0.4 at 300°K. The authors estimated the uncertainty to be ± 20$,
but did not explain how they made the estimate. Their reaction mechanism
included about twenty reactions, and it is possible that unknown systema-
tic errors have affected their results. Despite the chances for error
in our own data and in theirs, the results appear to be remarkably
consistent with one another, as well as with recent estimate!-33 for
the rate constant.
A number of other values for k17 have been reported in the litera-
ture. Most of these, however, were obtained by using "third generation"
methoxy radicals and a complex reaction mechanism. An example of the
production of "third generation" methoxy radicals is described by the
sequence of reactions:
!heat \
or ( -> CH3 (19)
light)
CH3 + 02 + M -> CH302 + M (20)
2 CH302 -> 2 CH30 + 02 (21)
Heicklen and Johnston34 and (later) Shortridge and Heicklen35 used
the reaction sequence given above to obtain values for the ratio k.^/k.,1/2
17 8
equal to 0.020 M"1/2 s~1/2 and 0.021 M"1/2 s""1/2, respectively, at 300°K.
Choosing kg «» 1010 M~J s"1 leads to the low values of k17 which Heicklen
used to estimate36the arrhenius parameters for the reaction. More recent
estimates33 gave a much faster rate.
47
-------
ID
in
(N
i
(A
M g CO
-------
In a similar study at 373°K, Alcock and Mile37 found k17 =
1.2 x 106 M"1 s"1, in good agreement with our results. Their data
analysis consisted of a computer simulation of the reaction mechanism,
and they found it necessary to include the reaction
CH302 + CH302 -» CH3OH + CH2O + O2 (22)
where k « ^21' Recent data obtained by Bayes et al.38 indicate that
reaction (23) should be considered along with reaction (20),
CH3 + 02 - CH20 + OH (23)
complicating the picture still further since other evidence8 indicates
that reaction (23) is unimportant. A possible alternative to reaction
(22) that would also give stable products and a lower MeO yield is:
2 CH302 - CH3OOCH3 + 02 (24)
* M
CH3OOCH3 - CH3OOCH3 (25)
-* 2 MeO (26)
39
Reaction (24) is about 43.5 Kcal mole"1 exothermic and D(MeO-OMe) is
about 37.6 Kcal mole~1,22making reaction (26) possible. The way the
reactions are now written, the yield of MeO will be pressure-dependent.
An alternative would be to assume that the 02 carries away much of the
excess energy, leaving mostly stabilized DMP behind and giving an even
lower yield of MeO.
In a recent paper, Heicklen and coworkers40 reported the results of
a study on the photo-oxidation of CD3N2CD3. They concluded that
reactions (21), (22), and (24) occur 43%, 50%, and 7% of the time,
respectively, in good agreement with the relative rate constants deduced
49
-------
by Alcock and Mile,37 They also concluded that k17 = (0.5 - 1.25) x 104
M"1 s"1 at 300 K, a value that is somewhat higher than those obtained
earlier,34'35 and is not inconsistent with our results. On the other
hand, the use of "third generation" radicals necessitates very complex
data analysis and much additional work is needed if such methods are
used to obtain unambiguous methoxy radical rate constants.
Summary
The present study has demonstrated that the decomposition of
dimethyl peroxide is now well understood. The value obtained for k =
6
10(i5.7+0.5)-(37 .i±o.9/6) ig consistent with those obtained by Takezaki
and Takeuchi23and by Batt and McCulloch.22 Due to the extra care taken by
Batt and McCulloch to eliminate the possibility of thermal gradients,
their determination o-f the A-factor of kj is probably the most reliable.
The data obtained by Hanst and Calvert5are explained by invoking a chain
reaction mechanism, and k? <=* 5 x 104 M"1 s"1 was obtained near 400°K.
By adding N02 to the decomposing DMP, a value of the disproportion-
ation/recombination ratio for MeO + NO2 was obtained; k12,/k12a = 0.30 + 0.05
The reaction of MeO with 02 was measured relative to the reaction
of MeO + N02, yielding log [k17/M~1s-1] = (8.5 ± 1.5) - (4.0± 2.8)/6,
where most of the uncertainty in the Arrhenius parameters is due to
the limited temperature range used. The Arrhenius parameters are quite
reasonable and compare well with recent estimates^ however, further
work is needed to reduce the uncertainties.
50
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SECTION 4
ESTIMATION METHODS
A. METHODS FOR THE ESTIMATION OF RATE PARAMETERS
The thrust in modern science and technology has been increasingly
to analyze complex systems at a molecular level. To the impatient
engineer, much of this may appear to be a narcissistic infatuation with
unimportant detail. For the working scientist, however, who has lived
with these complexities for some time, the exhaustive examination of
just this detail is his only guarantee that he has really understood
the phenomena involved. More important, it is the only reliable path
he has available to him for making any continuing progress in analyzing,
diagnosing and hopefully controlling the systems under study.
Almost all of the technical problems facing our society today (and
how many are not technological) share in common this molecular complexity.
It is strikingly evident in the subject of our current symposium, the
kinetics of atmospheric processes involved in pollution. Although
possibly half-a-dozen elementary reactions involving O2, O3, NO, NO2,
and O atoms dominate the diurnal chemistry of the troposphere and strato-
sphere, the secondary reactions which can affect the stationary concen-
tration of some of these species may run into the tens, and if we include
"pollutants", into the hundreds. The sheer volume of kinetic information
required to analyze these systems has put a large premium on theoretical
and semi-empirical methods for obtaining rate data. In principle, one
would prefer to have direct experimental measurements of the important
reactions under the prevailing atmospheric conditions of temperature,
pressure, and composition. Practically, this is not always attainable.
Some reactions involving excited atoms or free radicals are just not
51
-------
measurable by current techniques. Others can only be measured in temper-
ature or pressure regimes very far from atmospheric (tropo- or strato-)
and need to be extrapolated with, in some cases, great uncertainty.
It is the purpose of the present report to examine the techniques
which have been used to generate rate data from theoretical or empirical
considerations and to attempt to place some quantitative measures on
their reliability. The reactions to be considered will be elementary
gas-phase reactions and the emphasis will be on the ones significant in
atmospheric chemistry. For these reasons the bulk of our attention will
be given to biomolecular processes.
Transition State Theory
There is at present only one kinetic model with any broad claims to
generality which can be used quantitatively to describe elementary,
chemical rate processes. This is the model incorporated into what has
become known as Transition State Theory,
Transition State Theory rests on a number of independent assumptions,
The first of these is that any elementary chemical reaction can be des-
cribed in statistical mechanical terms by the passage through phase space
of a complex aggregate, containing the reactant species across an energy
maximum on the potential energy surface describing the complex. The
second and most important assumption is that the reaction complex in the
neighborhood of this maximum (i.e., the transition state) can be consid-
ered to be in thermodynamic equilibrium with the reactant species. This
gives rise to the familiar kinetic scheme for an elementary reaction of
any order:
K*' * V*
A + B + C + • • • < * [A • • -B • • -C • • •] *~ products
52
-------
with an overall rate constant k described by:
Rate = k*(A)(B)(C) = - —— = V*(A•. -B••«C•••)*
dt
= V*K*'(A)(B)(C) (27)
or k* = v*K*' (28)
where K ' is the equilibrium constant for formation of transition state
complex (TS) from reactants, and v* is the probability per unit time
(first-order rate constant) for decomposition of TS into products.
Making use of the extreraum properties of the potential energy sur-
face and the approximation that hv < kT we can factor K ' into a product
of a partition function for the reaction coordinate (i.e., passage across
the maximum), kT/hv and a remainder K* . Hence the well known result,
independent of v :
k* = (|r)K* (29)
or in thermodynamic language:
k* = llT=-J|e~ (30)
There is no evidence that indicates that the approximation hv < kT
is a source of appreciable error. It would require a very compact potential
o
energy surface with a very thin ( < 0.3 A) activation energy barrier to
invalidate this approximation and no a priori calculations have so far
indicated the existence of such surfaces.
If we confine our discussion to thermodynamic language, Transition
State Theory is a two-parameter theory, the two parameters being AS and
AH . The situation is actually more complex than this since both of these
53
-------
are temperature dependent. Because of this latter, it is not easy to
relate k* to the more familiar Arrhenius form, k = A exp(—E/RT) , except
in a limited temperature range (T = Tm ± AT). The relation is:*1
E = AH* + RTm (31)
(12)
A = I «u- I e" 1U" " v«"»/
\ h /
where Tm is the center of the temperature range chosen, and AH and
AS_ are calculated at T_. Remember that AH* and AS*, if calculated
mm *
statistically, must be calculated with the "reaction coordinate" (v*)
contribution to the TS omitted. Its contribution has already been
counted in the (kT/h) term.
To make use of equations(31) or (32) requires either a total knowledge
of the potential energy surface for the reaction or an empirical knowledge
of the surface in the neighborhood of the transition state (i.e., the
barrier). The former alternative is probably not viable for the near
future, and so we must have recourse to the latter. To have empirical
knowledge of the potential energy surface in the neighborhood of the TS
implies that we have reliable rate data (E and A) for one or more of a
related class of reactions from which we can extract experimental values
of AH* and AS . This has proven a very fruitful approach and is the one
we shall now explore.
A-factors and Entropies of Activation
Equation (32) relates directly the Arrhenius A-factor to the entropy
of activation, AS . Since this latter is the difference between the
entropies of reactants and transition state, and the former can be deter-
mined directly, equation (32) gives us a method for relating A-factors to
54
-------
the entropy of the transition state S . This by itself might not be too
useful a relation were it not for the circumstance that the molar entropy
of a gas-phase species is relatively insensitive to its structure. If we
examine the contributions to the entropy of a gas-phase species from the
different external and internal degrees of freedom, we find the following:43
S° ~ S° + S° + S° + S° (33)
trans rot vib elec
Strans = 3?'° + 2 Rln (40) + I Rln + Rln(n) (34)
S° [linear molecule] = 6.9 + Rln(I/O + Rln(T/298)
rot
[non-linear molecule] = 11.5 + Rln [ (ABC) 1/2/J ] + - Rln(T/298)
S° t [ 1-dimensional rotor] = 4.6 + Rlnd1/2/^) +- Rln(T/298) (35)
t .
where M = molecular weight in atomic mass units (AMU) , I = moment of
inertia about the center of gravity, ABC = product of moments of inertia
(AMU-Ang2) , a = total symmetry number, and n is the number of optical
isomers .
The vibrational entropy consists of contributions from each of the
internal vibrations. Each of these is usually small compared to the
contributions from translation and rotation, and generally only the bend-
ing motions involving atoms heavier than H or D are significant in the
range 200-400°K. The only significant (i.e., > 0.5 e.u.) contributions
from internal modes arise from hindered internal rotations. These can
be in the range of 2 to 5 gibbs/mole per rotor, and hence are comparable
to the contributions from external rotations.
55
-------
Electronic contributions generally take the form of Rln g , where
ge, the electronic partition function, is usually the electronic degener-
acy of the ground state. For free radicals this usually reduces to a
contribution of Rln2 =1.4 gibbs/mole from their spin degeneracy. In
exceptional cases of atoms, such as O, and odd radicals such as NO and O2 ,
the electronic partition function is more complex and changes significantly
with temperature in the range of atmospheric interest 200-300°K.
High frequencies (v i 800 cm-1) contribute less than 0.2 gibbs/mole
to S° at 300°K. We can thus make gross errors in guessing them (± 20$)
without incurring a significant error in S°. A frequency of 400 cm-1
will have an entropy of 1.0 e.u. at 300°K and a 10$ error in its value
will introduce an uncertainty of ± 0.1 e.u. in S°. This doubles at 200 cm"1
and triples at 100 cm-1, but only torsional motions have frequencies in this
range. We thus observe that in estimating S°* the chief structural features
of interest are the moments of inertia and barriers to internal rotation.
The moments of inertia can be guessed from simple empirical rules
involving bond lengths and angles39and even errors of ± 10$ in the latter
will introduce uncertainties in S° of only + 0.2 e.u. At low temperatures
it is the uncertainty in barriers to internal rotation which constitute our
chief source of error.
The relative intensity of molar entropy to precise structural details
and to the number of H-atoms in a species is illustrated in the following
Tables IX, X, and XI, which compare the molar entropies and heat capacities
at 300°K of some structurally similar species.43
56
-------
Table IX . Standard entropies and heat capacities at 300°K of some structurally similar molecules.5
Molecule
A H20
NH3
CH4
BH3
B CH3CH3
NH2NH2
HOOH
CH3NH2
CH3OH
BH,BH,
C°
P300
8.0
8.5
8.5
8.7
12.7
12.2
10.3
11.9
10.5
13.9
CO "
300 (int)
46.5
48.2
49.3
48.4
60.6
58.5
58.0
59.9
59.5
58.5
a
2
3
12
6
18
2
2
3
3
4
S300
45.1
46.0
44.5
44.9
54.9
57.1
56.6
57.7
57.3
55.7
aUnits of Cp and
bSSoo (intrinsic) =
S are gibbs/mol.
S^oo + Rln a.
57
-------
Table X . Standard entropies and heat capacities of some complex, but structurally similar,
molecules.
Molecule C?;
A CH3CH2CH3 17
CH3OCH3 15
CH3CH2OH 15
CH3NHCH3 16
CH3CH2NHZ 17
CH3NHNH2 17
B CHF3 12
BF3 12
NF3 12
COF2 11
FN02 11
N2F2 (cis) 11
CH2=CF2 14
3oO — CO j. J?ln
•^intrinsic " A + Kut
Table XI . Standard entropies
Molecule
A COC12
CH2=CC12
CHCfcaCHCl (cis)
B C6H6 (benzene)
C5NHK (pyridine)
B3N3H6(borozole)
B303H3(boroxine)
S30o(lnt)a
.7 70.3
.8 70.4
.7 69.7
.6 69.8
.6 69.9
.0 68.8
.2 64.2
.1 64.3
.8 64.5
.3 63.3
.9 63.6
.9 63.4
.2 64.8
a; units are gibbs/mol for CL and 5° .
and heat capacities of some complex,
molecules.
Cpaoo S°00(int) a
13.8 69.2
16.1 69.7
15.6 70.8
19.7 69.2
18.8 69.1
22.0 72.1
21.0 71.6
o
18
18
3
9
3
3
3
6
3
2
2
2
2
but structurally
0
2
2
2
12
2
6
6
oO
°300
64.6
63.7
67.5
65.4
67.7
66.6
62.0
60.7
62.3
61.9
62.2
62.0
63.4
similar,
qO
"300
67.8
68.3
69.4
64.3
67.7
68.5
68.0
aco _ co JL. Diji
"intrinsic "
a; units are gibbs/mol for C% and 5°.
58
-------
For convenience, the intrinsic entropies (corrected for symmetries) are
compared, as well as the absolute entropies. We note that in any of the
five series of molecules compared, we would make an error less than
+ 1.0 e.u. in choosing the average in the group to represent any one of
them. We could do about the same for Cp and improve the latter by mak-
ing a correction of about 0.4 e.u. for the contributions of H atoms.
This becomes a reliable method10(± 1.0 e.u.) for assigning C ° and S°
to free radicals and ions. Extensions of these methods have been made
with about the same success to cyclic and polycyclic compounds.
In applying these methods for estimating entropy to transition states,
we proceed by selecting an initial structure which would seem reasonable in
terms of the overall structural changes in the reaction. We then calculate
a value of AS and an A-factor (eq. 32) and compare it with the experimental
data. It generally turns out that once we have "calibrated" our intuition,
there is not too much latitude in varying the initial structure if the
agreement is not good.
The largest range in S occurs between what has been designated a
"tight" and a "loose" transition state. A tight transition state is one
in which the bond lengths and bond angles are within 0.3 A and 2O°, respec-
tively, of the values which describe stable structures. Loose transition
states which appear to occur in simple bond fission reactions only, are
characterized by unusually long bonds between nascent free radical centers.
These can be as much as 2.5 to 3 times the ground bond distance. The best
documented example is the transition state for CH3»««CH3 recombination in
o o
which the C.. .C distance is at least 3.8 A, and possibly 4.5 A, long in
comparison to a normal C-C single bond distance of 1.54 A.
59
-------
A-Factors for Metathesis Reactions
Bimolecular reactions can be divided into three categories:
(1) Energy transfer processes
(2) Metathesis reactions (atom transfer)
(3) Addition reactions
Each of these is characterized by a "strong" collision between two
discrete species and can from this point of view be looked upon as a type
of addition reaction. We distinguish the true addition reaction from the
others by using it to characterize those exothermic reactions in which the
adduct is more stable than the reactants, for example, the recombination
of radicals and addition of atoms to double bonds.
The formation of the transition state in a bimolecular event can be
looked upon as involving the net transformation of translational and
rotational degrees of freedom of reactants into vibrational and torsional
degrees of the complex TS. Because of the relative magnitudes of the
entropies associated with these degrees of freedom, &S for the process
is always negative. It is more negative for heavy species than for light
and becomes increasingly more negative with increasing complexity of the
colliding species.
In the reaction of a light atom, such as H or D, with a large poly-
atomic molecule, the TS complex has about the same intrinsic entropy as
the molecule, and hence —AS* ~ S°(H) corrected for spin and symmetry.
S£88(H) = 27.4 gibbs/mole (e.u.) or 21.0 e.u. (mole/liter standard state).
Correcting for spin, Rln 2 = 1.4 e.u., and adding R for the change in
An = —1 (bimolecular event), we find AS* ~ —17.6 e.u. per atom attacked.
Since ekT/h = io13'25 sec"1 at 300°K, this would lead to a minimum A-factor
60
-------
for metathesis by H-atoms of 109*5 I/mole-sec per atom attacked. For
attack on C2H6 , which has six equivalent H-atoms, we would raise this
by a factor of 6 to 1010*3. Observed A-factors could be a power of
10 higher than these values if the TS complex had a structure in which
the H*«*X«*R bonds were bent and possessed a torsional mode with low
or zero internal barrier-to-rotation of the H atom.
The observed values for H-atom metatheses, some of which are shown
in Table XII, are in excellent agreement with these conclusions. Moreover,
the values are sufficiently above the lower limits to suggest that the
TS complexes have an H-atom which is not co-linear with the H-R bond being
attacked. The attack of H-atoms on 1? and I2 have A-factors even more than
a power of ten higher than the minimum values,and only a very nonlinear
TS can account for these high A-factors. This may, in fact, be typical
of H-atom attacks on all group V, VI, and VII elements and thus the inverse
reactions as well. A simple rule of thumb for H-atom metatheses is that
their A-factors are io10-5i°'5 I/mole-sec.
It would be extremely difficult to defend,on structural grounds,
A-factors (per atom) for metathesis by H-atoms which were less than the
minimum values calculated. Hundreds of reported rate constants 45,46,47
support these conclusions and reported A-factors which fall below these
limits must be looked upon as suspect.
When we consider atoms heavier than H or D, the analysis is not so
simple. While these heavier atoms have larger translational entropies,
their TS complexes in compensation will also have increased translational
and rotational entropies and the net result is not expected to be much
different than for H-atoms. Table XIII shows rate parameters for heavy atom
metathesis, and we note that again an average value of 1010'5—°'5 I/mole-sec
will bracket most of the results.
61
-------
Table XII. Arrhenius Parameters for Some Metathesis Reactions Involving
H-Atoms.
Ref .
la
.b
2
3
4a
b
5
6
7
8
Reaction
H + D2 - HD + D
H + HOH - H2 + OH
ft + F2 - HF + F
H + HC1 - H2 + Cl
H + CH4 - H2 + CH3
H + C2H6 - H2 + C2H5
H + I2 - HI + I
H + N20 - HO + N2
Tm (°K)
900
(177-477)
(300-2500)
(300-560)
(200-500)
(500-700)
(300-600)
(300-1100)
(400-465)
(450-1487)
log A
(M-1 sec-1)
10.6
10.7
10.9
11.1
10.4
10,4
11.1
11.1
11.6
10.7 ± 0.4
E
(kcal/mole)
8.0
9.4
20.5
2.4
3.5
4.2
11.9
9.7
0
13 ± 1.5
la. G. Boato, et al., J. Chem. Phys., 24, 783 (1956).
b. A. A. Westenberg and N. de Haas, Ibid. 47, 1393 (1967).
2. D. L. Baulch, et al., Evaluated Data for High Temperature Reactions,
Vol. I., Butterworth, London (1972).
3. R. G. Albright, A. F. Dedonov, G. K. Lavrovskaya, I.I. Morozov, and
V. L. Talrose, J. Chem. Phys., 50, 3632 (1969).
4a^ A. A. Westenberg and N. deHaas, J. Chem. Phys., 48, 4405 (1968).
b<. S. W. Benson, F. R. Cruickshank, and R. Shaw, Int. J. Chem. Kinetics,
_!, 29 (1969)
5. R. R. Baldwin, D. E. Hopkins, A. C. Norris, and R. W. Walker,
Combustion and Flame, 15, 33 (1970).
6. R. R. Baldwin and A. J. Melvin, J. Chem. Soc., 1785 (1964).
7. J. H. Sullivan, J. Chem. Phys., 30, 1292 (1959).
8. G. Dixon-Lewis, Sutton and Williams, J. Chem. Soc., 5724 (1965).
62
-------
Table XIII. Arrhenius Parameters for Metathesis Reactions Involving Atoms
Ref .
1
2
1
1
3
4
5,6
5,6
7,
8a
1
1
9
Reaction
0 + NO2 -* O2 + NO
0 + OH -* O2 + H
O + O, - 200
0 £.
O + C2H6 -» OH + C2H5
Cl + C2H6- HC1 + C2H5
Br + C2H6- HBr + C2H5
I + CH4 - HI + CH3
I + CH3I - I2 + CHj
I + CF3I - I2 + CF3
N + NO - N2 + 0
N + O2 - NO + 0
S + OCS - S2 + CO
Tm(°K)
300
300
(220-1000)
(300-650)
300
(490-590)
560
580
(350-550)
370-450
(300-5000)
300
300
log A
(M-1 sec"1)
10.0
10.3
10.08
10.4
10.6
11.0
11.7
11.4
10.9
9.6
10.2
9.3
9.0
E
(kcal/mole)
0.
0
4.6
6.4
0
14.0
33.5
20.5
17.8
16.0
0
6.3
3.6
1. D. Garvin and R. F. Hampson, Editors "Chemical Kinetics Data Survey,"
VII, NBSIR 74-430, Washington, D.C. (1974).
2. D. L. Baulch, D. D. Drysdale, D. G. Home, and A. C. Lloyd, Evaluated
Data for High Temperature Reactions. I., Buttersworth, London (1972).
3. D. D. Davis, W. Braun, and A. M. Bass, int. J. Chem. Kinetics, £, 101 (1970).
4. K. D. King, D. M. Golden, and S. W. Bmson, Trans. Faraday Soc., 66,
2794 (1970).
5. D. M. Golden, R. Walsh, and S. W. Benson, J. Amer. Chem. Soc., 87, 4053 (1965).
6. M. C. Flowers and S. W. Benson, J. Chem. Phys., 38, 882 (1963).
7. Amphlett and E. Whittle, Trans. Faraday Soc., 63, 2695 (1967).
8. (a) Lawrence, Trans. Faraday Soc., 63, 1155 (1967).
9. R. B. Klemm and D. D. Davis, J. Phys. Chem., 28, 1138 (1974).
63
-------
The reaction of N + O2 - NO + O has a sufficiently low A-factor
to warrant further inspection. If we assume it has a tight transition
state (N-O-O) , we can approximate the entropy of the latter by either
the value of NO2 if it is nonlinear or N20 if it is linear. Starting
with the former and correcting for symmetry and spin (TS must be doublet) ,
we find AS* > -20.5 which leads to A > 109 *2 I/mole-sec, in excellent
agreement with the data. A linear TS (NNO model) would yield a minimum
A of about 108'4 I/mole-sec from which we can conclude that if the
observed A-factor is correct, then the TS must be bent.
The last result makes the much larger A-factor for N + NO -• N2 + O
of some interest. The TS complex must be a triplet and a minimum A-factor
for a tight linear transition state is 108<0 I/mole-sec, while a bent
transition state has A £ 109'° I/mole-sec. The observed value of 1010*2
I/mole-sec suggests that in actual fact we must have the equivalent of
a very loose TS, equivalent to those effective in radical recombination.
This would be reasonable if the N••«NO interaction were attractive up
to distances of about 3.2 A on the triplet surface.
The other low A-factor reported in Table XII is for the reaction
S + SCO -* S2 + CO. If we model the TS using S°nt(COCl2) = 69.2 e.u.
and correct for spin (triplet), we find A % 109*8 I/mole-sec. There is
no plausible structure for the TS that could account for an A-factor as
small as 109a° I/mole-sec.
The very important atmospheric reactions 0 + NO2 -» NO + O2 and
0 + 03 -* 202 are structurally very similar. If we assume common non-
planar transition states for both, or planar ones with low rotation
barriers, we can simulate TS by FNO2 (Table X) with corrections for
spin and internal free rotation. On this basis we estimate A(O + 0) >
109'9 I/mole-sec and A(0 + N02) ^ 109'8 I/mole-sec, in excellent agreement
with the data.
64
-------
We observe in Table XIII a peculiarity unique to I atoms; that is, their
abstraction reactions have unusually high A-factors , much higher in fact
than we would calculate from minimum A-factors. For the reaction I + CH,
in fact, we estimate A ^ 109'8 I/mole-sec at 300°K in contrast to the
observed 1011'7 I/mole-sec (based on CH3I as a model for TS). This suggests
an extremely loose complex since even a .nonlinear TS would still have an
A-factor only 10-fold higher.
A postulate of Hammond48 proposes that for very exothermic reactions
having low activation energies the TS complex resembles reactants . This
is, in fact, the case for the reverse of the I-atom reactions, i.e., for
CH3 + HI and for CH3 + I2 with E t = 1 + 1 and 0 kcal/mole, respectively.
Applied to the I + CH4 reaction, this suggests that the TS looks
like a very weakly coupled CH3 • • *HI with the C"*H*"I axis bent. If we
assume that in this complex the CH3 is freely rotating about the C••«H
bond (3.6 e.u.), has two rocking modes about this bond of about 350 cm"1
each (2.4 e.u.) and the C-'-H-'-I bend is about 200 cm"1 (2.2 e.u.), we
can account for an A-factor of about 1011*5 I/mole-sec in reasonable
agreement with the results. A similarly loose model can account for the
I + CH3I - I2 + CH3 A-factor.
A-factors for some metatheses by diatomic and polyatomic radicals
are shown in Table XIV. Although the table covers a range of radicals
and atoms varying conr--t
-------
Table XIV. Arrhenius Parameters for Some Metathesis Reactions of Radicals.
Ref .
1
la
1
la
1
Ib
2
3
3,4
5
6
6
6a
7
6
6
6
Reaction
HO + CH4 - HOH + CH3
HO + C2H6 - HOH + C^HS
HO + CO - H -1- CO2
HO + O3 - H02 + O2
HO2 + 03 - HO + 202
H02 + NO - HO + NO2
CH3 + C2H6- CH4 + C2HS
CH3 + CH3COCH3 -
CH4 + CH2COCH3
CH3 + CC14 - CH3C1 + CC13
CF3 + C2H6 - CF3H + C2H5
CF3 + CC14 - CF3C1 + CC13
C2HS + n-C7H16 -
C2H6 + n-C7H15
n-C3F7 + acetone -
C3F7H + acetonyl
(300-500)
770
(300-500)
770
(3OO-500)
(220-450)
(225-298)
300
420
(400-500)
400
(320-450)
(400-560)
(360-510)
450
(300-600)
log A
(NT1 sec-1)
9.5
10.3 (10.9)c
10.1
10.9
8.1
8.5
8.8
7.8
>9.2 (10.3)d
8.5
8.6
10.4
8.6
8.0
8.8
9.6
8.7
8.8
E
(kcal/mole)
3.8
4.9 (6.6)c
2.5
3.5
0.2
0.6
1.9
2.5
0(?)(1.4)d
10.8
9.7
13
9.1
6.5
9.3
10.4
10.6
7.2
i. N. R. Greiner, J. ^hom , Phys. , 5J., 5049 (1969).
(a) R. R. Bakor , K K. Baldwin, and R. W. Walker, Trans Faraday
Soc., 66, 2812 (1970) .
(b) W. E. Wilson, Jr., J. Phys. Chem., Ref. Data _1, 535 (1972).
(c) S. Gordon and W. A. Mulac, Int. J. Chem. Kinetics, Symp. 1, 289 (1975)
(d) W. Hack and K. Hoyerman, this symposium.
2. J. G. Anderson and F. Kaufman, Chem. Phys. Lett., 19, 483 (1973).
3. Table XII], ref. 5.
4. Activation energy not determined, estimated on the basis of
radical recombination.
5. A. F. Trotman-DickenscKi and E.W.R. Steacie, J. Chem. Phys., 19, 329 (1951).
6. Reference 45; (a) J. Currie, H. Sidebottom, and J. Tedder, Int. J. Chem.
Kinetics 6, 481 (1974).
7. Reference 46.
66
-------
A ^ 109-3 I/mole-sec. A similar analysis lor C2H6 + OH gives A ^ 109 "°
I/mole-sec. A nonlinear complex would have A-factors about a power of
10 higher for both. The valuu of 1010 I/mole-sec would seem to be
reasonable for C2H6, and this would suggest that the higher of the two
values listed, 1010*3, might be a better choice for CH4 + OH.
The very important reaction CO + HO has a TS which can be modeled
by HONO. This yields A ^ 108'6 I/mole-sec, suggesting that both listed
A-factors are probably on the low side. All reasonable models for the
HO + 03 reaction yield A-factors in excess of 109'3 I/mole-sec, about
three-fold higher than the reported value. The A-factor for HO2 + 03
is in much worse agreement. The TS entropy would have to be 78.1 e.u.
at 300°K to account for the anomalously low A-factor of 107'8. The
estimate for TS is about 84 e.u., suggesting A > 109*° I/mole-sec.
The CH3 metathesis reaction from C2H6 can be modeled using C3H8 for TS.39
This leads to A ^ 108'° I/mole-sec. Correcting for a larger moment of
inertia increases this to 108"3 and a further correction for a lower CH3
rotation barrier of 1.5 kcal/mole instead of 3.0 increases it further
to 10s'5. If we assumed either a nonlinear C «H-C structure in TS or two
weakened CH3-H'C rocking modes, this would increase to 109*° I/mole-sec.
The bulk of A-factors for CH3 abstraction45"47 suggests that the TS struc-
tures are probably nearly co-linear.
The A-factor listed in lable XIV far CH3 + CC14 is at least a factor
of 101>8 higher than can be accounted for in terms of any reasonable TS
structure. The new value presented by Tedder et al. agrees quite well
with TS estimates.
67
-------
Addition Reactions
Addition reactions in which atoms or radicals attach themselves to
vmsaturated systems usually involve small activation energies and hence
can be considered to pass through tight transition states, not unlike
those for metathesis reactions. This is more or less in agreement with the
much sparser data for these reactions, some of which are tabulated in Table
XV. It should be observed that these are much more difficult reactions to
measure experimentally since the products are not themselves stable and go
on to react further. They are usually not observed directly, and their rates
are often inferred from the rate of disappearance of reactants with the aid
of some assumptions on chain lengths and secondary reactions. In addition,
the adducts are energetically excited, and their stabilization will require
subsequent deactivating collisions. In consequence, many of these reactions
show a rate dependence on total pressure which may or may not be properly
accounted for in the published data.
With these cautions made, we note that for H + C2H4 the simplest model
for a tight transition state give A ^ 1010>1 I/mole-sec, in excellent agree-
ment with the data. For 0 + C.-.H4 we estimate A ^ 109 '° I/mole-sec. This
is probably in reasonable concurrence with the data for which the reported
values are uncertain by a factor of 3. For Cl + C2H4, a tight transition
state, using CH2=CHC1 as a model, leads to A ^ 109*1 I/mole-sec, very much
lower than the reported 1010'6. Only a loose transition state character-
istic of radical recombinations can account for such a large A-factor. The
zero activation energy is in agreement with such a structure and can be
rationalized in terms of a charge transfer attraction. The ionization
potential of C2H4 is 10.5 e.u.49 while the electron affinity of Cl is 3.6
e.u.49 The difference of 6.9 e.u. is made up by coulombic attraction at
distances of 2.1 A, which is about 0.3 A larger than the C-C1 covalent bond.50
68
-------
Table XV. Arrhenius Parameters for Some Addition Reactions
of Atoms and Radicals to Pi Bonds.
Ref
1
1
2
1
3,2
4
5
6
6
React ants
H + C2H4
0 + C2H4
Cl + C2H4
OH + C2H4
OH + C3H6
0 + C2H2
CH3 + C2H4
C2H5 + C2H4
Tm(°K)
(296-540)
(223-613)
310
(210-460)
300
300
400
400
log A
(^/mole-sec)
10.4
9.9
9.5
10.6
9.7
9.5
[9.8](?)
8.5
8.3
E
(kcal/mole)
2.0
1.6
1.1
0
0.2
0 (?)
[2.8](?)
7.7
7.5
V. N. Kondratiev, "Rate Constants of Gas Phase Reactions," Reference
Book, Trans, by L. J. Holtschlag, Ed. by R. M. Fristrom, NSRDS,
U.S. Government Printing Office, Washington, D.C. (1972).
2. Table XIII, ref. 1.
3. I.W.M. Smith and R. Zellner, J. Chem. Soc., Far. Trans. II, 69, 1617 (1973)
4. J. Bradley, et al., Ibid., 1889 (1973).
5. F. Stuhl and H. Niki, J. Chem. Phys., 55, 3954 (1971). Authors did not
measure A and E, but. reported only k300 = 107'9 -t/mole-sec; A and E are
our choices.
6. J. A. Kerr and M. J. Parsonage, Evaluated Kinetic Data on Gas Phase
Addition Reactions, Buttersworth, London (1972).
69
-------
Thus, unless there is some large van der Waals1 repulsion between Cl and C2H4 ,
one could expect that their interaction would correspond closely to that of a
recombination curve. In fact, it is expected that halogens (atoms and molecules)
will form attractive Pi-bond complexes at van der Waals1 distances.
One would expect all of the halogen atoms to show a similar facility in
adding to Pi systems. The case of the OH radical is,from this aspect, very
interesting. Its electron affinity of about 1.8 e.u. is not enough to form
an ion pair with C2H4 except at smaller distances of the order of about 1.7 A.50
o
This is again about 0.3 A larger than the C-0 single bond distance, and hence
would constitute tight complex for which we would calculate a minimum A-factor
(based on CH2=CHOH) of about 108'5 I/mole-sec. The reported values, though
uncertain, are about a power of ten or more higher, suggesting again a loose
transition state characteristic of radical recombinations. A very loose
transition state with two rocking modes of HO relative to C2H4 of about 200
cm""1 and a weak 0«--C-C bending mode of about 200 cm'1 would raise this value
to 109'6 I/mole-sec in good agreement.
Collision Theory which is a zero order limit of Transition State Theory
will give a similar A-factor for OH + C2H4 collisions if the collision (i.e.,
o
impact) diameter is taken as 1.8 A, and it is assumed that 1/3 of the surface
surrounding the C2H4 does not permit a proper collision because of steric
repulsion of the H-atoms and an additional factor of 1/2 is used to correct
for the geometry of the OH approach, i.e., the H of OH should be pointing
away from the C2H4.
The reactions of O atoms with acetylene gives, for a tight complex,
A ^ 109'8 I/mole-sec, suggesting that the observed rate constant (the authors
did not measure A and E), which is 107'9 I/mole-sec at 300°K, must have at
70
-------
least 2.8 kcal/mole of activation energy or else is too low because of pressure
effects. For 0 + C2H4 a tight complex has A ^ 109*° 1/mole-sec, in reasonable
agreement with the data. Note that in this reaction and in that of O + C H0
2 2
the reaction must be mechanistically complex since the initial adduct is a
triplet biradical which must eventually be transformed into a singlet species.
The addition of alkyl radicals to olefins has activation energies suffi-
ciently high that we model the TS by tight complexes. For CH3 + C2H4 propylene
(C3H6) is a good model and yields A ^ 107'7 I/mole-sec. Corrections for a
lower barrier, a slightly larger moment of inertia and a lower C-C-C bending
frequency raises this to 108'4, in excellent agreement with the reported values.
Recombination Reactions Involving Atoms
The recombination of free radicals is an exothermic process which
produces an excited species that will redissociate into the initial fragments
unless stabilized by a de-exciting collision. For large radicals, such as ethyl,
with many internal degrees of freedom f into which the recombination energy can
be partitioned, the lifetime of the energized adduct is sufficiently long and
energy transfer is sufficiently efficient so that at pressures of 1-10 torr
deactivation is almost always faster than redissociation. Consequently, in
this pressure range, radical recombination of large radicals is bimolecular and
independent of total pressure. With small species, such as atoms, the reverse
is true, and recombination appears to be a third-order process.51 It can be
looked upon as a succession of bimolecular events:
1 *
A + B 52 AB
* 2
AB + M ^ AB + M
*
When A is an atom and B is a diatomic molecule, the lifetime of AB is so
short that AB* can be considered to be in virtual equilibrium with A and B.
71
-------
In that case (k_j » k2), the overall rate can be written as:
= k8K1(A)(B)(H) (36)
and the third-order, recombination rate constant kr is:
kr = k2Kj (37)
Since k2 is the rate constant for an energy transfer process, we can
write it as a product Xkz, where kz is a simple hard-sphere collision frequency
and X is the probability of deactivation of AB on collision. For highly
energized species possessing many quanta of energy, X is expected to be in
the range 0.2 to l.O,52 while kz ~ 1011'3 I/mole-sec.
*
The pseudo-equilibrium constant K can be looked upon in two
different ways. If the recombination energy of AB is readily partitioned
among its internal degrees of freedom, then on the average there will be
equal numbers of quanta in each mode. If the modes are comparable in
frequency and there are n of them, each will have about l/nl— the recombin-
ation energy, and the molecule is not expected to look very different from
the normal unexcited molecule, in that case we can write K as:S3
RlnK* = -AS°B + AS^g (38)
where AS° is the standard entropy change in forming ground state AB from
f\Jj
A + B, and AS^g is tne extra entropy that results from the high energy
content of AB . AS.Q may be evaluated as Rlnp*, where p is the number of
.g.
ways of distributing the energy of recombination E among the n internal
72
-------
degrees of freedom of AB . If the geometric mean frequency of the
active degrees of freedom of AB is v , then a reasonable approximation
to p is:
09)
If we apply this to the recombination of 0 + NO -* N02 , we find:
ASj^Q = —31.5 e.u. (atmospheric-standard state)
= —25.1 e.u. (M/liter-standard state)
vm « 1200 cm-1
E300K ^ E° +l RT = 73 kCal
p* ~ 530/2 = 265 = 102'4
and
kr = \kz(10-5)(102 -4) =X(10~2'6)kz (40)
If we set kz equal to 1011'4 I/mole-sec and employ a maximum value of
1 for X, this yields kr = 108*8 I/mole-sec as compared to the measured value
of 1010'3 I/mole-sec. The discrepancy of a factor of 30 cannot be reconciled
with any anharmonicity assignment or reasonably distorted structure for NO*.
The inclusion of excited electronic states simply does not help since their
lifetime would be significantly less than that of the ground state due to
•x-
their lower kinetic energy content E (eq. 39). We may thus conclude that
the (ONO) that leads to recombination cannot be a simple structural variant
of the ground state NO2 .
Another way to examine this anomaly is to consider a trajectory of
O + NO with impact parameter in the range ~ 3.0 A. The rate constant kx(NO*)
for such collisions is 1.3 x 1011 I/mole-sec. The average relative collision
73
-------
velocity vr is 7.5 x 104 cm/sec (300°K). If we make the arbitrary, but
reasonable, assumption that the range A of potential interaction between NO
o
and o extends over 1 A (1 x 10~8 cm) and that the average relative radial
velocity during this portion of the collision is 1/2 the initial velocity,
then the duration of the collision is:
TC Si -— = — = 5.3 x 10-13 seconds
The first-order rate constant k_t for the breakup of this collision
\t
complex of N02 may be taken as I/TC , and hence we can write:
= 7 x 10"2 1/raole
v.
This value of K is a factor of 28 larger than the value of 1Q-2 '6
computed for the tight collision complex and yields an excellent value for
kr when combined with a strong collision deactivation (\=1) . We are thus
forced to conclude that the TS complex for 0 + NO recombination is loose,
just as it is for all other radical recombinations. While this is not in
agreement with some shock tube results55 obtained recently, it is the only
way to explain the results of Pitts, Sharp, and Chan56 on the threshold
wavelengths for NO2 photolysis. The usual rule of a loose transition state
± o
complex for (0=No<<0) would have an N • • *0 distance of about 3.0 A. At an
o
N-«»0 distance of 1.8 A, the ion-pair curve"1 would have zero energy if we
neglect ion-dipole interactions and polarization. It is likely, however,
that polarization effects will stabilize the ion-pair curve out to even
larger distances, and this type of interaction S7 could account for the
relative ease of formation of the loose complex. Such a loose complex could
74
-------
also account for the much discussed anomaly in the fluorescence lifetime of
electronically 58excited NO,,.
In further support of this "loose" model of the NO + O recombination
is the atom exchange data for the exchange reactions: 57»59
O18 + NO16 a (018...N016)* si 18NO + O16
It was found that the rate of complex formation which is just twice the
observed exchange rate is 199'3 I/mole-sec at 300°K. This is about ten
times slower than the rate of formation of the loose "collision" complex
•x-
of NO2 we have just considered, but it corresponds very closely to the
rate of formation of a semi-tight NO2 transition state in which the bending
mode at 760 cm"1 is replaced by a restricted (~ 60°) 1-dimensional rotation.43
Such a semi-tight structure is required if the two 0-atoms are to become
equivalent, which is needed to allow the exchange. A loose TS with large
moments of inertia will have a centrifugal barrier which v/ill prevent the
two O-atoms from becoming equivalent.
Additional evidence comes from the findings obtained by Hippler et al.60
where a limiting bimolecular rate constant for 0 + NO — N02 in high pressures
of inert gases (1000 atm) is 1.8 x 101° I/mole-sec. This now coincides with the
rate of formation of a genuine loose TS for N02 ' and suggests that at these
very high pressures, every complex is quenched (TconiSiOn — 10~12"5 sec),
even rotationaly hot NO^ .
The high ionization potential of O2 (12.06 e.v.)49 will permit ion-pair
formation only at distances of about 1.3 A,which is practically the normal
o
covalent (1.28 A) bond length in 03. Thus, no loose transition state can be
f ormed.
75
-------
Again, supporting data comes both from O18 + O2 exchange measurements57'59
where the rate of complex formation is 109'0 I/mole-sec, only a factor of two
less than that found for NO,, and presumably corresponding to the rate of
formation of a semi-tight transition state. The difference in rates corres-
ponds very closely to the differences in AS0 . Further support is provided
by the data of Hippler et al.,60who find for the limiting bimolecular rate
constant k(0 + 02) ~ 109'*, only slightly greater than the rate of formation
of the serai-tight transition state, and indicating that no loose transition
state is possible for 03.
One would expect that halogen atoms with their large electron affinities
would similarly form loose ion-pair complexes with NO and this is indeed
compatible with the termolecular rate constants observed for the recombination
of Cl + NO,59 all in the range of lo10'5-*0'1 l/mole-sec. In distinct and
pardoxical contrast is the low recombination rate constant observed for
O + 02 + M - 03 + M5jl of about 108-2 lVmole2-sec at 300°K. This is clearly
incompatible with a loose transition state complex and can instead be inter-
preted in terms of a tight transition state complex. Using the same analysis
as for NO, we find:
AS°(O3) = —30.4 e.u. (atmospheres)
= —24.0 e.u. (moles/liter)
VM « 930 cm-1
E* ~ 26.5 kcal
300K
P* ~ 101'7
and kr(O3) = A.kz(10-4 %8) (101 -7) = X(10-3'1)kz. If ^ = 1 and kz = 1011 '*
I/mole-sec, then kr = 10s*3 12/mole2-sec, in excellent agreement with the
observed data.
76
-------
Activation Energies
The only activation energies which can be said to be reasonably well
understood are those for simple bond fission reactions. The bulk of the data
on these reactions support the loose transition state model for bond rupture,26
and the activation energies are simply equal to the bond dissociation energy
(DH)°-RT. Hence the reverse recombination reactions have zero activation
energies (for standard state, of mole/liter). This loose transition state,
originally proposed by Gorin, is compatible with a potential function which
extends out to form 2.5 to 3 times the covalent bond radius.
The activation energies for bimolecular processes do not fall into such
a simple pattern. If we restrict our attention to what has been called the
intrinsic activation energy of a reversible reaction, i.e., the activation
energy in the exothermic direction, they are generally low, in the range
0-15 kcal/mole. This is true both for atom metathesis reactions and for
addition reactions. Perhaps 80 percent of measured, intrinsic E&ct fall in
the range 8 ± 3 kcal/mole, while over 90 percent are in the range 8 ± 5
kcal/mole. A few fall conspicuously outside of this range, and within
homologous series of reactions there are occasionally some curious deviations
from general trends.
A number of semi-empirical efforts at treating metathesis reactions, such
as the bond energy-bond order model61>62 (BEBO) have succeeded in estimating
Eintrinsic to — 2 kcal/m°le- More recently, Alfassi and Benson63 have demon-
strated that Extrinsic can be represented by simple formulas of the form:
E = 13.0 - 3.3 I (4i)
or
E = XA + Xc (42)
or
E = FA • FC (43)
77
-------
where Eintrinsic is in kcal/ra°le> I is tne SUJn of the electron affinities
of the entering (A) and leaving (C) radicals (or atoms) in the metathesis
reaction:
A + BC ^ (A • • -B • • 'C) - AH3 + C + energy
In relation (42), XA and Xc are constants, characteristic of the radicals
A and C, respectively, and turn out to correlate with their ionization potentials
F and FQ are similar group constants.
All three relations are capable of estimating E for broad categories
3-Ct
of reactions to an average of + 1 kcal and a maximum deviation of about 2.6
kcal/mole.
In a few cases larger deviations can be explained on the basis of dipole-
dipole repulsion (CF3 + HX). In the abstraction of halogen atoms (B = halogen) ,
there must be a strong influence of the migrating atom B on the activation
energy, but this is neglected in the-correlation. The data currently available
are not sufficient to further examine this point.
We have already noted that addition reactions of atoms or radicals to
Pi bonds are especially sensitive to the ionization potentials and activation
energies of the reacting pair. This is strikingly parallel to the empirical
finding for metathetical reactions and suggests that the ability to form
donor-acceptor (ion-pair) complexes plays an important role in determining
the crossing of the two potential energy surfaces represented by reactants
and products.
There are a few examples of exceptionally high activation energies in
exothermic metathesis reactions which are worthy of further examination.
78
-------
Two examples are: CO + O2 -* CO2 + O (Eact — 47 kcal) and CO + N02 -*
CO2 + NO (Eact ~ 25 kcal) which are exothermic by some 8 and 46 kcal,
respectively.
If we examine the intermediates formed in each case, we find that they
are very endothermic biradicals, such that the intrinsic activation energy
is in each case only 8-10 kcal/mole above the endothermicity of the addition.64
If we neglect such exceptional cases, then we find that the intrinsic activ-
ation energies for exothermic addition reactions fall into the same range as
for metathesis reactions, namely 8 ± 5 kcal/mole. Data on these activation
energies is not abundant, and so empirical analyses have been made in an
effort to correlate them with simple bonding properties.
79
-------
B. RATE PARAMETER EVALUATION AND ESTIMATES
Extensive efforts are underway throughout the world to accurately
model atmospheric chemistry. Whether the efforts are directed toward
modeling tropospheric or stratospheric phenomena, there is a need to evaluate
existing rate constant data and to estimate unknown rate parameters in a way
that is consistent with current knowledge for similar reactions. We are
developing an explicit reaction mechanism to explain data obtained in smog
chambers and we are constantly faced with the fact that too few accurate
rate data for elementary reactions are available.
Since the kinetic data on particular families of reactions ranges from
"excellent and extensive" to "nonexistent," a variety of methods must be
used for evaluation and/or estimation. As a general guiding principle, it
has been found that best results are obtained when reactions are treated as
"families" rather than as individuals,because only rarely are enough data
available for an individual reaction to make a meaningful evaluation.
A second guiding principle often overlooked is that an estimate
or evaluation is not useful unless accompanied by a fair assessment of its
probable accuracy. Since A-factor and activation energy combine to give a
single rate constant, we have adopted the method of propagation of errors
to estimate the uncertainty in rate constants, based on the probable uncer-
tainties associated with A-factor and activation energy. This estimate of
uncertainty is very useful since it is a quantitative measure indicating
over what range an estimated rate constant can be varied legitimately.
80
-------
Alkoxyl Radical Decomposition Reactions
The decomposition reactions of alkoxyl radicals provide a good example
of a family of reactions for which an adequate number of accurate studies
have been made. Most of the studies have been made on t-butoxyl radicals,
but several other radicals have been studied as well. All the studies
were determinations of relative rate constants and so we returned to the
original data and recomputed it on the basis of current values for the
reference reaction rate constants.
Three different reference reactions have been used:
9' M ONO
RjCR2R3 + NO -* RiCRjjRg (44)
?'
IH
(CH3)3CH -» R^R-jR;, + (CH3)3C (45)
9' 9
+ NO - R±CR2 + HNO (46)
Values chosen for k^ were those obtained by Batt et al.,86 and are
in good agreement with those obtained by Golden et al.33; the value of k4s
chosen was that determined by Berces and Trotman-Dickenson66 ; the values
chosen for k46were derived from disproportionation/combination ratios and
values of k44.34 >65 Other reported data were not used because their reference
reaction rates are not sufficiently well known.
The recalculated data are presented in Figures n through 14, and the
corresponding Arrhenius parameters are presented in Table XVI . The data
81
-------
Table XVI
EXPERIMENTAL VALUES FOR RO" DECOMPOSITION RATESa
Radical
EtO'
i-PrO'
s-BuO-
t-BuO*
log A
13.7
16.1
16.4
14.9
15.1
log E
22.1
20.6
18.0
15.3
16.2
ASg
33.4
37.8
37.7
41.2
log Ar
8.2
8.2
8.0
8.0
lo* Aest
13.7
14.6
14.4
15.2
E'
22.1
17.4
13.9
14.2
16.3
Ref .
67
68,69
70
65d
71-74
Units: E in kcal/mole; Ar in M-1 s"1; A in s-1.
for t-BuO* are the most extensive (Figure 11), covering nearly four orders of
magnitude. The individual sets of experimental data taken independently show
a rather wide range of Arrhenius parameters and appear to be inconsistent,
but taken together, the actual data give a reasonably good straight line
with parameters, log k/s'1 = 15.1 - 16.2/9. Given the entropy change of
the reaction, As£ = 41.2 Gibbs/mole, the A-f actor for the reverse reaction
is Ap = 107 -8 M"1 s"1 , a value very close to that for the reaction of methyl
radicals with isobutene (log A = 8.0).75 This suggests a self -consistent
method for evaluating and codifying the limited data available for the other
alkoxyl radical reactions: choose an A-f actor for the reverse reaction and
find the corresponding activation energy. If this unified scheme is used, the
alkoxyl decompositions can be considered together as a class, rather than
individually.
The decomposition of an alkoxyl radical is the reverse of the addition
of an alkyl radical to the carbon atom of a carbonyl group, which is analogous
82
-------
o
a
6
83
-------
o
X
V
S
•f
+J
w
S t
9
CQ
n
4)
a
•H
•H
•o
«
tO
»
«H
4>
K
•
0
>
£1
g
84
-------
to alkyl radicals adding to the 2-position of a primary olefin. Since data
are only available for alkyl radicals adding to the 1-position of primary
olefins, the assumption was made that the A-factors for addition to both
ends of an olefin double bond are the same and only the activation energies
differ. Thus, A-factors for analogous alkyl radical plus olefin reactions
were chosen from the tables of Kerr and Parsonage,7& corrected for any
difference in reaction path degeneracy, and applied to the alkoxyl reactions.
Assumed A-factors for the reverse reaction, Ap, are summarized along
with ASn, log A , and corresponding activation energies E in Table XVI. A
plot of E vs AH^ is presented in Figure 15 and gives a good straight line:
E = 12.8 + 0.71 AH£ AH£ > 0 (47)
=12.8 AHg < 0
This equation predicts activation energies with an uncertainty of about
±.0.5 kcal/mole. It predicts that the reverse reaction has an activation
energy given by:
Er = E - AH° + RT = 13.6 - 0.29 AH£ (48)
Although these equations apply to ~ 400 K where most of the experiments
were carried out, the estimated activation energies will be negligibly
different at ~ 300 K.
Estimated decomposition rate constants for a number of alkoxyl radicals
at 300 K and atmospheric pressure are presented in Table XVII. Fall-off
corrections were obtained by use of the Emanuel RRK Integral Tables.76'77
For the experimental data available, the estimated rates are accurate to
about a factor of two, as demonstrated by comparing estimated and observed
rate constants (Figures 11-14). The differences apparent between the estimated
85
-------
25,
20
8
^
815
^
In
10
I I
E(400K) = 12.8 + 0.71 (AH|,)
8 9 10 11 12 13
AH* / kcal mol'1
n
SA-2SS4-47R
FIGRJRE 15 Correlation Between Activation Energy E and Enthalpy
of Reaction
86
-------
Table XVII
ESTIMATED HO' MtX'OMPOSITION RATES
Radical
C-CO-
CC-CO-
6
i
c-cc
ccc-co-
6
cc-cc
c
c-co.
6
IBC-CC
HOCCC-CO'
6
IIOCCC-COII
0
( 110) 2CCC -COI1
9
UK».,CCC-C(OII)2
6
(lK))3CCC-C(01l)a
c
i
IIOC-CO-
o o'
II 1
cc-cc
A1.JJ
12.4
9.4
7.1
8.9
2.6
4.3
6.8
(3.5)°
8 .7
-9.7
-9.6
-30.9
-24.5
11.4
(8.2)e
-5.1
^R
33.4
35.0
37.8
36.3
37.7
41.2
38 .0
36.6
39.2
39.2
37.7
37.7
37.7
40.3
log Ar
8.2
8.0
8.2
7.5
8.0
8.0
8.O
7.1
7.1
6.8
6.8
6.5
7.5
7.5
log A(s-')
13.7
13.8
14.6
13.6
14.4
15.2
14.5
13.3
13.8
13.5
13.2
12.9
13.9
14.5
21.6
19.5
17.8
19.1
14.6
15.9
17.6
(15.3)e
19.0
12.8
12.8
12.8
12.8
20.9
(18.6)e
12.8
k/U
00
O.OO3
0.6
0.5
0.8
0.7
0.5
0.8
1
1
1
1
1
0.9
0.8
kdiiln-1)
2.1 x 10^
1.7 x 10'
1.6 x 10*
2.9 x 10'
2.9 x 10s
1 .5 x 10s
2.8 x 103
(2.i!xl06)u
2.1 x 10*
2.1 x 10b
1 .0 x 10s
5.2 x 10*
2.6 x 10s
3.6 x 10°
(2.2 x 102 f
8.2 x 106
? ? • L
Notation: IIOC-CC represents IIOCII^CIICII, - 11OC1I., + IICCIIj , etc.
b
A-liic(or for analogous alkyl rudicul i- ulkene association reaction.
CKC.S( l^.B I 0.71 illjj (kcal/woJe) .
K.ill-oif us I united from RUK Tables lor 1 atm, 3«>00K.
llasud f>n (iroii|> Ailditivity , not on expcrimental Allf lor propane-1 ,2
Rule constunls 1'or 300 K .incl 1 aim. air.
-diol.'
89
87
-------
and experimental rate constants are due to the ±0.5 kcal/mole uncertainty
in estimating the reaction activation energy and round-off errors on the
A-factors.
Estimates made when no experimental data are available can be appraised
by using the propagation of errors equation. Since A-factor and activation
energy are usually estimated independently, the uncertainty in log k can be
written
cr2 = a2 + a2/92 (49)
log k log A E
where cr , a , and cr are standard deviations in log k, log A, and
log k log A E
activation energy, respectively, and 6 = 2.303 RT. Since log A is probably
uncertain by ± 0.5, and the activation energy is uncertain by about + 1
kcal/mole, the value for a « 0.88 at 300 K, and k is uncertain by
log k
about a factor of eight. This represents a relatively favorable case for
estimations, since an adequate amount of kinetic data is available, and
it is fairly consistent. For the reactions discussed below, very little
data is available, and the reliability of the estimates is much lower.
88
-------
Alkoxyl Radical Reactions with Oxygen
7 o
The only reliable Arrhenius parameters known for this class of
reactions are:
CH30 + 02 -. CH3O + H02 log k/M-1 s-1 = 8.5 - 4.0/8 (50)
Rates for other members of this class can only be estimated after making
assumptions regarding variations in A-factors and activation energies. The
concomitant uncertainties in estimating rate constants will be relatively
large since little is known about such variations.
The A-factors for this group of reactions are expected to be similar to
that for methoxy radicals, aside from the reaction path degeneracy (n) factor;
therefore, log A can be estimated as follows:
log Aegt/M-1 s-1 = 8.0 + log n (51)
Estimates for activation energy variations are rather problematical,
especially when EQ is low. Two alternative methods can be used:
cl
(1) Assume E& is constant for the entire homologous series
(2) Assume that an empirical relationship that holds for other
radical reactions applies to this series as well.
A simple empirical relationship79 that gives E with an uncertainty of about
cl
±. 3 kcal mol"1 for exothermic H, OH, and CH3 reactions is given by equation (52)
E& = 11.5 + 0.25 (AHjj) , (52)
89
-------
where £HR is the enthalpy of reaction. For reaction (50) , equation (52)
predicts Ea = 5 kcal mol"1, about 1 kcal mol"1 too high. Equation (52) has
two parameters and can be modified in two different ways to give the proper
E& for reaction (44):
E = 10.5 + 0.25 (AHP) (53)
a n
Ea = 11.5 + 0.29 (AHR) (54)
Rate constants for a number of alkoxyl radical reactions were estimated
by the three methods and are presented in Table XVIII. Considering the large
uncertainty associated with equation (45) and the low activation energies,
the estimates in column III of the table are highly uncertain and may well
be upper limits to the correct rate constants. Similarly, rate constants
in column I of the table may be near the lower limits.
The overall uncertainties for this family of reactions may be estimated
as before. Log A is probably uncertain by ±. 0.5 and the activation energy
is probably uncertain by an average of + 1.5 kcal/mole. Thus, CT^oe jj « 1.2,
and the estimated rate constant is uncertain by about a factor of 16. If
the activation energy is uncertain by an average of ~ ±. 2.5 kcal/mole, the
estimated rate constant is uncertain by a factor of ~ 80.
90
-------
ra
§
i—i
EH
O
3 °
t* +
« §
f~H
oS ••
^ |
M
O
^— v
+ oort
•°. 2
rH
rH X
II
M
m
N
O
CO <3
o
rH X
II
q
^
u
cS
W
I-H
-P
0)
0)
I
§
•H
-P
U
01
0)
OH
^-^
H
•H
e
•*
*
j
^
^
«
g
^x
10 CD to to in to
o o o o o o
X X X X X X
O CO CO t^ 00 d
CM rH rH CO in M
in in m to in cc
O O O O O O
X X X X X X .
O CM (N m in rH
• •••••
CM 00 00 rH CO rH
m in m «f in «
O O O O O O
rN ?N ?S rS rS rS
O CO CO t~ CO t*
• •••••
CM rH rH 1 1 1 1
o w e -H c n
I
m
O
•H
cd
CO
-p
a
a)
•p
CO
C
O
U
0)
-p
cd
0)
•a
•P
m
•H
-------
Alkoxyl Radical Isomerization Reactions
The importance of alkoxyl radical isomerization reactions has been
inferred from smog chamber data,80 as well as from more qualitative
considerations.81 The estimation of the isomerization rates is relatively
straightforward, but the estimates are somewhat uncertain, as discussed below.
A-factors for 5-membered ring (5R) and 6-membered ring (6R) isomerizations
were estimated to be 1011'2 s"1 and 1010 '9 s"1 (per H-atom), respectively. The
estimate for the 5R transition state was made by noting that in tying up the
methyl and ethyl internal rotations, the change in entropy is about —6.6
Gibbs/mole; subtracting another 0.3 Gibbs/mole for the reaction coordinate,
we obtain log A =11.7 for three abstractable H-atoms. Thus, for each
5R
abstractable H-atom, log A5R (per-H) = 11.2.
For the 6R transition state, a model transition state was used. For the
decomposition of ethyl vinyl ether (EVE), log A = 11.4 at 700°K. If log A
is about the same at 300°K and S°(EVE) = 82.6 Gibbs/mole,82 then the entropy
of the transition state is 74.3 Gibbs/mole. In comparing the EVE transition
state and that of n-butoxyl radical, EVE has some double bond character, and
that of n-butoxyl will be looser by about 0.6 Gibbs/mole. n-Butoxyl has one
more hydrogen atom, worth about 0.2 Gibbs/mole, and has spin, contributing
1.4 Gibbs/mole. Adding all of these corrections, gives S° = 76.5 and
log A = 11.4 for three abstractable H-atoms; thus log AgR(per H) = 10.9.
The uncertainties in these estimates are probably + 4 Gibbs/mole and log A
is uncertain by + 1.
92
-------
Activation energies may be estimated from the activation energies
for H-abstraction by alkoxyl radicals2a by adding a "strain" energy of
0.5 kcal/mole for 6R reactions and 5.9 kcal/mole for 5R reactions.82
These activation energies are rather uncertain, probably ±. 2 kcal/mole.
The combination of the two sources of error by the propagation of errors
formula gives an estimated uncertainty in log k of ± 1.8 at room
temperature. Thus, the rates are estimated to be uncertain by about a
factor of 60.
The method for estimating these rates is summarized in Table XIX, and
estimated rates for several alkoxyl radicals are presented in Table XX.
All reactions are assumed to be at the high-pressure limit.
93
-------
Table XIX
RO' ISOMERIZATION REACTIONS—ESTIMATION PROCEDURE
E = E (abstraction) + E (strain)
Hydrogen Abstracted
RCH2-H
RCH(OH)-H
RC(OH)2-H
E (abstraction), kcal/mole
7.2
6.0
4.1
4.1
4.1a
Strain Energy
5-membered ring
6-membered ring
5.9 kcal/mole
0.5 kcal/mole
A-Factor (per abstractable H)
5-membered ring
6-membered ring
A = 1011-2
A = 1010'9
Estimated.
94
-------
Table XX
ESTIMATED RO' ISOMERIZATION REACTION RATES
a
Reaction
OCCCC - HOCCCC
0 OH
CCCC - CCCC •
HOCCCCO -* HOCCCCOH
0*
HOCCCCOH -» (HO)2CCCCOH
0'
(HO)2CCCCOH - (HO)2CCCC(OH)2
0
(HO)2CCCC(OH)2 - (HO)3CCCC(OH)2
OH QH
1 .1
cccco • - CCCCOH
log A(s-1)
11.4
11.7
11.2
11.2
10.9'
10.9
11.4
E(kcal/mole)
7.7
13.1
6.5
6.5
4.6
4.6
7.7
kdnin-1)
3.7 x 107
8.6 x 103
1.9 x 10s
1 .9 x 10s
2.2 x 109
2.2 x 109
3.0 x 108
OH
Notation: CCCCO*
OH OH
.1 I
CCCCOH represents CH3CHCH2CH20»
OH
CH2CHCH2CH2OH
95
-------
Reaction of NO, with HOg
These species have long been thought to react via a radical dispropor-
tionation to give HONO and 02:
H02 + N02 - HONO + 02 (55)
Recently, however, Niki and coworkers83 have studied the reaction and could
not detect any HONO. They concluded that the predominant reaction is:
M
H02 + N02 * HOONQ2 (56)
This conclusion is also supported by some of Heicklen's data,84 but the
reaction was not considered explicitly, and k13 was not determined. Both
Heicklen85 and Cox86 found that the loss rate due to H02 + N02 is about
2-10 x 107 M"1 s-1. This value is uncertain, however, because they did not
consider the effect of HOON02. Calvert and coworkers 87 have also observed
H02N02 and have attempted to obtain some kinetic information from the chemical
system, but the system is too complicated to allow unambiguous interpretation.
Both Niki and Calvert observed the lifetime of HO2N02 to be ~ 6-8 minutes
and both ascribed the loss mechanism to wall reactions. Thus, quantitative
kinetic information on the homogeneous reaction is virtually nonexistent.
Because H02N02 can act as a radical reservoir or sink, the kinetics of
H02N02 can have far-reaching effects in photochemical smog and in stratos-
pheric chemistry. According to this scheme, HO2 and NO2 react to form
H02NO2, which can "store" the reactive species until it homogeneously decomposes
at its natural unimolecular decomposition rate. At that time, it releases the
HO- and NO- back into the reaction mixture to react further with the other
& A
species present. Thus, it is important to estimate the rate constants for
association and decomposition.
96
-------
As a starting point for estimating the rate constants, we can use the
rates determined by Hendry88 for the reaction of peroxyacetylnitrate (PAN) :
0
CH-COONO, -* CH.COO + N00 log k/s'1 = 16.2 - 26.8/9 (57)
O £, O £, *-*
This reaction is analogous to that for HO2N02 and its Arrhenius parameters
provide a good starting point. The major uncertainty is whether the
[OO-NO2] bond dissociation energy in PAN is equal to that in H02N02 . For
most radical association reactions there is no activation energy. Thus the
A-factor for the association reaction can be derived from that of the
decomposition step and AS^ for the reaction. In the case of PAN decomposition,
AS§ for the reaction is estimated to be 42 Gibbs/mole, giving log A_57 =8.8
for the association. This value is not unreasonable for radical association
reactions, but may be a little low.
A detailed estimate for the entropy of H02NO2 was made based on the
value of 72.2 e.u. for MeONO289 by adjusting for the change of internal
rotor from a methyl to an OH and including the corresponding rotational
barrier change due to the loss of two hydrogen atoms, and correcting for
spin gives S^(HO2NO2) = 71.6 e.u. The frequency assignment for the molecule
is given in Table XXI . The first five frequencies listed are those actually
observed by Niki, et al.83; the remaining frequencies are based on those for
FNO3, H2O2, and HNO3, with the low frequency torsions adjusted to give
S°(HO2N02) = 71.6 e.u. The values used are compatible with the known
torsion barriers for 0-OH and O-NO2. In the transition state, the N-O stretch
is assumed to become the reaction coordinate, and the N02 group is assumed
to be free rotor. Other vibrational frequencies were lowered as in Table XXI
to give an entropy for the transition state that yields the desired high
pressure A-factor. If E56 = 0 and Iog10 AS6 = 9.0 (similar to PAN), then
log A_56 = 15.9. The results of the calculations are given in Table XXII
97
-------
Table XXI
FREQUENCY ASSIGNMENT FOR H02N02
Frequency in
Molecules
(cm-1)
3540a
1728a
1304a
803a
1396a
633
500
735
125
400
880
200
Frequency in
Transition State
(cm-1)
3540
1728
1304
803
1396
Reaction coordinate
200
435
Free rotor
100
580
150
Type
OH stretch
N03
N03
N03
OH bend
NO stretch
NO2 rock
NO2 wag
O-N02 torsion
OOH bend
00 stretch
HO-0 torsion
From reference 83,
98
-------
Table XXII
RRKM CALCULATED k/k FOR HO,NO, DECOMPOSITION
00 £ £
E = 23.1 kcal/mole
log A/s-1 = 15.9
E = 25.1 kcal/mole
log A/s-1 = 15.9
E = 27.1 kcal/mole
log A/s-1 = 15.9
Collision Efficiency
0.4
0.46
0.56
0.65
0.5
0.50
0.60
0.68
0.6
0.53
0.63
0.71
99
-------
for three high-pressure activation energies and three values of Y, the
collision efficiency. The values of k/k are near unity at 1 atm and
300 K and are presented as a function of E_56 in Figure 16 for two values
of the collision efficiency that are expected to bracket that of N2 or O2 .
These results show that reactions (56) and (-56) may be very important in
controlling the concentration of NO2 in smog chamber experiments. In the
following section, the effects of this reaction will be illustrated by
computer simulations.
The major question here is whether HO2N02 and PAN are expected to have
the same activation energy for decomposition. Since this question cannot be
answered with any confidence, the activation energy E_56 may be used as an
adjustable parameter in simulating smog chamber data. Although this procedure
is not very satisfactory, it does illustrate the necessity for accurate rate
data if this issue is to be resolved.
100
-------
1.0
0.5
7
0.6
0.4
23
25
EM(kcal/mole)
27
SA-2554-51
FIGURE 16 Falloff Calculated by RRKM Theory as a Function of
Activation Energy for the Reaction H02N02
H0_
N0
101
-------
Simulations of Smog Chamber Experiments
A major use for an explicit photochemical smog mechanism is to establish
U.S. Environmental Protection Agency regulations for controlling pollutant
emissions into the troposphere. While it is important to validate a proposed
mechanism, it is difficult to use real atmospheric data for this purpose
because of the wide variety of organic reactants, the complexity of products,
and the presence of capricious transport phenomena. Smog chambers are often
employed for carrying out experiments on relatively simple reaction mixtures
thought to represent pollutants in the real urban atmosphere; the results
obtained are useful in testing assumed mechanisms because the effects of
transport phenomena are minimized while temperature and light intensity can
be controlled.
Associated with smog chambers, however, are several troublesome problems.
The most obvious problem is that the pollutant concentrations are generally
higher in a smog chamber than in the real atmosphere; thus when a reaction
mechanism is applied to real atmospheric problems, there is an extrapolation
into regimes where the mechanism has not been validated. This extrapolation
could tend to magnify errors in the chemical mechanism and thus it is important
to devise a mechanism which is as accurate as possible in relation to the
smog chamber data. A second and most troublesome problem is that of "chamber
effects" in which chemical species interact with the walls of the chamber or
even appear to desorb from the walls. This manifests itself in a poor mass
balance between reactants and products, and in the sometimes observed necessity
for postulating a radical source associated with the chamber. Although every
attempt must be made to understand the sources of such problems, there is
always the possibility that an effect ascribed to "chamber effects" is really
102
-------
due to a deficiency in the postulated reaction mechanism; conversely, an
error in the reaction mechanism might conceal effects better ascribed
to the smog chamber.
Since the postulated reaction mechanism must be tested against smog
chamber data, it is important that the data be of high quality and that
care be taken to minimize "chamber effects." We have been using data
reported by Pitts and coworkers90 at the Statewide Air pollution Research
Center located at the University of California, Riverside, who have taken
great care in an effort to minimize chamber effects and to characterize
their experimental conditions.
The reaction mechanism is complex and partly speculative, and therefore
not all elementary reaction steps have been individually measured, yet many
important reaction rates are now well known.91 One may hope that the effects
of the unknown rate constants will not predominate in the reaction mecha-
nism. Calvert and coworkers,1 Pitts et al.,21 Niki et al.,92 and Hechl
et al.,93 have made major strides in elucidating the mechanisms of photo-
chemical smog. Our efforts are built upon their work, with the emphasis
placed upon systematically estimating and evaluating families of reactions,
as described in the preceding sections. Our guiding philosophy has been to
start with a "first guess" mechanism, consisting of well-known reactions and
our own best estimates for other reactions, and then to make any refinements
necessary, within the uncertainties of the experimental data and estimated
rate constants.
Our work thus far has been primarily concerned with the photooxidation
of propene, butane, and propene/butane mixtures. Although we are continuing
103
-------
to work on the reaction mechanisms for these species, we feel that the
postulated mechanisms are substantially complete, and that it is possible
to point out the areas of greatest uncertainty.
Reactions of n-Butane
Since n-butane is thought to be representative of the straight chain
alkanes present as pollutants in the urban atmosphere, it is used as a
model compound in smog chamber experiments. The experiments are performed
on air mixtures containing a few ppm of n-butane and somewhat less NO and
N02 ; CO is often present as well. The initial concentrations and relative
ratios of RH to NO and NO to N02 have been varied somewhat in different
experiments to provide data over a range of initial conditions.90
The major reaction pathways for carbon-containing species in the
n-butane system are depicted in Figure 17. The rate constants shown corres-
pond to 300 K and one atmosphere of air and are expressed in units of
min"1 and ppm"1 min"1. For bimolecular reactions involving 02 , the concen-
tration of 02 (2.1 x 10s ppm) has been multiplied by the appropriate
bimolecular rate constant (units of ppm"1 min"1) to give an effective
first-order rate constant (units of min"1). The rate constants shown represent
our best estimates or the best experimental data available.
The initial attack of OH radical on n-butane is known to give ~ 86%
sec-butyl radical and ~ 14% n-butyl radical.91 These radicals combine
very rapidly with O2 to give the corresponding peroxyl radicals. As long
as NO is present, the peroxyl radicals oxidize NO to form N02 and alkoxyl
radicals, which can go on to react as described in the preceding sections.
104
-------
at
-p
3
c
o
9)
03
g
B"
4
105
-------
s-Butoxyl radicals can either react with oxygen to give 2-butanone and
H02 , or they can decompose to give acetaldehyde and ethoxyl radical; the
major fate of ethoxyl is to react with oxygen to give acetaldehyde. Although
acetaldehyde and 2-butanone react with OH and photolyze, they disappear
only slowly, and the ratio of their yields gives a sensitive measure of the
relative rates for loss of s-butoxyl: decomposition versus reaction with O2 .
Since the s-butoxyl decomposition rate is known fairly accurately, and its
reaction with 02 is rather uncertain, the rate constant for the latter
reaction can be adjusted to give the proper relative value.
n-Butoxyl radical also can react with 02 or slowly decompose, but it has
the additional reaction channel of isomerization. In fact, the estimated
isomerization rates are so fast that the other possible reactions hardly
compete. Examination of Figure 17 shows that about 98% of the original
n-butoxyl radical formed ends up as the polyhydroxylated aldehyde (HO)3CCH2CHO
and only a small amount appears as butanal and other products. The fate of
(HO)3CCH2CHO is not known, but if it dehydrates, the product HO(CO)CH2CHO
might photolyze quickly to give free radicals that can continue the chain
mechanism. Although only 14% of the butane reacts by the n-butoxyl reaction
pathways, n-butoxyl accounts for about 36% of the NO oxidized directly by
alkoxyl radicals. This is directly attributable to the isomerization reactions
A reaction not included in our mechanism which might dramatically alter
the course of reactions is:
R^R2 + 02 - R1CR2 + H02 (58)
0 0
106
-------
If this reaction is fast compared to simple addition of O2 to form peroxyl
radical, the isomerization steps would not have an opportunity to take place,
and the character of the n-butane reaction would be quite different from
that described above. Reliable experimental data are needed in order to assess
the importance of reaction (58), but we would not expect it to compete effectively
with addition of 02 , which has the same A-factor and no activation energy.
Another area of uncertainty in the mechanism that deserves mention is
the photolysis reactions of aldehydes and ketones. Photolysis rate constants
and products for many of the carbonyl compounds are not known and must be
estimated. Radical photolysis products serve to accelerate the overall reaction
and so are very important. In the absence of good data, many of the rates have
simply been estimated by analogy with those rates that are known. In the butane
simulations presented below, a radical influx from the chamber walls must also
be assumed in order to reproduce the observed rate of butane consumption. It
is quite possible that the assumed radical influx is merely compensating for
an underestimate of the photolysis rates of carbonyl reaction products, or
some other reaction sequence that has been overlooked so far. Further exper-
iments are necessary to clear up this point.
Two computer simulations of the smog-chamber experiment on the n-butane
system are presented in Figures 18 and 19. The first simulation (Figure 18)
represents our "first guess" mechanism, consisting of experimental rate constants,
where available, and our best estimates for unknown rate constants. The activ-
ation energy for HO2NO2 decomposition was assumed to equal that of PAN (26.8
kcal/mole). Using these rates, an influx of ~ 10~3 ppm min-1 of HO2 radicals
is necessary to approximate the correct conversion rate of n-butane. It is
noteworthy that H02NO2 acts as a radical reservoir—storing H02 radicals from
the early period of the reaction and slowly releasing them in the later stages.
107
-------
12
4.1
10
3.90
3.80
O
<
cc
o
O
o
01
0.3
0.2
0.1
0
»-*—.
BUTANC
H02N02
45
90
270
315
360
135 180 225
TIME/MINUTES
(a) Simulation of Run EC-41 in Reference 90. Initial Concentrations:
Butane, 4.03 ppm; N02, 0.068 ppm; NO, 0.524 ppm.
The points are experimental results; the lines represent the
computed concentration profiles for butane and peroxynitric acid.
Radical input is 1 x 10~3 ppm min"1 of HO,. The rate of decom-
position of H02NO2 has an assumed activation energy of 26.8 kcal/mole.
T
T
I*'-.
90 135 180 225 270 315 360
(b) Simulation of run EC-41, as in 7(a) , showing the Concentrations of
NO2 , NO, and ozone.
FIGURE 18
108
-------
PI
n
i-.
U)
UJ
I-
g,
ft
X to
to
M CIS
M fi
•H OJ
•P in
ti
•H
r-l CT
g *„
3§
Oj
O
• ti
O O
O^ "H
-P
0) -H
o w
c o •
Q) C^ Q)
rl S rH
Q) O O
«H O B
a> cu \
OJ -O rH
a)
d Oj
r-l rH >
3 I -H
s e -p
-H -H O
W 6 01
IAIdd/NOIlVHlN30NOO
109
-------
Much of the nitrogen is tied up as H02NO2, and relatively less is present as
N02, affecting both the PAN yield and 03 production. It may be argued that
HO2NO2 is expected to contribute to the experimental N02 measurement (as does
PAN), and thus the NO2 data may represent the sum of contributions from
H02N02 and N02. This question about the correct interpretation of the exper-
imental N02 concentration adds an extra element of uncertainty in comparing
the simulation to the experiment and must be resolved by laboratory experiments,
Another feature of this first simulation is that ozone and PAN production are
greatly underestimated as is the consumption of butane. This is due to the
quenching effect HO2N02 formation has on the reaction mechanism.
If the H02N02 decomposition activation energy is less than 26.8 kcal/mole,
the influence of H02N02 formation becomes less important. If the activation
energy for decomposition of H02N02 is assumed to be ~ 23 kcal/mole, H02NO2
has little effect , and the simulation is in much better agreement with
experiment (see Figure 19). Moreover, an influx of 2 x 10~4 ppm min"1
of radicals must be assumed to match the observed conclusion rate of n-butane.
Note that PAN and ozone formation are near the experimental values and HO2NO2
concentrations are too low to be shown in the figure. Our experience with
simulations of this nature is that the activation energy for HO2NO2 decompos-
ition probably falls somewhere between 23 kcal/mole and 25 kcal/mole, but
this number is highly tentative, and we must await an experimental determination
before this major uncertainty can be resolved.
Once the overall mechanism has been brought into good agreement with
experiment, various rate constants can be adjusted within their uncertainties
to bring the various product yields into agreement. For example, our first-
guess mechanism predicts .018 ppm of 2-butanone and .17 ppm of acetaldehyde
110
-------
after 360 minutes, but .125 ppm and .082 ppm, respectively, are observed
in the experiment. As mentioned earlier, these product yields depend
mainly on the following reactions:
O* 0
CH3CH2CHCH3 -» HCCH3 + CH3CH2 (59)
0
II
-* CH3CCH2CH3 + H02 (60)
Since the rate of reaction (59) is fairly well known, and the rate of
reaction (60) is quite uncertain, the latter can be changed to 8.8 x 105
min"1, in order to produce the correct product yields. Unfortunately, not
many different product species were measured in the experiments, making it
impossible to assess the estimated rate parameters for many of the reactions.
Reactions of Propene
The reactions of alkenes in photochemical smog are quite different
from those of alkanes. Not only is hydroxyl radical attack important, but
the reactions of oxygen atoms and of ozone must also be considered (see
Figure 20). Generally, the reactions which involve addition of these species
to the double bond are very fast and result in alkenes reacting substantially
more quickly than alkanes in the smog environment.
Although the total rate constants for the reactions of O, O3, and OH
with propene are well known, neither the products of the reaction, nor
specific branching ratios into the various product channels are known with
certainty for environmental conditions. Thus, the propene mechanism relies
considerably on the products observed in the smog chamber data to define
specific reaction channels.
Ill
-------
OH
un2=^ru^n3
CH0=CHCH,
2 «*
CH2=CHCH3
_ 0 ,-4 1 : T — *~ nucii utiUH,
3.8 x 10* ppm-1 min-1 * \
02 /6.7xl04 NV 2.7 x 10s
V min-l\ min-1 Q
X y ^v "
HOCH2CCH3 ^ HOCH2 ' + CH3CH
°/\°S
/ CH20 + H02
/ o2 \
HOCH20' >- HCOH + H02
0
0(3P) •
!,, T 1- TH.^H PH
1.8 x 103 min-1 J '
0
fW3pN II
0( P) » ^H.O/ + rH.ro *
1 .8 x 103 min-1 2 J ^
0
0(3p) II °2
1.8 x 103 min-1 2
0 0
03 ll II 0,
7.5 x 10-3 min-1 ' ° 2
?
7.5 x 10~3 min-1
FIGURE 20 Reactions of Propene
112
-------
Unlike the butane system, it has been found that propene reacts quickly
enough so that it is not necessary to assume a constant influx of radicals
due to chamber effects. Rather, one can postulate that HONO is present
initially (due to H2O + NO + NO2 5± 2 HONO) and provides a radical source
when photolyzed. Once the reaction has been initiated, further chamber
sources of radicals need not be postulated. On the other hand, if a chamber
source of radicals is assumed, as in the butane system, good results are
still obtained.
The most important reactions of propene are shown in Figure 20 . As
noted above, the overall rate constants for the reaction of OH, O, and 03
are known, but the branching ratios were obtained by computer simulations
of the smog chamber data. The aldehydes produced in the initial reactions
can be photolyzed to give shorter carbon skeletons and free radicals; peroxy-
acetyl radicals formed in the initial steps can react with N02 to give PAN
or can oxidize NO to NO2 .
A typical simulation of the smog chamber data is presented in Figure 21.
Inspection of the figure shows that product yields are well represented by the
assumed mechanism; while better agreement certainly would be desirable,
variation between smog chamber runs suggests that there are also some uncer-
tainties in the reported data which contribute to lack of precision in the fit,
Conclusions
There are many uncertainties associated with the complex mechanism for
degradation of hydrocarbons in photochemical smog. In several cases, we have
used estimation techniques to exploit the limited experimental data for
reactions important in these mechanisms. However, experimental information
113
-------
n
r~
in
M E O
a a -H
o o. -P
•H 0!
•P ** >
OS O -H
fc • -P
o
§ .
O O
O O
O K M
i-H •• -H
cs e to
•H a a
•P ft
•H TJ
a o v
M rH -P
•
o
d)
o
a
V
FH
0)
a)
B3
d
•H
rH
M
rH
1
O
rt
3
05
J
bO
0>
C
0-
lAldd/NOIlVdlN30NOD
(N
3
114
-------
on branching ratios, chamber effects, identities and concentrations of
minor products, and laboratory data on critical reaction rate constants
are necessary to reduce the remaining uncertainties present in our updated
model mechanisms for butane and propene. Available experimental data can
be simulated fairly well, but there is still considerable latitude in
adjusting many individual rate constants. Although these uncertainties
do not seem severe in simulating the available data, it is currently
difficult to predict the reliability of the mechanisms when applying them
to atmospheric concentrations.
115
-------
REFERENCES AND FOOTNOTES
1. K. L. Demerjian, J. A. Kerr, and J. G. Calvert, Adv. Environ. Sci.
Technology, 4, 1 (1974).
2. (a) P. Gray, R. Shaw, and J.C.J. Thynne, Progress in Reaction
Kinetics, 4, 63 (1967) ;
(b) S. W. Benson and H. E. O'Neal, Kinetics Data on Gas-Phase
Unimolecular Reactions, NSRDS-NBS 21, U.S. Government Printing
Office, Washington, D.C. (1970).
3. L. Batt, R. D. McCulloch, and R. T. Milne, Int. J. Chem. Kinetics,
Symposium !_, 441 (1975); L. Batt and R. T. Milne, Int. J. Chem.
Kinetics, 6, 945 (1974).
4. M. Delepine, Bull. Soc., Chim. Fr., (3) 13_, 1044 (1895); Beilstein I,
p. 284. The compound is reported to detonate by shock.
5. P. L. Hanst and J. G. Calvert, J. Phys. Chem., 63, 104 (1959).
6. Procedure from J. A. Gray and D.W.G. Style, Trans. Faraday Soc., 48,
1137 (1952) .
7. D. M. Golden, R. Walsh, and S. W. Benson, J. Amer. Chem. Soc., 87,
4053 (1965) .
8. S. W. Benson and G. N. Spokes, J. Amer. Chem. Soc., 89, 2525 (1967);
D. M. Golden, G. N. Spokes, and S. W. Benson, Angw. Chemie (Int'l Ed.),
12, 534 (1973) .
9. G. Emanuel, Int. J. Chem. Kinetics, 4, 591 (1972).
10. H. E. O'Neal and S. W. Benson in Free Radicals, Vol. II, Chapter 17,
275 (1973), edited by Jay K. Kochi, John Wiley and Sons, Inc., New York.
11. L. Phillips and R. Shaw, Tenth Symposium (International) on Combustion,
453 (1968), Williams and Williams, Baltimore, Md.
12. G. Baker and R. Shaw, J. Chem. Soc., 6965 (1965).
116
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13. G. N. Spokes and S. W. Benson, J. Amer. Chem. Soc., 89, 6030 (1967).
14. S. W. Benson, et al. , Chem. Rev., 6J3, 279 (1969).
15. D. R. Stall, E. F. Westrum, Jr., and G. C. Sinke, The Chemical
Thermodynamics of Organic Compounds, John Wiley and Sons, Inc.,
New York, 1969.
16. R. Silverwood and J. H. Thomas, Trans. Faraday Soc., 63, 2476 (1967).
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Soc., 95, 7 (1973) .
21. J. N. Pitts, Jr. and B. J. Finlayson, Angew. Chem. (Int. Ed.), 14,
1 (1975) and references cited therein.
22. L. Batt and R. D. McCulloch, Int. J. Chem. Kinetics, 8, 491 (1976).
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4053 (1965) .
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536 (1956) . """
26. C. W. Gear, The Numerical Solution of Initial Value Problems,
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27. H. E. O'Neal and W. H. Richardson, Comprehensive Chemical Kinetics,
Vol. 5 (C. H. Bamford and C.F.H. Tippler, Ed., Elsevier, Amsterdam,
1972) .
28. D. Gray, E. Lissi, and J. JHeicklen, J. Phys. Chem., 7£» I9*9 U972) .
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117
-------
31. S. W. Benson, Foundations of Chemical Kinetics, McGraw-Hill Book
Co. , New York, 1960.
32. K. J. Reed and J. I. Brauman, J. Amer . Chem . Soc . , 97, 1625 (1975).
33. G. D. Mendenhall, D. M. Golden, and S. W. Benson, Int. J. Chem.
Kinetics, 7, 725 (1975), see Section
34. J. Heicklen and H. S. Johnston, J. Amer. Chem. Soc., 84, 4030 (1962).
35. R. Shortridge and J. Heicklen, Can. J. Chem., 5^, 2251 (1973).
36. J. Heicklen, Advances in Chemistry Series, No. 76, Vol. II, 23 (1968)
37. W. G. Alcock and B. Mile, Combustion and Flame, 24, 125 (1975).
38. K. D. Bayes and N. Washida, 12th ternational Symposium on Free
Radicals (January 4-9, 1976), Laguna Beach, California.
39. S. W. Benson, Thermochemi ca 1 Kinetics, John Wiley and Sons, Inc.,
New York, 1968.
40. J. Weaver, R. Shortridge, J. F. Meagher, and J. Heicklen,
J. Photochem., 4, 109 (1975).
41. Note that only for unimolecular reactions is ^3* independent of the
choice of standard states. For bimolecular reactions with standard
states in units of concentration, the Arrhenius rate constants are
related by kc = (RT)kp; for termolecular reactions, kc = (RT)2kp.
Since thermochemical quantities for gases are tabulated in terms of
atmosphere as standard state, this requires considerable care in
relating forward and reverse reactions (see Ref . 42).
42. D. M. Golden, J. Chem. Educ . , 48, 235 (1971).
43. S. W. Benson and D. M. Golden, "Reactions in Condensed Phases,"
Chapter II, Vol. 7, in Advanced Physical Chemistry, edited by
H. Eyring and D. Henderson, John Wiley and Sons, Inc., New York (1975)
44. H. E. O'Neal and S. W. Benson, J. Chem. and Eng . Data, 1J>, 266 (1970).
45. A. F. Trotman-Dickenson and G. S. Milne, Tables of Bimolecular Gas
Reactions, NSRDS-NBS9 , U.S. Government Printing Office, Washington,
D.C. , 1967.
118
-------
46. E. Ratajczak and A. F. Trotman-Dickenson, Supplementary Tables of
Bimolecular Gas Reactions, OSTI, Publishing Department, UWIST,
Cardiff, Wales (1969.
47. J. A. Kerr and E. Ratajczak, Second Supplementary Tables of Bimolecular
Gas Reactions, The University, Birmingham (1972).
48. G. S. Hammond, J. Amer. Chem. Soc. , 77, 334 (1955).
49. J. L. Franklin et al., lonization Potentials, Appearance, Potentials,
and Heats of Formation of Gaseous Positive Ions, NSRDS-NBS 26,
U.S. Government Printing Office, Washington, B.C. (1968).
50. The potential energy, vion» of the ion pair (separation = r A)
relative to the separated neutral species of infinity is given by:
V. = — —— + (ionization potential-electron affinity)
14 .4
All energies in electron volts, Vion = 0 when r = _' (A) .
51. Reference 39, p. 110.
52. S. C. Chan. J. T. Bryant, L. D. Spicer, and B. S. Rabinovitch,
J. Phys. Chem., 74, 2058 (1970).
53. Thermodynamically, RTln K = - AG° = - AH° + TAS°. For an adiabatic
reaction with standard state in atmosphere, AH° = - RT, and the
energy of AB is just the sum of the energies of the reactants A + B.
54. D. Garvin and R. F. Hampson, editors of Chemical Kinetics Data Survey
VII, NBS IR74-430, Washington, B.C. (1974),
55. J. Troe, Ber. Buns. Physiki. Chem., 73, 144 (1964); 73, 906 (1969);
H. Gaedtke, H. Hippler, and J. Troe, Chem. Phys. Letters, 16, 177 (1972)
56. J. N. Pitts, Jr., J. H. Sharp, and S. I. Chan, J. Chem. Phys., 40,
3655 (1964) .
57. S. Jaffe and F. S. Klein, Trans. Faraday Soc., 62, 3135 (1966).
58. F. Kaufman in Chemiluminescence and Bioluminescence, edited by
M. J. Cormier, D. M. Hercules, and J. Lee, Plenum Publ. Co.,
New York, 1973, p. 83.
59. J. T. Herrpn and F. S. Klein, J. Chem. Phys., 40, 2731 (1964).
119
-------
60. H. Hippler, C. Schippert, and J. Troe, Int. J. Chem. Kinetics,
Symposium !_, 27 (1975) .
61. H. J. Johnston and C. Parr, J. Amer. Chem. Sdc., 85, 2544 (1963).
62. A. A. Zavitsas, Ibid., 94, 2779 (1972). !
)
63. Z. B. Alfassi and S. W. Benson, Int. J. ChemJ Kinetics, 5, 879 (1973).
64. AH°(-CO-OCr) is obtained by starting with AH^(HCOOOH) = - 65 kcal/mole.
Assuming the H-C and 0-H bonds are the same as in formic acid (93
kcal/mole) and H202 (90 kcal/mole), respectively, we find
AHf('CO-OOO = 14 kcal/mole and ffLT = 40 kcal/mole, endothermic.
In similar fashion we estimate AH°(ON-O-NO) = 22 kcal/mole;
AH$(H-CO-ONO) = - 44 kcal/mole, and AHj('CO-ONO) = - 3 kcal/mole.
This yields for the reaction NO2 + CO -* -CO-ONO, AHr = 15 kcal/mole.
65. (a) L. Batt, R. D. McCulloch, and R. T. Milne, Int. J. Chem.
Kinetics, 6, 945 (1974).
(b) L. Batt, R. D. McCulloch, and R. T. Milne, Int. J. Chem.
Kinetics, Symposium No. !_, 441 (1975).
(c) L. Batt and R. T. Milne, Int. J. Chem. Kinetics, 8, 59 (1976).
(d) L. Batt and R. D. McCulloch, Int. J. Chem. Kinetics, 8, 911 (1976)
66. T. Berces and A. F. Trotman-Dickenson, J. Chem. Soc., 348 (1961).
67. C. Leggett and J.C.J. Thynne, J. Chem. Soc., (A), 1188 (1970).
68. J. M. Ferguson and L. Phillips, J. Chem. Soc., 4416 (1965).
69. D. L. Cox, R. A. Livermore, and L. Phillips, J. Chem. Soc., (B) ,
245 (1966) .
70. R. L. East and L. Phillips, J. Chem. Soc., (A), 1939 (1967).
71. P. Cadman, A. F. Trotman-Dickenson, and A. J. White, J. Chem. Soc.,
(A) , 2296 (1971) .
!
72. F. W^Bires, C. J. Danby, and C. M. Hinshelwood, Proc. Roy. Soc.
(London), A239, 154 (1957) .
T ~~ i
73. N. J./Quee and J.C.J. Thynne, Trans. Faraday (Soc., 63, 2970 (1967).
120
-------
74. G. R. McMillan, J. Amer. Chem. Soc., 82, 2422 (1960).
75. J. A. Kerr and M. J. Parsonage, Evaluated Kinetic Data on Gas-Phase
Addition Reactions, CRC Press, Cleveland, Ohio (1972).
76. G. Emanuel, Aerospace Report No. TR-0200(4240-20)-5.
77. D. M. Golden, R. K. Solly, and S. W. Benson, J. Phys. Chem., 75,
1333 (1971) .
78. J. R. Barker, S. W. Benson, and D. M. Golden, Int. J. Chem. Kinetics,
9, 31 (1977). See Section 4, A.
79. "Semonov Rule," see K. J. Laidler, Chemical Kinetics, McGraw-Hill, Inc.,
New York, 1965, p. 132.
80. W.P.L. Carter, K. R. Darnall, A, C. Lloyd, A. M. Winer, and J. N. Pitts,
Jr., Chem. Phys. Letters, 42, 22 (1976).
81. G. Z. Whitten and H. H. Hugo, SAI Report EF76-126, Draft Final
Report (1976) .
82. S. W. Benson, Thermochemical Kinetics, 2nd Ed., John Wiley and Sons,
Inc., New York, 1976.
83. H. Niki, P. D. Maker, C. M. Savage, and L. P. Breitenbach, Chem. Phys.
Letters, to be published.
84. D. Gray, E. Lissi, and J. Heicklen, J. Phys. Chem., 76, 1919 (1972).
85. R. Simonaitis and J. Heicklen, J. Phys. Chem., 78, 653 (1974).
86. R. A. Cox, Int. J. Chem. Kinetics, Symposium No. !_, 379 (1975);
R. A. Cox and R. G. Derwent, J. Photochem., 4, 137 (1975).
87. S. Z. Levine, W. M. Uselman, W. H. Chan, J. G. Calvert, and J. H. Shaw,
Chem. Phys. Letters, to be published.
88. D. G. Hendry and R. A. Kenley, J. Amer. Chem. Soc., 99, 0000 (1977).
89. Reference 15; J. D. Cox and G. Pilcher, Thermochemistry of Organic
and Organometallic Compounds, Academic Press, Inc., 1970.
121
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90. J. N. Pitts, Jr., K. R. Darnall, A. M. Winer, and J. M. McAfee,
Mechanisms of Photchemical Reactions in Urban Air, Vol. II,
Chamber Studies, U.S. Environmental Protection Agency, 600/3-77-014b,
February 1977.
91. For a recent review, see NBS Technical Note 866 (1975) .
92. See, for example, H. Niki, E. E. Daby, and W. Weinstock, Advan.
Chem. Series, 113, 16 (1972).
93. T. A. Hecht and J. H. Seinfeld, Environ. Sci. Technol., 6, 47 (1972);
T. A. Hecht, J. H. Seinfeld, and M. C. Dodge, Environ. Sci. Technol.,
8, 327 (1974) .
122
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APPENDIX A
INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, VOL. VII, 943-949 (1975)
VLPP Unimolecular Rate Theory
JOHN R. BARKER
Department of Thermochemistry and Chemical Kinetics, Stanford Research Institute, Menlo Park,
California 94025
Abstract
The exact theory is derived for the thermal unimolecular decomposition of gas-phase
molecules activated and deactivated exclusively through heterogeneous collisions with the
walls of a spherical vessel. This theory is appropriate for the treatment of very-low-pressure
pyrolysis (VLPP) experiments and other experiments carried out at very low pressures.
It is shown, however, that the exact theory is closely approximated by ordinary gas-phase
unimolecular rate theory and that for practical application to experiments the results of
both theories are indistinguishable.
Introduction
In most gas-phase thermal unimolecular reaction studies, heterogeneous
de(activation) is a complication arising at low pressures and which is best avoided.
Maloney and Rabinovitch [1] considered such heterogeneous effects for the case
of a spherical reactor. They derived expressions for the heterogeneous con-
tribution by writing down the diffusion equation and solving it subject to the
proper boundary conditions. Implicit in their treatment are the usual assump-
tions of unimolecular rate theory [2, chap. 8], (1) the lifetimes of activated mole-
cules are random, and (2) the time intervals between colisions are random. These
assumptions lead to time-independent rate constants for decomposition and
deactivation [2, chap. 8].
In very-low-pressure pyrolysis (VLPP) experiments [3] the pressure is deliber-
ately maintained so low that heterogeneous (de)activation predominates, and gas-
gas collisions are a complication to be avoided. This corresponds to the low
pressure limit of the analysis by Maloney and Rabinovitch [1]. Under these
conditions, when an activated molecule leaves the wall, it has a good chance of
drifting through a collision-free region for a relatively long period of time, a cir-
cumstance not matched in the gas-gas collision case. Consequently, the distribu-
tion of time intervals between collisions (flight times) is not random, and the
gas-phase formulation of thermal unimolecular rate theory is not exactly correct
for these conditions.
In the following analysis, the exact expression for the flight time distribution
(in a spherical reactor) is derived and compared to the random distribution. The
123
-------
differences between the two distributions are relatively small, leading to only
small errors (<5%) if the usual gas-gas unimolecular theory is employed instead
of the exact theory.
General Expression for kunl
If a particle is activated to the energy range E to E -f- dE, the "random life-
time assumption" [2, p. 9] states that in the absence of collisions the probability
of not decomposing during the time interval (0,t) is
(1) Pd(t) = exp {-k(E)t |
where k(E) is the rate constant for decomposition of particles excited to energy E\
k(E) can be calculated by statistical theory [2, chap. 4—7].
Presumably the probability of surviving decomposition in the absence of
collisions is not correlated with Pc(t), the probability of not experienceing a colli-
sion during the same time interval. Thus the joint probability of surviving the
time interval (O,/) is Pc(t)Pd(t) = Pc(/)exp{ -k(E)t\. The probability of decom-
posing during any given increment of time (t to t + df) is just k(E)dt. Thus the
probability of an activated particle decomposing in the next time increment after
having survived the interval (0,t) is
(2) Pd(t)Pc(t)k(E)dt = Pc(t)k(E)cxp{-k(E)t\dt
This probability must be integrated over all lifetimes possible during a given
experiment in order to get the total probability of decomposition during the course
of the experiment [2, p. 10].
(3) Ptot k(E) = / Pd(t)Pe(t)k(E)dt
Jo
The upper limit r is the maximum lifetime possible in the experiment, that is,
the duration of the experiment. Since T is usually many times longer than the
average flight time or lifetime with respect to decomposition, little error is intro-
duced by assuming r =w .
If the particles are activated at the rate Re, the steady-state rate of decomposi-
tion is RcPtot, which may be written [2, chap. 8]
where [A *] is the concentration of active particles of energy E.
For collisional activation (strong collision assumption), in the absence of any
other process, the collisional rate of activation equals the rate of collisional deacti-
vation :
A + M T=± A* + M
(5) Rc = *,[M][A] = MM][A*] = «[A*J
124
-------
where [A] is the total concentration of species A. Under these conditions [A*]
is the equilibrium concentration: [A*] = [A]Pe(E)dE for energy range E to E -f
dE, where Pe(E) is the equilibrium distribution function. It follows that the
rate of activation is given by Rc = u[A.]Pe(E)dE, and this expression holds (for
activation), regardless of whether other channels are open for depletion of [A*].
It should be pointed out that Rc is the average rate of activation, regardless of
whether it takes place due to gas-gas collisions or due to gas-wall collisions. The
collision rate w is calculated differently depending on the mode of activation, but
this fact makes no difference. The difference between VLPP unimolecular rate
theory and gas-gas unimolecular rate theory is due to the distribution of "flight
times" at the same average collision rate.
Under steady-state conditions the expression for the rate of decomposition is
— = / — — dE = £UI1i[
at Jo at
(6)
where the unimolecular rate constant is
(7) /tuni = u i \ P,(E)k(E)exp{- k(E)t\Pc(t)dtdE
Jo Jo
In the next section an expression for Pc(t) will be derived for a spherical
reactor and VLPP conditions. It is informative, though, to derive k^m for gas-gas
collisions. In this case the random flight time assumption [2, chap. 8] applies and
(8) Pf(0 = exp(- co/)
Thus for gas-gas collisions,
(9)
which is the usual expression for a unimolecular rate constant. It will be shown
below that the final rate constant for heterogeneous (de)activation can be ex-
pressed in similar form with a multiplicative factor B(E), which is always close to
unity for a spherical reactor:
(10) CPP = / B(E)P.(E)
co +
for Spherical VLPP Reactor
A direct way of calculating Pc(t), the probability that the flight time equals
or exceeds /, is to first calculate the path-length distribution and then fold in the
Maxwell-Boltzman velocity distribution.
The probability that a particle will leave the inner surface of a sphere and have
its velocity vector directed in the range of solid angle w to w + dw is assumed to be
random:
(11) p(w)dw =
125
-------
If 8 is the angle between the velocity vector and the normal to the surface (that is,
the radius vector), eq. (11) can be written
(12) P(8)d8 = -2r ™J * = sin 0 dB
If the sphere is of radius r, the length of the path within the sphere at angle 8 is
s' = 2r cos 0, giving the probability for a path length s' to s' + ds'\
(13) p(s')ds' = |-
The probability that the path length is greater than or equal to s is
(I*)
If a particle is moving along a path with speed v to s + dv, the probability that
the flight time is greater than or equal to / is the joint probability that 2r > s > vt
and that the speed is in the range v to v + dv:
(15)
r rti
p(v,t)dv = /»(») 2r
The total probability (for all speeds) that the flight time is greater than t is the
integral over speed from 0 to » . The conditions on p(v,t) can be incorporated
into the integration limits, and the result is
vt~\
- — jfc
(16) Pe(t) =
where P(v)dv is the Maxwell-Boltzman speed distribution,
(17) PW.- <, "V =!•(-=£.)*
and the symbols have their usual meanings.
Equation (16) can be integrated exactly [4] to give
- m}\
where iFi(p,q,x,) is the confluent hypergeometric function [5].
The collision frequency co for particles with the walk of a sphere is [3]
(19)
126
-------
Using this identity and the known transformations of the hypergeometric function
[5], the expression for Pc(t) can be put in more familiar terms:
(20)
Pc(t) = Pe(a) = erf (a1/2) - -£= \\ - exp(-a))
V« ( )
where a = 9/7r(o>/)2. A semilog plot of this function versus ut is presented in
Figure 1 along with Pf(f) for comparison. It may be observed that the pure
exponential function Pf**(t) is a good approximation to the overall behavior of
Pe(t), but with slight deviations due to three factors: (1) the fixed geometry of the
reactor allows a considerable collision-free region not found in a homogeneous gas
(ut ^ 1); (2) the boundaries of the reactor limit the flight times of particles moving
at average speeds (1 % ut % 5); (3) the broad velocity distribution causes a
deviation from the pure exponential after long times (ut ^5). It is qualitatively
clear, however, that
P
is closely approximated by
1.0
10"
~a 1C'2
a.
10"
10"
6 8 10 12
cot
14
Figure 1. Flight-time probability distribution functions. Solid line—exact prob-
ability for a spherical vassel; dashed line—pure exponential behavior appro-
priate to gas-gas collisions.
127
-------
For the quantitative assessment of A:^ it is necessary to integrate eq. (7)
with eq. (20) substituted for Pc(t). Before carrying out the integration, however,
it is convenient to scale the integral by transforming to a new variable x =
[u + k(E)]t. This substitution gives
(21)
I.VLPP _
1 uk(E)Pe(E)dE
« + k(E)
I'
J o
-^ dx
where Pe(x,z) is just Pe(t) expressed in terms of the new variable x and the para-
meter z — w/[k(E) + «], a function of energy E. From this it is clear that the
factor B(E) in eq. (10) is just
(22)
/'
Jo
1-* dx
Results and Conclusions
Equation (21) was evaluated numerically by a fifteen-term Gauss-Laguerre
integration [5, chap. 25], and the B factor is presented in Figure 2 as a function of
a/k(E). From inspection of this figure it is clear that B never differs from unity
by more than ± 5%. Under the usual VLPP conditions, ta <3C k(E), and B is
very close to unity. Even in the worst of cases, gas-phase unimolecular rate
theory eq. (9) should be quite adequate since VLPP experimental errors are
generally expected to exceed ± 5%.
The interesting behavior of B(E) is a direct consequence of the positive and
negative deviation of the flight time distribution relative to the random collision-
time distribution. When k(E) » u, the distribution is hardly sampled at all and
1.05 -
1.00
0.95
0.90
I
0.01
0.10
10
1.0
cj/ME)
Figure 2. B factor dependence on a/k(E).
100
128
-------
B(E) ^ 1. When k(E) « u, the collision-free drift region of the spherical reactor
is important, and more decomposition takes place than in the random collision
time distribution, leading to B(E) > \. When k(E) < 5 in Figure 1), has a slight effect on B(E), but is far less important
than the other two effects mentioned.
In principle, an expression for Pe(t) can be derived for any geometrical con-
figuration; most VLPP reactors are approximately cylindrical. The factor B(E)
for other reactor geometries will probably be of magnitude similar to that calcu-
lated here for the sphere, since the major feature of VLPP appears to be the exist-
ence of a collision-free region not present in a homogeneous gas.
In conclusion, it was found that the exact theory for a spherical VLPP reactor
differed only slightly from the usual gas-phase unimolecular rate theory.
Acknowledgment
Useful discussions with Sidney W. Benson and David M. Golden are gratefully
acknowledged, as are some helpful suggestions from the referees.
This work was supported by the U. S. Environmental Protection Agency
under grant R802288.
Bibliography
[1] K. M. Maloney and B. S. Rabinovitch, J. Phjs. Chan., 72, 4483 (1962).
[2] W. Forst, "Theory of Unimolecular Reactions," Academic Press, New York, 1973.
[3] For a review, see D. M. Golden, G. N. Spokes, and S. W. Benson, Angav. Chem., Int. Eng. Ed.,
12, 534 (1973).
[4] I. S. Gradshteyn and I. M. Ryzhik, "Table of Integrals, Scries, and Products," Academic
Press, New York, 1965.
[5] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions," Dover, New
York, 1968, chap. 13.
Received April 8, 1975
Revised June 11, 1975
129
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/3-77-110
2.
4. TITLE AND SUBTITLE
MEASUREMENT OF RATE CONSTANTS OF IMPORTANCE IN SMOG
7. AUTHOR(S)
John R. Barker, Sidney W. Benson, and David M. Golden
9. PERFORMING ORGANIZATION NAME AND ADDRESS
SRI International
333 Ravenswood Avenue
Menlo Park, California 94025
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTP, NC
Office of Research and Development
U. S. Environmental Protection Agency
Research Triangle Park., Nnrth r.arnl-ina 27711
15. SUPPLEMENTARY NOTES
3. RECIPIENT'S ACCESSION- NO.
5. REPORT DATE
October 1977
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT
10. PROGRAM ELEMENT NO.
lAAfim AF-m (FY-77)
11. CONTRACT/GRANT NO. ;
R 802288
NO.
-
13. TYPE OF REPORT AND PERIOD COVERED
Final 4/73 - 7/77
14. SPONSORING AGENCY CODE
EPA/600/09
16. ABSTRACT
To provide understanding of elementary reactions of importance in smog, a
three-part investigation has been carried out: (1) experimental determinations of
certain elementary reaction rate constants, (2) development of general techniques for
estimating elementary reaction rate constants, and (3) estimation of many reactions
important in smog.
Specific estimated rate constants included the following reactions:
(1) Decomposition of alkoxy radicals
(2) Isomerization of alkoxy radicals
(3) Reactions of alkoxy radicals with oxygen
(4) The reaction H02 + N02 T H02N02
In addition, a limited number of computer simulations were carried out for the photo-
oxidation of n-butane and propene.
17.
a. DESCRIPTORS
* Air Pollution
* Smog
* Reaction kinetics
* Photochemical reactions
Ozone
Hydrocarbons
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
KEY WORDS AND DOCUMENT ANALYSIS
b. IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
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04B
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07E
07B
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19. SECURITY CLASS (This Report) 21. NO. OF PAGES
UNCLASSTFTFn 144
20. SECURITY CLASS (This page) 22. PRICE
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