Kinetics of the reactions of chlorine atoms with C2H4 (k1) and C2H2 (k2): A determination of ΔHf,298° for C2H3

Article abstract of DOI:10.1021/jp953178u

The rate constant (k₁) for the reaction of Cl atoms with C₂H₄ has been measured as a function of pressure (0.2-100 Torr) at 297 K using the relative rate technique in two reactors with either FTIR or GC analysis. The results of these and previous experiments (100-3000 Torr) can be described to within ±10% by a Tree expression with the limiting rate constants k₁(∞) = (3.2 ± 0.15) × 10^-10 cm³ molecule^-1 s^-1; and k₁(0) = (1.42 ± 0.05) × 10^-29 cm⁶ molecule^-2 s^-1 using F_cent = 0.6. The stated uncertainties are statistical only, and the true uncertainties in the limiting rate constants must include uncertainty in F_cent. Temperature-dependent (297-383 K) measurements of k₁ were carried out in the low-pressure regime (0.2-2 Torr) yielding the rate constant expression k₁(0) = (1.7 ± 0.3) × 10^-29(T/298)^-3.28 cm³ molecule^-1 s^-1. The rate constant, k_1b, for the abstraction channel of reaction 1 to form the vinyl radical was determined at 300, 343, and 383 K. This measurement of k_1b in combination with literature values of k_-1b allows a determination of the heat of formation of the vinyl radical by the third law method [ΔH_f,298^o(C₂H₃) = 70.6 ± 0.4 kcal/mol]. Using the same data with the second law yields ΔH_f,298^o(C₂H₃) = 69.6 ± 1.6 kcal/mol. These measurements agree satisfactorily with a recent negative-ion photoelectron spectroscopy determination of this quantity (71.6 ± 0.8 kcal mol^-1). The pressure dependence of the rate constant (k₂) for the reaction of Cl with C₂H₂ was determined over the range 0.3-700 Torr. The results of these and previous experiments (100-6000 Torr) can be described to within ±10% by a Troe expression with the limiting rate constants k₂(∞) = (2.0 ± 0.1) × 10^-10 cm³ molecule^-1 s^-1 and k₁(0) = (6.1 ± 0.2) × 10^-30 cm⁶ molecule^-2 s^-1 using F_cent = 0.6.

Full text of DOI:10.1021/jp953178u

J. Phys. Chem. 1996, 100, 4111-4119
4111
Kinetics of the Reactions of Chlorine Atoms with C2H4 (k1) and C2H2 (k2): A Determination
of ∆Hf,298° for C2H3
E. W. Kaiser* and T. J. Wallington*
Ford Motor Company, Research Laboratory, Mail Drop 3083/SRL, Dearborn, MI 48121-2053
ReceiVed: October 30, 1995; In Final Form: NoVember 20, 1995X
The rate constant (k1) for the reaction of Cl atoms with C2H4 has been measured as a function of pressure
(0.2-100 Torr) at 297 K using the relative rate technique in two reactors with either FTIR or GC analysis.
The results of these and previous experiments (100-3000 Torr) can be described to within (10% by a Troe
expression with the limiting rate constants k1(∞) ) (3.2 ( 0.15) × 10-10 cm3 molecule-1 s-1; and k1(0) )
(1.42 ( 0.05) × 10-29 cm6 molecule-2 s-1 using Fcent ) 0.6. The stated uncertainties are statistical only, and
the true uncertainties in the limiting rate constants must include uncertainty in Fcent. Temperature-dependent
(297-383 K) measurements of k1 were carried out in the low-pressure regime (0.2-2 Torr) yielding the rate
constant expression k1(0) ) (1.7 ( 0.3) × 10-29(T/298)-3.28 cm3 molecule-1 s-1. The rate constant, k1b, for
the abstraction channel of reaction 1 to form the vinyl radical was determined at 300, 343, and 383 K. This
measurement of k1b in combination with literature values of k-1b allows a determination of the heat of formation
of the vinyl radical by the third law method [∆Hf,298°(C2H3) ) 70.6 ( 0.4 kcal/mol]. Using the same data
with the second law yields ∆Hf,298°(C2H3) ) 69.6 ( 1.6 kcal/mol. These measurements agree satisfactorily
with a recent negative-ion photoelectron spectroscopy determination of this quantity (71.6 ( 0.8 kcal mol-1).
The pressure dependence of the rate constant (k2) for the reaction of Cl with C2H2 was determined over the
range 0.3-700 Torr. The results of these and previous experiments (100-6000 Torr) can be described to
within (10% by a Troe expression with the limiting rate constants k2(∞) ) (2.0 ( 0.1) × 10-10 cm3 molecule-1
s-1 and k1(0) ) (6.1 ( 0.2) × 10-30 cm6 molecule-2 s-1 using Fcent ) 0.6.
Introduction
our previous measurement of the pressure dependence of
reaction 1a, the rate of reaction 1b will become equal to that of
(1a) at a pressure of approximately 1 Torr. Thus, the pressure
dependence of reaction 1 would be influenced significantly by
the abstraction reaction at pressures below approximately 5 Torr,
and at sufficiently low-pressure the rate constant of reaction 1
(k1 ) k1a + k1b) will become pressure independent at the value
of k1b. In addition, the low-pressure measurements on reactions
1 and 2, reported herein,
The pressure-dependent reactions of Cl atoms with both C2H4
and C2H2 have been examined at 295 K in our laboratory
previously.1 However, data were not obtained at pressures
below 25 Torr. In the present experiments, we have carried
out relative rate measurements of these rate constants at total
pressures from 0.2 to 700 Torr using both FTIR and GC analyses
to determine their pressure dependence relative to pressure-
independent reference reactions. The primary motivation for
carrying out measurements at low-pressure was to examine the
possibility that the abstraction channel for the reaction of Cl
with C2H4 (reaction 1b) might be observed at sufficiently low
total pressure:
C2H2 + Cl (+M) ) C2H2Cl (+M)
(2)
provide a 100-fold extension of the pressure range over which
measurements have been made previously and consequently give
better determinations of the low-pressure limiting rate constants
for both reactions.
C2H4 + Cl (+M) ) C2H4Cl (+M)
C2H4 + Cl ) C2H3 + HCl
(1a)
(1b)
Experiment
Two experimental setups were used; both have been described
previously. The first system6 consisted of a Mattson Instruments
Inc. Sirius 100 FT-IR spectrometer interfaced to a 140 L, 2 m
long, evacuable Pyrex chamber. White-type multiple reflection
optics were mounted in the reaction chamber to provide a total
path length of 26.6 m for the IR analysis beam. The
spectrometer was operated at a resolution of 0.25 cm-1. Infrared
spectra were derived from 32 coadded interferograms. Reagents
and products were quantified by fitting reference spectra of the
pure compounds to the observed product spectra using integrated
absorption features. Reference spectra were obtained by
expanding known volumes of the reference material into the
long pathlength cell. C2H4, C2H2, 1,2-C2H4Cl2, C2H3Cl, CH4,
C2H5Cl, CH3Cl, CHCl3, and C2H6 were identified and quantified
using features over the following wavelength ranges: 850-
1050 and 1850-1950; 660-800; 700-770 and 1200-1300;
A measurement of k1b will assist in determining the heat of
formation of the vinyl radical. The heat of formation of C2H3
has been the subject of experiments by different experimental
techniques. However, as discussed by Ervin et al.2 and by
Berkowitz et al.,3 there remains a discrepancy of ∼5 kcal mol-1
in the heat of formation of C2H3 determined by radical kinetics
(66.9 ( 0.3 kcal mol-1) and by negative-ion photoelectron
spectroscopy (71.6 ( 0.8 kcal mol-1). The kinetics determi-
nation is based in part on measurements of k1b by Parmar and
Benson4 and by Dobis and Benson5 using the very low pressure
reactor (VLPR) technique. The rate constants obtained in these
two studies were k1b ) (5.66 ( 0.7) × 10-13 cm3 molecule-1
s-1 at 293 K and (5.0 ( 0.17) × 10-13 cm3 molecule-1 s-1 at
298 K, respectively. On the basis of these measurements and
X Abstract published in AdVance ACS Abstracts, February 1, 1996.
0022-3654/96/20100-4111$12.00/0 © 1996 American Chemical Society

4112 J. Phys. Chem., Vol. 100, No. 10, 1996
Kaiser and Wallington
TABLE 1: Representative Initial Conditions for FTIR and
850-1000; 1200-1400; 1240-1520; 1300-1600; 700-1250;
and 800-980 cm-1, respectively. Systematic uncertainties
associated with quantitative analyses using these reference
spectra are estimated to be <10%.
GC Measurements of k1
Cl2
[C2H4]0 [ref]0
P (Torr) method
ref
C2H5Cl 1127
(mTorr) (mTorr) (mTorr)
k1/kref
The second system consisted of a spherical, 1 Liter, Pyrex
reactor which was irradiated by a single Sylvania F6T5 BLB
fluorescent lamp. The reactants were premixed in a separate
flask, and the reactor was filled to the desired pressure. The
mixture was then irradiated for a predetermined time, after which
the contents of the reactor were analyzed by gas chromatography
(GC) using flame-ionization detection. Experiments were also
carried out using two other Pyrex reactors during the C2H4
experiments with GC analysis: an 80 cm3 × 20 cm long
cylindrical reactor and a 200 cm3 × 10 cm long cylindrical
reactor surrounded by a temperature-controlling jacket.7 The
rate constant k1 was independent of the reactor used in these
experiments. For reaction 1, experiments were also carried out
over the temperature range 297-383 K at pressures between
0.65 and 0.75 Torr to measure the temperature dependence of
k1 in the low-pressure limit.
100
100
5
5
1.5
1.5
GC
FTIR C2H5Cl
GC CH3Cl
FTIR CH3Cl
GC CH3Cl
FTIR CH3Cl
114
13
85
10
26
10
6
112
67
81
16
25
15
6
3.1, 2.9
3.1 ( 0.3
209
323
68
4.5
4.2 ( 0.3
1.45 ( 0.05
1.50 ( 0.08
1.9
98
56
31
43
0.34 GC
0.33 GC
CH4
CH4
44
2
1.80 ( 0.15
Average Cl atom concentrations for both techniques typically
were in the range (1-4) × 1010 cm-3. The GC and FTIR data
at 100 Torr in Table 1 were obtained at very different Cl atom
concentrations (GC ) 2.5 × 1010 cm-3; FTIR ) 6 × 108 cm-3
)
with no difference in the observed rate constant ratio.
Results
The determination of the relative rate constant ratios in ref 1
were carried out in air as the diluent gas. During the present
measurements, we discovered that the apparent rate constant
of reaction 1 increased when the amount of O2 in the diluent
gas was raised. This effect was observed only for pressures
below 100 Torr and became larger as the total pressure
decreased. In the FTIR experiments, the rate constant ratio using
a C2H5Cl reference, k1/k6, was a factor of two higher in O2
diluent than in N2 diluent at a total pressure of 1.5 Torr. GC
experiments at 1.5 Torr using CH3Cl as the reference showed
that the ratio k1/k5 increased by approximately 25% when using
O2 diluent in comparison to that in N2.
Previous experiments have shown that oxidation of C2H5Cl
produces CH3CO radicals in approximately 80% yield.8-10
Michael et al.11 and Tyndall et al.12 have demonstrated that OH
radicals are generated with approximately 100% yield during
the reaction of CH3CO with O2 at total pressures of 1-3 Torr.
Tyndall et al. also determined that a similar effect occurred
during the oxidation of CH3COCO radicals at low-pressure and
that OH generation did not occur when acetyl radicals were
oxidized at 760 Torr. Thus, OH radicals are certainly formed
at low-pressure when CH3CO is oxidized and may be formed
during the oxidation of many aldehydes.
In both systems, the rates of reactions 1 and 2 were measured
relative to the abstraction reactions of Cl atoms with five
reference compounds: CH4 (reaction 3); CHCl3 (reaction 4);
CH3Cl (reaction 5); C2H5Cl (reaction 6); or C2H6 (reaction 7).
The rate constants of the reference reactions used to calculate
absolute rate constants for k1 and k2 at 297 K were k3 ) 1.0 ×
10-13; k4 ) 1.1 × 10-13; k5 ) 4.9 × 10-13; k6 ) 8.05 × 10-12
;
and k7 ) 5.7 × 10-11 cm3 molecule-1 s-1. The reference
species for each experiment was chosen such that the rates of
reactions 1 or 2 were within a factor of ∼10 of that of the
reference reaction in the pressure range over which the reference
species was used. Experiments were carried out over the
pressure range 0.2-700 Torr in N2 diluent.
In the FTIR experiments, the consumptions of C2H4 (or C2H2)
and the reference compound were determined after each of three
irradiations for each mixture, spanning a consumption range of
a factor of 3-4. The relative rate constants (e.g. k1/kref) were
then obtained from the slopes of plots of ln{[C2H4]0/[C2H4]t}
or ln{[C2H2]0/[C2H2]t} vs ln{[ref]0/[ref]t} over the consumption
range. In all cases, straight lines were obtained extending
through the origin, indicating that reactions with products were
not occurring to within experimental error.
During the GC measurements, the experiment was ended at
a chosen time and the contents were analyzed. Therefore,
samples after varying amounts of consumption of the reactants
during one experiment could not be obtained. However,
consumptions of C2H4 varying from 15 to 98% were observed
during this series of experiments with no systematic change in
the measured rate constant ratios. Thus, these experiments also
indicate that secondary reactions with products do not affect
the determination of the rate constant ratios.
The observation that O2 affects the measured rate constant
ratios indicates that reactions of C2H4 with radicals other than
Cl may occur at low pressures in our relative rate measurements,
leading to erroneous results in the presence of O2. The
magnitude of this interference may depend on the total pressure,
possibly on the reference compound chosen, and on the initial
reactant concentrations. In the absence of O2, Cl is the only
radical that can consume the reactants since the alkyl radicals
formed react rapidly with Cl2 to form stable chlorides and
regenerate Cl atoms. The alkyl radical concentrations are kept
very low by the reaction with Cl2 and cannot affect the results.
Thus, measurements of the rate constant ratios must be made
in N2 rather than O2 at low pressure to avoid possible
interference from reactions involving OH radicals.
In addition, the measurements of k2 published in ref 1 at
pressures below 100 Torr are slightly in error because of a
recently discovered nonlinearity in the concentration dependence
of the C2H2 IR absorbance at low pressure caused by the
narrowing of the line widths. This nonlinearity increases as
the pressure decreases, and the rate constant ratios at 10 Torr
will be underestimated by ∼30% if a correction for the
nonlinearity is not made. Because of these two systematic errors
at pressures below 100 Torr, only the rate constants at pressures
Initial reactant concentrations varied substantially between
the FTIR and GC experiments, providing verification that the
measured rate constants do not depend on mixture composition.
Selected examples of initial conditions studied using both FTIR
and GC are presented in Table 1 for data obtained over the
pressure range 0.3-100 Torr. Also included in Table 1 are
the rate constant ratios derived at each pressure. As described
above, the FTIR data were obtained from several successive
irradiations during each experiment, and a statistical error (2σ)
for each measurement is quoted. Only single points are
normally available for each GC experiment, and the individual
rate constants determined from these data are tabulated. At two
pressures (0.33 and 1.5 Torr), multiple GC determinations were
performed, and for these data a 2σ uncertainty is quoted.

Reactions of Cl with C2H4 and C2H2
J. Phys. Chem., Vol. 100, No. 10, 1996 4113
Figure 1. k1 plotted as a function of total pressure of N2. Filled symbols ) FTIR experiments; unfilled symbols (for P e 100 Torr) ) GC
experiments; unfilled circles ) data from ref 1. Reference compounds are indicated by symbol shape. Lines represent Troe fits to the data using
the constants shown. k(int) is the value of the intercept rate constant (see text).
of 100 Torr or above from ref 1 were used in the redetermination
of the pressure dependencies of k1 and k2 in the present paper.
C2H4 Measurements. Figure 1 presents all measurements
of the rate constant k1 at 297 K as a function of total pressure
both in the present experiments from 0.2-100 Torr and in the
previous experiments at pressures g100 Torr. Note that five
different reference compounds have been used in these experi-
ments, and the pressure ranges for different reference species
overlap. For the present experiments, the GC data are shown
as unfilled symbols in Figure 1, while FTIR experiments are
presented as filled symbols. The data from ref 1 were all
obtained using C2H6 as the reference species and are shown as
unfilled circles for both GC and FTIR measurements. At
pressures where multiple measurements were performed, the
values of k1 agree to within (10% of the mean, and the values
obtained from different reference compounds also agree. The
agreement between rate constants determined using a variety
of reference compounds with different initial reactant concentra-
tion ratios (see Table 1) provides strong evidence that k1 is being
determined accurately in these relative rate measurements. The
fact that the GC and FTIR measurements are indistinguishable
demonstrates that heterogeneous effects and unknown systematic
errors do not affect these measurements of the pressure
dependence of k1 except possibly at very low pressure, as
discussed in the following paragraph.
manifolds to the minimum pressure achievable with a rotary
vacuum pump and then setting the manometer reading to zero.
If the pressure at the manometer was not exactly zero, this
technique would lead to an underestimate of the true pressure
and could contribute to the observed nonzero intercept.
This apparent intercept becomes negligible to within the
experimental data scatter for pressures above 1 Torr. For this
reason, only the pressure dependent data for 1 Torr and above
were fitted to the Troe expression13 (using eqs 6.1 and 6.3-6.6
of ref 13) with a fixed intercept of 4.5 × 10-14 cm3 molecule-1
s-1 to determine values of the high- and low-pressure limiting
rate constants for reaction 1. Because reaction 1 approaches
its low-pressure limit at 100 Torr, the presence of this nonzero
intercept does not affect the determination of k1(0) significantly
provided that the fit is limited to data at pressures g1 Torr.
Inclusion of the intercept does provide a slightly better fit to
the data below 1 Torr.
The lines in Figure 1 represent the falloff curves generated
by Troe fits to the data using two different center-broadening
factors, Fcent ) 0.6 (solid line) and Fcent ) 0.4 (dotted line).
For Fcent ) 0.6, the high- and low-pressure limiting rate
constants are k1(∞) ) (3.2 ( 0.15) × 10-10 cm3 molecule-1
s-1; and k1(0) ) (1.42 ( 0.05) × 10-29 cm6 molecule-2 s-1
.
For Fcent ) 0.4, k1(∞) ) (5.7 ( 1.5) × 10-10 cm3 molecule-1
s-1 and k1(0) ) (1.64 ( 0.05) × 10-29 cm6 molecule-2 s-1
.
Results at the lowest pressures measured (0.2-2 Torr) are
presented in the inset to Figure 1. An extrapolation of these
low-pressure data indicates a possible nonzero intercept in this
plot of (4.5 ( 4) × 10-14 cm3 molecule-1 s-1 at P ) 0 Torr,
although the estimated uncertainty is large. This intercept could
result from the presence of a pressure-independent reaction
between C2H4 and Cl atoms such as k1b. However, it could
also result from a systematic underestimate of 0.1 ( 0.1 Torr
in the pressure measurements for both experiments. The reactor
pressures were measured by capacitance manometers, and the
zeros for these manometers were set by pumping out the vacuum
The error limits quoted above are statistical (2σ) only as
determined by the quality of the fit and do not include systematic
errors. While the curve calculated using Fcent ) 0.4, gives a
slightly better fit in the range 50-500 Torr, the difference
between the curves is less than 10% over the entire pressure
range and is within the data scatter. This illustrates the difficulty
of determining a value of Fcent from falloff measurements unless
data are available in both the high- and low-pressure limiting
regions. Thus, even though data spanning more than 4 orders
of magnitude in pressure have been obtained, the high-pressure
limit has not been reached at 3000 Torr, and Fcent cannot be

4114 J. Phys. Chem., Vol. 100, No. 10, 1996
Kaiser and Wallington
Figure 2. Plot of k1 as a function of total pressure at 349 K.
Figure 3. Temperature dependence of the measured value of k1/[M]
at a constant total pressure of 0.7 ( 0.05 Torr (unfilled circles). Rate
constant from Figure 2 is shown as the filled circle. The solid line
represents the fit to the data giving the low-pressure limiting rate
constant presented in the figure.
determined accurately. Decreasing Fcent from 0.6 to 0.4
increases k1(0) by only 15% because the falloff curve is very
near the low-pressure limit at 1-10 Torr. However, the high-
pressure limiting rate constant is more sensitive to the choice
of Fcent, increasing by 80%. While either falloff curve in Figure
1 predicts the observed data to within the (10% data scatter,
Torr is a factor of ∼(4 ( 1) smaller than the rate constant
measured for k1b by Parmar and Benson4 and by Dobis and
Benson.5 However, k1 is still decreasing with pressure at 0.2
Torr (see Figure 1), and the true value of k1b is likely to be
much smaller than k1 at 0.2 Torr.
our best estimates of the true values of k1(0) [)(1.64 ( 0.2) ×
+0.2
10-29] and k1(∞) [)(5.7 ( 2.5) × 10-10], Fcent ) 0.4 , are
-0.1
uncertain to approximately (15% and (50%, respectively
(assuming that Fcent lies within the range 0.3-0.6), largely
It is possible that the small intercept in the fall off curve
discussed above might be caused by the abstraction reaction.
However, the value of this intercept is very uncertain, and
part or all of the intercept may result from systematic errors,
particularly in the pressure measurement. Thus, an alternate
method of determining k1b is needed. Measuring the product
yields offers such a method. The CH2ClCH2 radical formed in
reaction 1a will react with Cl2 to form CH2ClCH2Cl. The rate
constant for this reaction will be fast on the basis of the rate
constant determined by Knyazev et al.15 for the isomeric
1-C2H4Cl radical [k298 ) 4.4 × 10-12 cm3 molecule-1 s-1].
Formation of the vinyl radical by reaction 1b will result in the
production of C2H3Cl by a fast reaction16 with Cl2 [k ) 8.7 ×
10-12 exp(480/RT) cm3 molecule-1 s-1]. Thus, measurement
of the yields of 1,2-C2H4Cl2 and C2H3Cl provides a method for
determining k1a/k1 and k1b/k1, respectively. A potential difficulty
in these measurements is that the rate constants for reaction of
Cl with 1,2-C2H4Cl2 or C2H3Cl are faster than k1, and secondary
consumption of products will be important:
because of uncertainty in Fcent
.
Temperature Dependence of k1(0). The ratio k1/k3 (methane
as the reference species) was measured over the temperature
range 298-383 K at a nearly constant pressure of 0.70 ( 0.05
Torr using the jacketed reactor with GC analysis. The tem-
perature-dependent rate constant expression for reaction 3 used
to calculate k1 from this ratio is k3 ) 9.6 × 10-12 exp(-2683/
RT) cm3 molecule-1 s-1 14
At this pressure, k1a is essentially
.
in the low-pressure limit at 297 K, as shown by the data in
Figure 1, and the addition reaction should also be in the low-
pressure regime at higher temperatures. The pressure depend-
ence of k1 was determined near the middle of this temperature
range (349 K) to verify that a linear relation exists between k1
and P. The results of this experiment, presented in Figure 2,
show that k1 is in the third-order regime over the pressure range
0.3-2 Torr at 349 K. The third-order rate constant can be
calculated [k1(0) ) 1.13 × 10-29 cm6 molecule-2 s-1] from the
slope of the line in this figure. Figure 3 presents k1/[M]
measured as a function of temperature at 0.7 ( 0.05 Torr. As
expected, the addition reaction has a negative temperature
coefficient, which can be described by the expression k1(0) )
(1.7 ( 0.3) × 10-29(T/298)-3.28 cm6 molecule-2 s-1 assuming
that the reaction is in the low-pressure regime at 0.7 Torr
throughout this temperature range. Included as a filled circle
in the plot is the value of k1(0) determined from the slope of
the pressure dependence of k1 in Figure 2. This agrees with
the temperature-dependent data obtained at constant pressure.
Determination of k1b/k1: FTIR Experiments. At 0.2 Torr,
k1 ) (1.3 ( 0.25) × 10-13 cm3 molecule-1 s-1 (see Figure 1).
Since total C2H4 consumption is being measured, the relative
rate measurements include all possible paths for C2H4 removal,
and the rate constant k1b cannot be greater than the smallest k1
measured in these experiments. Therefore, the value of k1 at
0.2 Torr represents an upper limit to the pressure-independent
abstraction rate constant k1b. Our measured rate constant at 0.2
Cl + 1,2-C2H4Cl2 ) C2H3Cl2 + HCl
Cl + C2H3Cl + M ) C2H3Cl2 + M
(8)
(9)
The rate constant of reaction 8 has been measured previously
by Wine and Semmes17 (k8 ) 2.2 × 10-11 exp(-793/T) cm3
molecule-1 s-1) and by Tschuikow-Roux et al.18 ()1.33 × 10-12
after correcting the value of his reference reaction [Cl + CH4]
from 0.955 to 1.0 × 10-13 at 297 K). The kinetics of reaction
8 was also studied at 297 K as part of the present work. A
value of k8/k10 ()3.9 ( 0.12) was measured in our FTIR reactor,
Cl + CH3F ) CH2F + HCl
(10)
Using the measured value of k10 ) (3.2 ( 0.5) × 10-13 cm3
molecule-1 s-1 19 gives k8 ) (1.25 ( 0.2) × 10-12 cm3

Reactions of Cl with C2H4 and C2H2
J. Phys. Chem., Vol. 100, No. 10, 1996 4115
<10%, respectively, at 0.2 Torr total pressure. These results
show that more than 80% proceeds by channel 1a at this
pressure. Therefore, k1b e 0.2k1 (at 0.2 Torr) ) (2.6 ( 0.5) ×
10-14 cm3 molecule-1 s-1. This upper limit is a factor of 20
smaller than the values published by Parmar and Benson4 and
Dobis and Benson.5
Determination of k1b/k1: GC Experiments. Measurements
of the C2H3Cl yield were also carried out as a function of
pressure using the GC technique at three temperatures (300,
343, and 383 K). The GC measurement allows determinations
of vinyl chloride yields of ∼0.05%, providing a very sensitive
method for determining k1b. As discussed above, secondary
consumption of vinyl chloride is important in these measure-
ments. Therefore, the ratio k9/k1 was measured in the GC
experiments and found to be 2.25 ( 0.4 and 2.85 ( 0.6 at 383
and 300 K, respectively. Measurements were carried out at 4
and 20 Torr at both temperatures. The ratios determined by
GC are independent of pressure, and the measurement at 300
K is identical to that determined from the FTIR experiments at
0.2 Torr to within experimental error.
Figure 5 presents the raw, uncorrected C2H3Cl yields at the
three temperatures as a function of the fraction of the initial
C2H4 consumed (symbols) for several initial pressures. As
described above, each individual data point represents a separate,
single determination of the yield. In general, the measured
yields decrease as the C2H4 consumption increases because of
secondary consumption of C2H3Cl. However, this drop-off is
relatively slow, permitting extrapolation to zero C2H4 consump-
tion, and a comparison of the data at the three temperatures
shows that the yield of vinyl chloride increases substantially as
the temperature increases. In addition, the yield generally
decreases with increasing pressure, as shown most clearly in
the data at 343 K. Both of these effects are expected from a
competition between reactions 1a and 1b. Reaction 1b will have
a positive activation energy, while reaction 1a has a negative
temperature coefficient in the low-pressure region, as discussed
above. Increasing the pressure will increase the rate of reaction
1a, while the rate of reaction 1b remains constant, decreasing
the C2H3Cl yield as observed. Because k9 is 2.25 times larger
than k1 at 383 K, the apparent C2H3Cl yield should decrease by
∼50% at this temperature as the C2H4 consumption increases
from 0 to 60% because of secondary consumption of C2H3Cl
by Cl atoms. However, as shown in Figure 5, the vinyl chloride
yield at 383 K does not decrease to this extent at any of the
four pressures studied and at the lowest pressure actually
increases. This suggests that at elevated temperature a second-
ary source for the formation of C2H3Cl may exist in these
experiments.
Because 1,2-C2H4Cl2 is the major product from reaction 1
and is, therefore, a potential source for secondary generation
of C2H3Cl, two experiments were performed in which 16 Torr
of a mixture of 1,2-C2H4Cl2 (3980 ppm) and Cl2 (8220 ppm)
in N2 (balance) was irradiated by UV light at 383 K. These
experiments showed that C2H3Cl was indeed formed with a yield
of 6% independent of C2H4Cl2 consumption (22-68%) after
correction for loss of C2H3Cl by reaction with Cl. We believe
that this occurs by Cl elimination from the CH2ClCHCl radical
produced by the initial abstraction reaction. This elimination
reaction is in competition with the reaction of 1,2-dichloroethyl
radicals with Cl2 to form 1,1,2-trichloroethane.
Figure 4. Measured CH2ClCH2Cl yields from reaction 1 as a function
of the percentage C2H4 consumed for both FTIR and GC experiments.
Fits to the data with different choices of yield and secondary
consumption rate constants are shown as lines. P ) 0.2 Torr.
molecule-1 s-1. The measurements of k8 performed by Wine
and Semmes17 and Tschuikow-Roux et al.18 agree well with
our result at 297 K.
The measured yield of 1,2-C2H4Cl2 uncorrected for secondary
consumption is presented in Figure 4 as a function of the
percentage of the C2H4 consumed for experiments carried out
at 0.2 Torr in both FTIR and GC reactors. As expected, the
apparent yield decreases with increasing consumption of C2H4
because of reaction 8, but data for C2H4 consumption of <10%
indicate that the yield is >75%. The data in Figure 4 have
been fitted to a simple kinetic mechanism containing reactions
1a (to form 1,2-C2H4Cl2), 1b (to form C2H3Cl), and 8. Using
the estimates of the rate constant ratios (k8/k1 ) 10.5 and k1b/
k1a ) 0 [100% 1,2-C2H4Cl2 yield]) produces the solid line in
Figure 4, which fits the data well. Reducing the ratio k8/k1 to
8.4 (the maximum of the estimated uncertainty) yields the dash-
dot line, which does not fit the data as well, particularly in the
region where the FTIR data are the most accurate (15-30%
C2H4 consumption). Changing the yield of 1,2-C2H4Cl2 to 80%
by setting k1b/k1a ) 0.176 while maintaining k8/k1 ) 8.4
produces a fit which falls below the maximum of the error
bounds for the data at <10% C2H4 consumption and below the
measured data at higher consumption although within their error
bounds. The data in Figure 4 indicate that the 1,2-C2H4Cl2 yield
is 100 ( 20%. Thus, the yield of 1,2-C2H4Cl2 is >80%
including uncertainty in the data and in the rate constant ratios
used to correct for secondary consumption.
During the experiments in which the 1,2-C2H4Cl2 yield was
measured, we searched for infrared features attributable to
C2H3Cl, but none were found. On the basis of the C2H3Cl
detection limit, the upper limit to the C2H3Cl yield was
determined to be <8% for the three FTIR experiments in which
the C2H4 consumption was <10%. The rate constant ratio k9/
k1 was measured to be 3.0 ( 0.5 at 0.2 Torr, and correction for
vinyl chloride consumption in the determination of the vinyl
chloride yield would be e15% for these three data points. After
correction for secondary consumption, the measured upper limit
to the C2H3Cl yield based on these experiments is e10%,
indicating that k1b <1.3 × 10-14 cm3 molecule-1 s-1 at 297 K.
In summary, the yields of 1,2-C2H4Cl2 and C2H3Cl following
the UV irradiation of C2H4/Cl2/N2 mixtures were >80% and
CH2ClCHCl + M ) CH2CHCl + Cl + M
CH2ClCHCl + Cl2 ) CH2ClCHCl2 + Cl
(11)
(12)
On the basis of the yield (Y) of vinyl chloride corrected for

4116 J. Phys. Chem., Vol. 100, No. 10, 1996
Kaiser and Wallington
TABLE 2: Measurement of k1b and k11/k12
temp
(K) (Torr)
P
[C2H4]0
(ppm)
[Cl2]0
(ppm)
a
k1b
k11/k12
N/A
N/A
N/A
N/A
300
343
383
1.7b
4.9
5.5
9.8
68 × 103 106 × 103 <2 × 10-15
512
60
488
101
53
1.5
1.3
1.9
54
k1b (av) ) (1.56 ( 0.5) × 10-15
3.2
5.5
8.2
31 × 103 62 × 103
3.3 × 10-15 7.6 × 10-5
22
31
22
41
62
41
3.6
3.2
3.3
5.4
5.6
4.6
20.0
k1b (av) ) (3.35 ( 0.4) × 10-15
4.2
7.9
8.0
19 × 103 41 × 103
0.6 × 10-14 5.0 × 10-4
19
20
19
41
41
41
1.2
1.5
1.3
2.8
3.0
5.2
16.2
k1b (av) ) (1.16 ( 0.6) × 10-14
a Rate constants in units of cm3 molecule-1 s-1. k1b is calculated
from the C2H3Cl yield at zero C2H4 consumption in Figure 5 using
measured values of k1. The measured values of k1 at 343 and 383 K,
determined at each pressure, are consistent to within (20% with the
data in Figure 3 after correction for the change in pressure, including
a rollover (10-25%) toward the high-pressure limit, as shown in Figure
1. Values of k1 at 300 K are from Figure 1. b This point not used in
calculations, as discussed in the text.
of the ratio k11/k12 derived from the fits at 383 K is (4 ( 1.5)
× 10-4, in satisfactory agreement with the ratio ()4.9 × 10-4
)
determined above from the limited study of the Cl + 1,2-
C2H4Cl2 reaction. This agreement provides support for the
validity of the fits. At 343 K, the ratio k11/k12 deduced from
the fits at 343 K in Figure 5 is (6 ( 2) × 10-5. A sharp decrease
in this ratio with temperature is expected because of the
endothermicity of reaction 11, but a precise value for the
temperature dependence of this ratio cannot be determined
because of the substantial uncertainty. At 300 K, reaction 11
should be negligible and was set to zero for the data fits.
The C2H3Cl yield at 300 K becomes very small, approaching
the detectability limit for all data except that at 4.9 Torr, which
was determined at high C2H4 and Cl2 mole fractions. The data
for other pressures at 300 K are less certain, although it does
appear that at very low pressure (1.7 Torr) an additional source
of C2H3Cl may be present, causing a significant increase in yield
as the C2H4 consumption increases. This low-pressure point
was not used further in the data analysis, although it does
provide an upper limit to the value of k1b at 1.7 Torr and 300
K. The values of k1b calculated from the data at each
temperature and pressure are presented in Table 2. These rate
constants are plotted in Figure 6 as a function of T-1. The
activation energy for reaction 1b determined from the slope of
this plot is E1b ) 5.43 ( 1.4 kcal mol-1, and the preexponential
factor is 1.2(+8, -0.9) × 10-11 cm3 molecule-1 s-1. This pre-
exponential factor is smaller than is typical for H atom
abstraction by Cl from other small hydrocarbon molecules (e.g.
A(C2H6)7 ) 8.7 × 10-11 and A(C4H10)20 ≈ 1.8 × 10-10 cm3
molecule-1 s-1). On the basis of these data for ethane and
Figure 5. Plot of the raw, uncorrected vinyl chloride yield as a function
of the fraction of C2H4 consumed for three temperatures. The total
pressure is shown for each experiment.
secondary consumption at 16 torr in the above mixture, the ratio
of the rate constants k11/k12 can be estimated:
k11
[Cl2]av
[M]
Y
)
) 4.9 × 10-4
k12 1 - Y
n-butane, the average A factor per C-H bond is ∼1.5 × 10-11
,
To determine the best value of k1b from the data in Figure 5,
the measured yields at each pressure were fitted by a kinetic
mechanism containing reactions 1a, 1b, 8, 9, 11, 12. The values
of k1 at 343 and 383 K were obtained at the experimental
pressures from relative rate measurements using either CH4 or
CH3Cl as the reference reactant; the rate constants are consistent
with the results in Figure 3 after correction for pressure effects.
For each pressure, the values of k1b and k11/k12 were varied to
obtain the best fit to the experimental data. The fits are shown
as lines in Figure 5, and the optimum values of k1b and k11/k12
used to generate the fits are presented in Table 2. The average
and we might expect that the A factor for reaction (1b) would
be ≈ 4 × 1.5 × 10-11 ) 6 × 10-11 cm3 molecule-1 s-1. This
value is within the broad range of experimental error for A1b
and suggests that the best estimate for the activation energy of
k1b actually lies near the higher end of the error range quoted
above (≈6.5 kcal mol-1). The line determined by this “best
estimate” A factor and activation energy is shown as the dotted
line in Figure 5.
It is possible that reaction 1a could become reversible as the
temperature increases because its exothermicity is only ≈20

Reactions of Cl with C2H4 and C2H2
J. Phys. Chem., Vol. 100, No. 10, 1996 4117
TABLE 3: Determination of the Heat of Formation of C2H3
thermodynamic
species
property
300 K
343 K
383 K
a
C2H3
∆Hf,T
ST°
∆Hf,T
ST°
∆Hf,T
ST°
∆Hf,T
ST°
°
°
°
°
70.4 ( 0.3
55.68
12.52
52.45
28.97
39.49
-22.05
44.68
70.6 ( 0.2
57.11
12.20
53.9
29.02
40.20
-22.07
45.63
70.2 ( 0.4
58.37
11.91
55.20
29.08
40.78
-22.11
46.4
b
C2H4
Clb
HClb
a Heats of formation for C2H3 calculated from current data presented
in Table 2 using the third law as described in the text. Entropies for
C2H3 were obtained from W. Tsang using the following vibrational
frequencies and structural properties (vibrational frequencies: 776; 818;
948; 1002; 1383; 1669; 3004; 3090; 3331 cm-1. C2V symmetry. Bond
lengths: CdC, 1.298 Å; CH2, 1.08 Å; CH, 1.06 Å. Trigonal bond
angle for methylene group. Structure properties taken from Keil, D.
G.; Lynch, K. P.; Cowfer, J. A.; Michael, J. V. Int. J. Chem. Kinet.
1976, 8, 825).22 Units enthalpy ) kcal mol-1; entropy cal K-1 mol-1
.
b Thermodynamic quantity obtained from the JANAF Tables.23
Figure 6. Plot of k1b as a function of the reciprocal of the temperature.
The solid line is a linear least squares fit to the data [k ) 1.2 × 10-11
exp(-5430/RT)]. The dotted line represents the rate constant [k ) 6 ×
10-11 exp(-6500/RT)] obtained based on the A factor expected from
typical abstraction reactions of H atoms from hydrocarbons by Cl. See
discussion in the text.
reaction rate constant k1a from Figure 6 and that of the reverse
channel k-1a from ref 21 is ∆Hrx(1a) ) (5.43 ( 1.4) + (0.670
( 0.23) ) (6.1 ( 1.6) kcal mol-1. On the basis of this heat of
reaction and the known heats of formation of the remaining
reactants and products, the second law heat of formation for
C2H3 at 343 K is ∆Hf,343°(C2H3) ) 6.1 + 22.1 + 29 + 12.2 )
(69.4 ( 1.6) kcal mol-1. Correcting this to 298 K, the second
law determination gives ∆Hf,298°(C2H3) ) 69.6 ( 1.6 kcal
mol-1. As discussed above, the deviation of the A factor for
reaction 1b (derived from Figure 6) from that expected based
on data for other small hydrocarbons suggests that the heat of
reaction for (1b) is actually ∼1 kcal larger ()7.1 kcal mol-1).
This would increase the second law heat of formation to 70.6
kcal/mol. Thus, all of these determinations of the heat of
formation of the vinyl radical agree to well within the stated
experimental errors, and the more precise values determined
by the third law are 3.7 kcal larger than the previous best kinetic
estimate of this quantity determined by chemical kinetic
measurements of the equilibrium constant.21 The average of
the current third law measurements ()70.6 ( 0.4) agrees to
within experimental error with the determination of the bond
dissociation energy of ethylene at 298 K ()111.2 ( 0.8 kcal)
by Ervin et al.2 using negative-ion photoelectron spectroscopy.
This bond dissociation energy when combined with the heats
of formation of C2H4 and H can be used to calculate the heat
of formation of the vinyl radical ∆Hf,298°(C2H3) ) (71.6 ( 0.8)
kcal mol-1]. Therefore, the measurements reported herein have
removed the discrepancy between the kinetic measurement of
this thermodynamic quantity and that determined by negative-
ion photoelectron spectroscopy.
kcal. If the reaction was reversible on the time scale of these
experiments, the measured C2H3Cl yield would give an upper
limit to the true rate of reaction 1b because multiple passes
through reaction 1a would take place. To estimate this effect,
two mixtures of C2H5Cl, Cl2, and N2 were irradiated at 383 K.
Reaction 6 forms CH2ClCH2 radicals in 18% yield8 and can be
Cl + C2H5Cl ) CH3CHCl + HCl (82%)
Cl + C2H5Cl ) CH2ClCH2 + HCl (18%)
(6a)
(6b)
used to measure the fraction of CH2ClCH2 radicals which form
ethene by reaction -1a. The results indicate that at 383 K, the
ethylene yield per CH2ClCH2 radical formed at typical condition
in Table 2 (8 Torr total pressure and 20 000 ppm Cl2) is ≈0.7%.
Thus, at 383 K reaction -1a is negligible under our experimental
conditions.
Heat of Formation of C2H3. The measured values of k1b in
Table 2 can be used in combination with the rate constant for
the reverse reaction (k-1b ) 6.6 × 10-13 exp(670/RT) cm3
molecule-1 s-1 with an error of (15%) determined by Russell
et al.21 to calculate the heat of formation of C2H3 by either the
third law or second law methods. Table 3 presents the heat of
formation of the vinyl radical at each temperature as calculated
by the third law method using the average of the k1b at each
temperature. Table 3 also presents the entropies and heats of
formation of the other species used in the calculation. These
third law heats of formation of the vinyl radical are ∆Hf,300° )
70.4 ( 0.3; ∆Hf,343° ) 70.6 ( 0.2; and ∆Hf,383° ) 70.2 ( 0.4
kcal mol-1. After correcting each of these values to 298 K
using available heat capacity data,22 the measured heats of
formation at 298 K are ∆Hf,298°(C2H3) ) 70.4 ( 0.3, 70.8 (
0.3, and 70.6 ( 0.4 kcal mol-1 based on the data at 300, 343,
and 383 K, respectively. These agree with one another to well
within the estimated uncertainties, which include the statistical
data scatter of our measurements (2σ) combined with the 15%
uncertainty in the data of Russell et al.21 The entropies and
heats of formation for the other species used in the third law
calculation are assumed to have no error.
C2H2 Measurements. The rate constant for the addition of
Cl to C2H2 as a function of total pressure in N2 is shown in
Figure 7. As was described for Cl addition to ethylene, results
were obtained in both the FTIR and GC reactors. In these
experiments, the GC reactor was used at pressures of 0.3-10
Torr and the FTIR reactor for pressures of 10-700 Torr.
Methane and methyl chloride were the reference compounds
in the GC experiments, while methyl chloride, ethyl chloride,
and ethane were the reference compounds for the FTIR
measurements. The experiments in the GC reactor are shown
as unfilled symbols at pressures e10 Torr. The current FTIR
measurements are presented as filled symbols, while the previous
measurements1 of k2 with C2H6 as the reference species are
shown as unfilled circles for P g 100 Torr. For pressures near
10 Torr, experiments were carried out using both GC and FTIR
The heat of reaction for (1a) at the midpoint of the
temperature range based on the activation energy of the forward

4118 J. Phys. Chem., Vol. 100, No. 10, 1996
Kaiser and Wallington
Figure 7. k2 plotted as a function of total pressure of N2. Filled symbols ) FTIR experiments; unfilled symbols (for P e 10 Torr) ) GC experiments;
unfilled circles ) data from ref 1. Reference compounds are indicated by symbol shape. Lines represent Troe fits to the data using the constants
shown.
reactors and two reference compounds. Identical results were
obtained in all experiments at this pressure.
Conclusions
The pressure dependencies of the rate constants for the
reactions of Cl with C2H4 (k1) and C2H2 (k2) have been measured
at 297 K relative to several reference species (CH4, CH3Cl,
CHCl3, C2H5Cl, and C2H6) over the pressure range 0.2-100
Torr and 0.2-700 Torr, respectively. Experiments were carried
out in different reactors using both FTIR and GC detection.
These data, in combination with previous results obtained over
the pressure range 100-6000 Torr, have been fitted to Troe
expressions. These expressions fit the data to (10% over the
entire pressure range. However, the high- and low-pressure rate
constants for the reactions have correlated uncertainties of (50
and (15%, respectively, because of uncertainty in the center-
broadening factors. The temperature dependence of k1(0) was
measured over the range 297-383 K at 0.7 Torr. Its temper-
ature dependence can be described by the expression k1(0) )
Troe fits were performed to the data using two values of Fcent
()0.6 and 0.4), as was done for ethylene. The low- and high-
pressure limiting rate constants for Fcent ) 0.6 are k2(0) ) (6.1
( 0.2) × 10-30 cm6 molecule-2 s-1 and k2(∞) ) (2 ( 0.1) ×
10-10 cm3 molecule-1 s-1 at 297 K, where the uncertainties
represent 2 statistical standard deviations only. For Fcent ) 0.4,
k2(0) ) (7.1 ( 0.2) × 10-30 cm6 molecule-2 s-1 and k2(∞) )
(3.5 ( 0.1) × 10-10 cm3 molecule-1 s-1. As discussed for the
ethylene reaction, these expressions represent parametric fits
to the data accurate to within (10% over the entire pressure
range. However, the true values of the high- and low-pressure
rate constants have an additional uncertainty caused by the
uncertainty in the value of Fcent. The fit to the data is slightly
better using the smaller Fcent, although the difference between
the curves is <10%. Again this illustrates the difficulty of
determining a value of Fcent unless both the low- and high-
pressure regimes have been reached experimentally. The fact
that the pressure dependence of Cl addition to both ethylene
and acetylene is fitted better using Fcent ) 0.4 may indicate
that a value smaller than the commonly used Fcent ) 0.6 may
be appropriate. Ab initio calculations of the center-broadening
factor might resolve this question.
A previous study7 of the temperature and pressure dependence
of reaction 2 obtained the following rate constant expressions
using Fcent ) 0.6: k2(0) ) 5.4 × 10-30(T/300)-2.092 cm6
molecule-2 s-1 and k2(∞) ) 2.13 × 10-10(T/300)-1.045 cm3
molecule-1 s-1. Evaluating these expressions at 297 K gives
k2(0) ) 5.5 × 10-30 cm6 molecule-2 s-1; and 2.15 × 10-10
cm3 molecule-1 s-1. These values agree well with the Troe fit
to the current data calculated using Fcent ) 0.6. Thus, the
dependence of k2 on both pressure and temperature is well
established over the ranges 0.3-6000 Torr and 225-370 K,
although the true values of the high- and low-pressure limiting
rate constants are subject to correlated uncertainties caused by
1.73 × 10-29(T/298)-3.28 cm6 molecule-2 s-1
.
Finally, measurements were made of the rate constant of the
abstraction reaction (1b) at three temperatures by determining
the yield of vinyl chloride. These measurements permit a
determination of the heat of formation of the vinyl radical using
either the second or third law methods. The values obtained
by the third law [∆Hf,298° ) 70.6 ( 0.4 kcal mol-1] and the
second law [∆Hf,298° ) 69.6 ( 1.6 kcal mol-1] are substantially
larger than those obtained previously by chemical kinetics
methods. By examining the pre-exponential factor for k1b, it is
likely that the second law value is in fact underestimated by
≈1 kcal. Both of these determinations agree to within
experimental error with the recent measurement by negative-
ion photoelectron spectroscopy [∆Hf,298° ) 71.6 ( 0.8 kcal
mol-1]. Therefore, these experiments have removed the dis-
crepancy between these two methods of measuring the heat of
formation of this important hydrocarbon radical.
Acknowledgment. We thank W. Tsang for his very helpful
comments and for providing the entropies and heat capacities
for C2H3. We also thank the referees for their useful insights
into this problem.
uncertainty in Fcent
.

Reactions of Cl with C2H4 and C2H2
J. Phys. Chem., Vol. 100, No. 10, 1996 4119
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JP953178U