United States
Environmental Protection
Agency
Atmospheric Sciences
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S3-86/072 Apr. 1987
&EPA Project Summary
Structure-Reactivity
Relationships for
Predicting Environmentally
Hazardous Chemicals
Norman Cohen
A method previously developed for
extrapolating rate coefficients by con-
ventional transition-state theory was
applied to reactions of hydroxyl (OH)
radicals with 10 halomethanes and 18
haloethanes. For each reagent, the
entropy of activation AS* was calcu-
lated. That value, together with an ex-
perimental value of the rate of reaction
at 298 K, k(298), was used to calculate
k(T) at higher temperatures. The calcu-
lated values for all the haloalkanes dif-
fered from experimental values by no
more than 25%, except that of (OH +
CHCI3), for which the possibility of ex-
perimental errors was considered.
Those calculations were then used to
develop a simpler, approximate scheme
that can be applied to any haloalkane. For
a-hydrogen abstraction reactions,
AS*(298) can be fitted, with a maximum
error of 1.4 and an average error of 0.3
cal mor1 K~1 (entropy units, or eu), by
AS*(298) = -2.2 In M -18.0 + R In nH
where M = molecular weight of the
haloalkane and nH = the number of
abstractable a-hydrogen atoms. The
activation energy at 298 K, E(298). can
be fitted, with an average error of 0.3
and a maximum error of 1.1 kcal/mol,
by
E(298)/R=2100-85nF-51nc1 -
950nCH3 - 600cH2X -
650nCHx2 - 250nCX3
where the n, indicate the number of H
atoms on CH4 replaced with the in-
dicated substituents, and X is either Cl
or F. The above relations for AS*(298)
and E(298) are used to generate a
"universal" rate coefficient expression
that depends only on the molecular
weight and the number of abstractable
H atoms in the reagent haloalkane:
k(T) =
nH 10" M-1 T1 6
exp[-[E(298)/R-450]/T]
where E(298)/R is given by the pre-
ceding equation. For most reagents,
this expression predicts rate coefficients
within a factor of 3 of experimental
data and provides a useful predictive
tool if no reliable data are available.
This Project Summary was developed
by EPA's Atmospheric Sciences Re-
search Laboratory, Research Triangle
Park, NC, to announce key findings of
the research project that Is fully docu-
mented In a separate report of the same
title (see Project Report ordering In-
formation at back).
Introduction
The aim of this research has been to
develop the means for predicting reac-
tivities of potential man-made pollutants
in the stratosphere and troposphere.
Although it is possible to measure re-
activities in the laboratory, the number of
possible species of concern is enormous,
and the cost of studying each one in
detail would be prohibitive. The assess-
ment of the atmospheric fate of pollutants
can, for the most part, be satisfied by a
procedure that enables prediction of re-
activities to within a factor of 3 to 5,
without requiring the higher accuracy
attainable by elaborate laboratory
measurements.
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Consideration of the important oxidizing
species in the atmosphere and their rela-
tive reactivities leads to the conclusion
that for almost all reagents, the species
that determines the lifetime of an atmo-
spheric pollutant is the hydroxyl (OH)
radical. Consequently, any program con-
cerned with predicting reactivities of
potential pollutants should concern itself
first with the reactions of OH radicals.
For this reason, the work under this con-
tract focused on OH reactions.
The initial efforts proceeded in two
phases: The first addressed the problem
of calculating in detail the temperature
dependence of the reaction rate coef-
ficients; the second explored the pos-
sibility of developing simplified procedures
for estimating, with sufficient accuracy,
the rate coefficients of OH reactions at
any temperature. The second phase re-
quired estimating both the entropy of
activation (AS*), and, with more dif-
ficulty, the energy of activation (E).
These two parameters determine the
rate of reaction at any temperature, in
accordance with the general equation
k(T) = C exp(ASVR) exp(-Ea/RT) (1)
Finally, the problem of developing a
universal rate coefficient expression
that can predict with reliability the rate
coefficients, at various temperatures,
for reactions of OH radicals with im-
portant atmospheric pollutants was
addressed.
Procedure
Transition-State Theory
Calculations
The procedure follows our previous
studies. Here, the general reaction is
XN ,0,
XYZCH + OH - Y--C--H' 'H-
Z'
XYZC + HOH
where X, Y, and Z are each either H, C1,
F, CH3, or a halomethyl radical. The
principal problem is how to calculate the
entropy of the activated complex, S*. The
calculation involves using the haloalkane
reagent RH itself as a model compound,
then making suitable corrections to the
various degrees of freedom as indicated
below. The entropy S* is then given by
S* = SS,H + AS, + Av + ASr + .,,
AS,r + ASe + AS<, + ASn ' '
where the AS terms represent the cor-
rections required in replacing the pro-
perties (translation, vibration, rotation,
internal rotation, electronic, symmetry,
optical isomerism, respectively) of the
model compound by those of the acti-
vated complex.
It was assumed that the C-H, H-O,
and 0-H bond lengths and C-H-0 and
H-O-H bond angles are approximately
the same as those calculated by Walch
and Dunning1 for the reaction of (OH +
CH4): 1.2, 1.3, 1.0 A and 160° and
110°, respectively. From this information,
the product of moments of inertia of the
complex I* can be calculated, whence AS,
= R In (l*/l), where I is the product of the
moments of inertia of the reagent RH. AS,
is given by (3/2) R ln(M'/M). The
electronic degeneracy of the activated
complex is assumed to be 2, whence
AS8 = R In 2 - 1.38 eu (entropy units, or
cal mol"1 K'1). AS0 = R Info/a"), where a
abd at are the external symmetry num-
bers of the alkane and complex, respec-
tively, calculated assuming rigid rotation.
ASn = R In (nt/n), where n and n* are the
numbers of optical isomers in the alkane
and complex, respectively. Only the
vibrational frequencies and internal rota-
tions of the activated complex remain to
be determined.
Vibrational Frequencies
For each halomethane XYZCH, where
X, Y, and Z are either H, Cl, or F, we
estimated the vibrational frequencies in
the activated complex by using those in
the molecule XYZCF as guides, on the
assumption that the C-H-OH portion of
the activated complex is similar to the C-
F portion of a real molecule. The vibra-
tional-frequency changes in the activated
complexes for all the halomethanes are
summarized in the full report.
For the haloethanes, it was not possible
to examine each reaction in detail because
there are more frequencies, fewer mode
identifications, and fewer molecules for
which detailed spectra are available. In-
stead, the vibrational frequencies of
CH3CH3, CH3CH2F, CH3CHF2, and CH3CF3
were compared, the change in the first
pair representing the reaction of OH with
all haloethanes with only /3-hydrogen
atoms (i.e., no H atoms on the same C
atom as F or Cl atoms), and the changes
between the second and third pairs repre-
senting reactions with a-H atoms.
Because the experimental data indicate
that a reaction with haloethanes con-
taining only /?-H atoms is at least an
order of magnitude slower than for
haloethanes with some a-H atoms, it
was assumed that in those reagents con
taining both a- and y-H atoms, the re
action with the /J-H atoms could bi
neglected. In both kinds of reactions, i
was assumed that the newly formed C H-(
and H-O-H bonds have the same value:
that were used in the halomethane re
actions (1000cm1 each).
Internal Rotations
The properties of the internal rotation;
must be evaluated accurately, because
considerable entropy is associated witr
these two degrees of freedom. The
moments of inertia for the internal rota-
tions are calculated by the procedure 01
Herschbach et al.2 The entropy of free
rotation is given by Sf = R(ln 0 + 1/2),
where Q = 0.35(lrT)'/2/a for lr, the reduced
moment of inertia, in dalton-A. Here o is
the symmetry of the internal rotation,
which is 1 for most of the reagents
considered in this report but 3 for rotation
about the C-H bond in CH4, CHC13, and
CHF3. For rotation about the C-H bond, Q
«= 6.2/a for all halomethanes and 1.8 for
CH4. For rotation about the 0-H bond, Q
» 5.9 for all halomethanes and 5.1 for
CH4. The corrections to the entropy due
to the barrier to rotation, S( - Sh> are
interpolated from tables developed by
Pitzer and coworkers where SH = entropy
of hindered rotation.
For all the haloethanes, the reduced
moment of inertia lr for rotation about the
C-H bond is approximately 1.1 dalton-A,
which makes the partition function Q
equal to 6.5, and the entropy of free
rotation Sf, 4.7 eu. For rotation about the
H-O bond, I, = 0.95, Q = 6.0, and Si =
4.6 eu.
Unlike the halomethanes, the halo-
ethanes already have one internal rota-
tion — about the C-C bond. In a previous
study involving transition-state theory
calculations for reactions of oxygen (0)
atoms with alkanes, reasonable agree-
ment with experiment was obtained by
assuming that the barrier to internal rota-
tion was lowered by 1 kcal/mol in the
activated complex. The same assumption
was made here. The contributions to AS*
are shown in the full report. There is a
qualitative difference between the re-
actions abstracting a-H atoms and those
abstracting /3-H atoms, because the OH
adduct makes a much greater change in
the moment of inertia of a CH3 group
than it does when added to a halomethyl
group.
'Walch, S. P., and T H Dunning, Jr J. Chem. Phys ,
72:1303, 1980.
2 Herschbach, D R., H S Johnston, K S Pitzer, and
R F. Powell. J. Chem Phys., 25 736, 1956
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Empirical Correlations
The results of the detailed transition-
state theory calculations outlined above
were used to establish simple empirical
correlations between activation entropy
and activation energy for an arbitrary (OH
+ haloalkane) reaction with readily deter-
mined molecular parameters. The fol-
lowing procedure generates simple,
approximate expressions for ASt(298)
and for E(298) without requiring more
information than the molecular weight
of the reacting haloalkane and its gross
structural details.
Entropy of Activation
The entropy of the activated complex,
S*, is calculated from the entropy of the
reacting haloalkane RH by a series of
corrections terms:
S* = SttH + AS, + ASV + ASr + AS,r + .01
ASe + AS0 + ASn IJ'
where the AS terms represent the cor-
rections required in replacing the pro-
perties (translation, vibration, rotation,
internal rotation, electronic, symmetry,
optical isomerism, respectively) of the
haloalkane by those of the activated
complex. The translational contribution
AS, is given by (3/2)R In(MVM);
therefore, it will decrease to zero as the
mass M of the reagent RH increases
(since M* = M + MOH). The rotational
contribution AS, is given by (1/2)R
ln[(la'blc)*/(lalblc)]. where the three I factors
are the principal moments of inertia. Each
I depends approximately on M; hence ASr
too will decrease to zero as the size of the
reagent haloalkane (and hence its mole-
cular weight) increases. The vibrational
contribution, ASV, is the sum of contribu-
tions from each vibrational mode, each of
which varies approximately with vibra-
tional frequency. In this procedure, several
vibrational modes, all of comparable
frequencies in different reagents, are
replaced by other modes in the activated
complexes, for which the frequencies are
comparable for different reactions. A
similar argument, though somewhat
weaker, can be made for internal rota-
tions. The remaining three terms on the
right-hand side of Eq. (3) are independent
of mass. These arguments suggested that
there might be some correlation between
AS*(298) and M, a suggestion borne out
by graphic display of the data.
Activation Energy
Previously, workers attempted to cor-
relate activation energies with bond dis-
sociation energies (BDEs) of the dis-
sociating bond. This approach was tried
with moderate success for (OH + halome-
thane) reactions. However, the same
could not be done profitably for the
haloethanes because BDEs are known
for very few of the compounds. Instead,
an empirical correlation was made of the
activation energies with a set of six struc-
tural parameters; each parameter de-
scribes the correction to the activation
energy of CH4 that must be made as H
atoms are substituted by F, Cl, CH3,
CH2X, CHX2, or CX3, where X = F or Cl.
(At present there are temperature-
dependent rate data for only one bro-
minated haloalkane; hence, attention was
confined to fluorinated and chlorinated
compounds until more data become
available.) In other words,
E(298)/R = E(CH4)/R - aFnF -
aC1nC1 - aCH3nCH3 - acH2Xr>CH2X
- aCHx2ncHX2 - acx3ncx3 (4)
The calculated activation energies for all
halomethanes and haloethanes (except
CHF3 and CHsCFs, which pose unique
problems), which are derived from the
experimental values of k(298), were used
in deriving the values of the various a,.
The results of this effort are given in the
following section.
Results and Discussion
Transition-State Theory
Calculations
OH + Haloalkanes
Transition-state theory calculations
were carried out using the vibrational-
frequency changes and the entropies of
activation listed in the full report. There it
was shown that the temperature ex-
ponents n for all the a-hydrogen abstrac-
tions are 1.6 to 1.7, whereas for the
three ^-hydrogen abstraction reactions n
= 1.1. For the halomethanes, two models
were used for each reaction: one with
hindered internal rotation, and one with
free internal rotation. The two models
were otherwise identical. On the average,
the free internal rotation model appears
to give slightly better agreement with the
data. For all but one reagent, agreement
with experimental data is within the ex-
perimental uncertainties, and discrep-
ancies between experimental and cal-
culated rate coefficients are no greater
than 25%.
The single puzzling exception is CHCI3,
for which both models greatly underpre-
dict the activation energy and hence the
rate coefficients at T > 300 K. To obtain
agreement with the data requires a
greatly increased AS*(298) — from
-28.7 to —25.3 eu — for the free internal
rotation case. One way to achieve this is
by lowering the four low-frequency vibra-
tions in the activated complex to 150
cm"1. However, there is no a priori reason
for making the frequencies of this one
complex so much lower than those of all
the others.
The discrepancy between the calculated
and experimental values of k(T) for this
halomethane suggests either that k(300)
is really larger than the measured value
or, more likely, that at higher tempera-
tures (400-500 K), another process re-
moving OH radicals is occurring. Because
of the possible serious consequences for
the applications of the thermochemical
approach to conventional transition-state
theory as we have been using it, we
recommend that the (OH + CHCI3) re-
action rate be carefully remeasured over
a temperature range sufficiently wide to
eliminate any doubts concerning both
the absolute value of the rate coefficients
and the activation energy.
Empirical Correlations
Activation Entropies
In the full report, AS*(298) for the free
internal rotation model is plotted against
the molecular weight M of the reacting
haloalkane for all the a-hydrogen ab-
stractions. The least-squares fit through
all the points is described by
AS*(298) (eu/H atom) =
-2.2 In M -18.0
or
AS'(298) =
-2.2 In M- 18.0 + RlnnH
where S is in eu (entropy units, or cal
mol"1 K"1), M is in daltons, and nH is the
number of abstractable a-H atoms. This
expression fits all the data with a maxi-
mum error of 1.4 eu and an average error
of 0.3 eu. [The values of AS* for
CH3CC13, CH3CF3, and CH3CF2CI,
which have only 0-H atoms, are all 2 to 3
eu larger than Eq. (2) predicts.] When M
becomes large enough (approximately
220 daltons), the contributions to AS,
and ASr will be close to zero, and
AS*(298) per H atom should reach a
minimum value of —-30.3 eu.
(5a)
(5b)
Activation Energies
Using the approach outlined above, a
least-squares fitting program was applied
to activation energies for 28 (OH +
haloalkane) reactions to solve for the
parameters a, of Eq. (4). The derived
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values, based on E(CH4)/R = 2100 at 298
K, are:
a, = 85 aCH2x = 600
aa = 515 aCHx2 = 650
aCH3 = 950 aCX3 = 250
The values of E(298)/R predicted with
Eq. (4) are compared with the experi-
mentally derived values in the full report.
The discrepancy between predicted and
derived values is never worse than 570,
i.e., an error in E of 1.1 kcal/mol, and in
most casts is considerably smaller: The
average error is 150, i.e., 0.3 kcal/mol.
This approach to calculating the en-
ergetics of a reaction is not novel: It relies
on what is essentially a bond additivity
argument. Heicklen3 explored a similar
approach to predicting BDEs, from which
he predicted rate coefficients for reactions
of OH radicals with a wide variety of
organics. The difference here is the use
of the approach directly for calculating
activation energies, rather than BDEs.
This shortcut circumvents the problem of
the uncertainties in many BDEs — gen-
erally 1 to 2 kcal/mol. These uncertainties
may introduce errors into the bond
additivity expressions for predicting un-
measured BDEs and hence in activation
energies. Since the correlation factor in
the equation relating activation energies
with BDEs is approximately 0.4, a 2-
kcal/mol error in BDE imparts an error to
k(298) of a factor of 3.8.
A "Universal" Rate Coefficient
Expression
Equation (4) for E(298)/R and Eq. (5)
for AS*(298) can be substituted in the
general expression for k(T) from transi-
tion-state theory to yield a general rate
coefficient expression for (OH + halo-
alkanes) that depends only on the
molecular weight of the reagent and
the number of various substituents. We
can force a T1 5pre-exponential tempera-
ture dependence to agree with the
results of the calculations. The A factor
is determined by requiring the expres-
sion to yield the proper values of k(298)
and E(298). The result is
k(T) = nH 106 s M-' T15 exp(-B/T) (6)
where M is in daltons and T is in kelvins.
The pre-exponential factors have been
modified slightly to round off the ex-
ponent of the molecular-weight factor M.
3Heicklen, J. Int. J. Chem. Kinet, 13 651, 1981
The term B is calculated from E(298)/R
obtained from Eq. (4): B = [E(298)/R -
450]. The rate coefficients resulting from
Eq. (6) are shown for several typical re-
actions in figures given in the full report.
[Equation (6) does not apply to halo-
ethanes with only /3-hydrogens.] For
CH2CICHCI2 and CH2FCHF2, Eq. (6) was
applied separately to the two different
kinds of H atoms and the results summed
together. In general, the rate coefficients
calculated by Eq. (6) disagree with experi-
mental data (where they exist) by less
than a factor of 3.
Conclusions
Four principal conclusions emerge from
the present study. The first is that a
reasonable set of assumptions can be
applied consistently to all but one of the
reactions considered here to obtain
transition-state models that lead to cal-
culated rate coefficients in good agree-
ment with experimental data. This is true
even though the A factors at 298 K are
not in particularly good agreement with
experimental values. The good agreement
is a result of the tendency of activation
entropies and energies to compensate
one another.
The second conclusion is that one of
the reactions — that of (OH + CHCI3) — is
anomalous. Either the experimental data
are flawed or there is something unusual
about the dynamics of this reaction, re-
quiring a qualitatively different activated
complex to obtain agreement between
calculations and experiments. A new ex-
perimental investigation is recommended.
Third, the above two conclusions to-
gether demonstrate that, while one might
be able to tailor a model for the activated
complex to force reasonable agreement
with a particular set of experimental data
for one reaction, simultaneous agreement
with data for several homologous re-
actions is by no means a fortuitous
achievement. The greater constraints
imposed by treating an entire family of
reactions together rather than a single
reaction give greater confidence that the
model and the resulting calculations are
physically meaningful.
Finally, we used the calculations just
discussed as a guide for generating
empirical expressions for AS*(298) and
E(298) for a-hydrogen abstraction re-
actions of OH radicals from fluorinated
and chlorinated methanes and ethanes.
The calculated entropies and energies of
activation were then applied to generate
a "universal" rate coefficient that depends
only on the molecular weight and the
number of abstractable a-hydrogen atoms
of the reagent haloalkane. This expression
predicts rate coefficients within a factor
of about 3 of the experimental data for all
26 reactions for which data were available
(and generally much better), and offers
promise as a predictive tool when no
reliable experimental data are available.
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Norman Cohen is with Aerospace Corporation, EIS eg undo, CA 90245.
Bruce W. Gay, Jr.. is the EPA Project Officer (see below).
The complete report, entitled "Structure-Reactivity Relationships for Predicting
Environmentally Hazardous Chemicals," (Order No. PB87-140 497/AS; Cost:
$9.95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Atmospheric Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
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