Kinetics of the C2H3 + H2 ->//<- H + CH4 Reactions

Article abstract of DOI:10.1021/jp9606568

The kinetics of the reactions C2H3 + H2 -> H + C2H4 (1) and CH3 + H2 -> H + CH4 (2) have been studied in the temperature ranges 499-947 K (reaction 1) and 646-1104 K (reaction 2) and He densities (6-18)E16 atoms cm^-3 by laser photolysis/photoionization mass spectrometry.Rate constants were determined in time-resolved experiments as a function of temperature.Ethylene was detected as a primary product of reaction 1.Within the above temperature ranges the experimental rate constants can be represented by Arrhenius expressions k₁ = (3.42 +/- 0.35)E-12 exp(-(4179 +/- 67 K)/T) cm³ molecule^-1 s^-1 and k₂ = (1.45 +/- 0.18)E-11 exp(-(6810 +/- 102 K)/T) cm³ molecule^-1 s^-1.Experimental values of k₂ are in agreement with the available literature data.The potential energy surface and properties of the transition state for reactions (1, -1) were studied by ab initio methods.Experimental and ab initio results of the current study were analyzed and used to create a transition state model of the reaction.The resulting model provides the temperature dependencies of the rate constants for both direct (1) and reverse (-1) reactions in the temperature range 200-3000 K: k₁ = 1.57E-20T^2.56 exp(-(2529 K)/T) cm³ molecule^-1 s^-1, k_-1 = 8.42E-17T^1.93 exp(-(6518 K)/T) cm³ molecule^-1 s^-1.Data on reactions 1 and -1 available in the literature are analyzed and compared with the results of the current study.

Full text of DOI:10.1021/jp9606568

1
1346
J. Phys. Chem. 1996, 100, 11346-11354
Kinetics of the C2H3 + H2 a H + C2H4 and CH3 + H2 a H + CH4 Reactions
†
Vadim D. Knyazev,* AÄ kos Bencsura, Stanislav I. Stoliarov, and Irene R. Slagle*
Department of Chemistry, The Catholic UniVersity of America, Washington, DC 20064
X
ReceiVed: February 29, 1996; In Final Form: April 18, 1996
The kinetics of the reactions C
2
H
3
+ H
2
f H + C
2
H
4
(1) and CH
3
+ H
2
4
f H + CH (2) have been studied
in the temperature ranges 499-947 K (reaction 1) and 646-1104 K (reaction 2) and He densities (6-18) ×
1
6
-3
10
atoms cm by laser photolysis/photoionization mass spectrometry. Rate constants were determined in
time-resolved experiments as a function of temperature. Ethylene was detected as a primary product of reaction
1
. Within the above temperature ranges the experimental rate constants can be represented by Arrhenius
-12
3
-1 -1
expressions k
1
) (3.42 ( 0.35) × 10 exp(-(4179 ( 67 K)/T) cm molecule
s
2
and k
are in agreement with the
available literature data. The potential energy surface and properties of the transition state for reactions (1,
1) were studied by ab initio methods. Experimental and ab initio results of the current study were analyzed
2
) (1.45 ( 0.18)
-
11
3
-1 -1
×
10 exp(-(6810 ( 102 K)/T) cm molecule s . Experimental values of k
-
and used to create a transition state model of the reaction. The resulting model provides the temperature
dependencies of the rate constants for both direct (1) and reverse (-1) reactions in the temperature range
-
20 2.56
3
-1 -1
-17 1.93
2
(
00-3000 K: k
1
) 1.57 × 10
T
exp(-(2529 K)/T) cm molecule s , k-1 ) 8.42 × 10
T
exp-
3
-1 -1
-(6518 K)/T) cm molecule s . Data on reactions 1 and -1 available in the literature are analyzed and
compared with the results of the current study.
I. Introduction
of reaction 1 at 400 K to that at 300 K was determined
experimentally, providing only a measure of activation energy.
The ratios of k1 to the rate constants of the addition of vinyl
radicals to acetylene were also determined at these two
temperatures.
Vinyl radicals are recognized as important intermediates in
hydrocarbon combustion processes with elementary reactions
of C2H3 influencing both the rate and products of the overall
combustion process. The reaction
6
Fahr et al. obtained the value of the rate constant of reaction
1
at room temperature by using laser photolysis with kinetic
H + C H f C H + H
2
(-1)
2
4
2
3
absorption spectroscopy and gas chromatographic product
-
20
3
analysis. These authors’ result (k1 ) (3 ( 2) × 10
cm
is an important source of vinyl radicals in flames.1 No direct
measurements of the rate constant of this reaction are reported
in the literature, although several indirect studies
reported over the past 25 years. Yampol’skii and Nametkin
et al. studied reaction -1 by final product analysis of C2H4
pyrolysis at temperatures 1073-1213 K. Just et al. studied
-1 -1
molecule s ) is 3 orders of magnitude lower than that
7
reported by Callear and Smith.
2-5
have been
Mebel et al.8 studied reaction 1 using various ab initio
methods combined with variational transition-state theory.
These authors reported several different k1(T) dependencies
obtained by using different theoretical methods. Tsang and
4
5
2
the unimolecular decomposition of ethylene and reaction -1
behind reflected shock waves by applying optical methods for
the detection of H atoms and C2H4. These authors derived
approximate values of k-1 at temperatures 1700-2080 K.
9
Hampson provided recommendations for the temperature
dependencies of the rate constants of reactions 1 and -1 based
2
on a bond energy - bond order fit to the data of Just et al. on
1
0
3
reaction -1 and the reaction thermochemistry. Baulch et al.
Jayaweera and Pacey determined the rate constant of reaction
recommended somewhat higher k-1 values on the basis of an
-
1 by gas chromatographic analysis of the products of ethylene
pyrolysis at 900 K.
The kinetics of the reverse reaction,
1
1
analysis of the available literature data. Laufer et al. applied
the bond order - bond energy method to predict the rate
constants of reaction 1 at low temperatures, and Weissman and
Benson used transition-state theory to calculate k1 and k-1
temperature dependencies.
1
2
C H + H f H + C H
4
(1)
2
3
2
2
Here, we report the results of a study of reaction 1 obtained
using laser photolysis/photoionization mass spectrometry at
temperatures in the range 499-947 K and bath gas (He)
can be used to obtain information on k-1 via the known
thermochemistry of reactions (1,-1). Reaction 1 also plays an
important role in the modeling of the chemistry of hydrocarbons
in the atmospheres of giant planets.6
1
6
-3
densities (6-18) × 10 atoms cm . The experiments on
-
16
reaction 1 required measuring rate constants as low as 8 × 10
Reaction 1 has been studied by indirect methods only at low
3
-1 -1
cm molecule
s
and working with concentrations of H2 as
7
temperatures. Callear and Smith investigated reaction 1 at 300
17
-3
high as 1.07 × 10 molecules cm . Although the experimental
technique applied in the current study has been successfully
used for measuring rate constants of many reactions of
hydrocarbon radicals, including those of vinyl radicals (e.g., refs
and 400 K by a gas chromatographic product analysis. Although
the rate constants reported by these authors are widely cited as
experimental results, in fact, only the ratio of the rate constant
1
3-16 and references cited therein), there have been no prior
†
On leave from the Central Research Institute for Chemistry, Hungarian
studies of such slow reactions of free radicals with molecular
hydrogen using this technique. In order to confirm the accuracy
Academy of Sciences, P.O. Box 17, H-1525 Budapest, Hungary.
X
Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(96)00656-9 CCC: $12.00 © 1996 American Chemical Society

Kinetics of C2H3 + H2 and CH3 + H2 Reactions
J. Phys. Chem., Vol. 100, No. 27, 1996 11347
of the experimental method, we therefore also measured the
rate constants of reaction
CH + H f H + CH
(2)
3
2
4
at temperatures 646-1104 K and bath gas (He) densities (6-
16
-3
1
8) × 10 atoms cm . Both reaction 2 and the reverse reaction
H + CH f CH + H (-2)
4
3
2
have been studied by many groups using a variety of methods
see, for example, reviews in refs 9, 10, 17-19). Rate constants
(
of reaction 2 obtained in our experiments, as well as those of
the reverse reaction, -2, calculated from the k2 values and
known thermochemistry, agree well with the results of other
groups (see below). Such agreement indicates the absence (in
the technique used here) of significant sources of experimental
errors associated with measuring low rate constants of R + H2
reactions using high concentrations of molecule hydrogen.
In order to obtain the rate constant values for the reactions 1
and -1, accurate extrapolation to temperatures outside of the
range of the current experiments is required. Ab inition and
transition-state theory modeling, together with the known
thermochemistry of reactions (1,-1), resulted in k1(T) and k-1(T)
rate expressions that allow extrapolation to temperatures other
than those of our experiments. Tunneling was included by using
a method (applied earlier15 in this laboratory to the modeling
of C2H3 unimolecular decomposition) in which an important
parametersthe width of the potential energy barriersis obtained
from ab initio calculations.
Figure 1. First-order C
2 3 2
H decay rate k′ vs [H ]. The intercept at
[
H
2
] ) 0 corresponds to the rate of heterogeneous decay of C H
2 3
1
6
-3
radicals: T ) 601 K; [M] ) 18.0 × 10 molecules cm ; [C
2
H
3
Br] )
11
-3
6
.2 × 10 molecules cm . The insert shows the recorded C
2
H
3
decay
16
profile for the conditions of the open circle: [H
molecules cm ; k′ ) 249.8 ( 7.5 s
2
] ) 6.83 × 10
-3
-1
.
He was reduced accordingly so that the total density of gas ([M])
in the reactor remains constant. Values of k4 were determined
in the absence of H2. Values of k1 were obtained from the slope
of a linear plot of k′ vs [H2]. The average value of k′/k4 achieved
with the highest concentrations of H2 used at each temperature
is 4.2. This ratio was, however, necessarily reduced at the
higher end of the experimental temperature range due to (1) an
increase in k4 because of a contribution from the thermal
decomposition of vinyl radicals and (2) a decrease in the
sensitivity of the detection system with increasing temperature,
which resulted in greater difficulty in measuring k′ values above
II. Experimental Study and Results
Vinyl radicals were produced by the pulsed, 193-nm laser
photolysis of vinyl bromide13
-1
250 s . Experiments were performed to establish that the decay
constants did not depend on the initial C2H3 concentration
(provided that the concentration was kept low enough to ensure
that radical-radical reactions had negligible rates in comparison
to the reaction with H2), the concentration of the radical
precursor or the laser intensity. Rate constants of reaction 1
1
93 nm
C H Br
8 C H + Br
2
3
2 3
f other products
(3)
1
6
The decay of C2H3 was subsequently monitored in time-resolved
experiments using photoionization mass spectrometry. Details
of the experimental apparatus used have been described before.
were determined at T ) 499-947 K and [M] ) (6-18) × 10
-3
atoms cm . An example of a k′ vs [H ] plot is shown in Figure
2
20
1. The intercept at [H ] ) 0 corresponds to the rate of
2
In the current experimental setup, a quartz reactor coated with
boron oxide was used. Neither the laser intensity nor the
concentration of the radical precursor had any observable
influence on the kinetics of C2H3 radicals. Initial conditions
heterogeneous decay of C H radicals, k4. Ethylene was
detected as a product of reaction 1 with its rise time matching
that of C2H3 exponential decay due to reaction 1.
2
3
Rate constants of the heterogeneous loss of vinyl radicals,
k4, depend on the quality of the wall coating which, in turn,
depends on the history of exposure to the reaction environment.
At the highest temperatures used the “effective” k4 also included
a contribution from thermal decomposition of the C2H3 radical
(
precursor concentration and laser intensity) were selected to
11
-3
provide low radical concentrations (e10 molecules cm ) such
that reactions between radical products had negligible rates
compared to that of the reaction of vinyl radicals with molecular
hydrogen.
(Table 1), which determined the upper temperature limit of the
Experiments were conducted under pseudo-first-order condi-
1
4
17
experiments. The observed linear dependence of k′ on [H2] (k′
) k1[H2] + k4) is in agreement with the assumed first-order
nature of the heterogeneous reaction 4.
tions with [H2] in the range 8.4 × 10 to 1.07 × 10 molecules
-3
cm . The observed exponential decay of the C2H3 radical was
attributed to reaction 1 and heterogeneous loss:
In many earlier studies of reactions of hydrocarbon radicals
(including C2H3) with stable molecular reactants conducted by
the same experimental technique as used here, the contribution
of a potential bimolecular heterogeneous reaction was ruled out
by using different coating materials (e.g., ref 14). In these
studies, determinations of the R + reactant rate constants
conducted with different wall coatings yielded different het-
erogeneous decay rates (equivalents of k4) but identical bimo-
lecular gas-phase reaction rate constants. In the current study,
C H f heterogeneous loss
(4)
2
3
The vinyl ion signal profiles were fit to an exponential function
-
k′t
(
[C2H3]t ) [C2H3]0e , where k′ ) k1[H2] + k4) by using a
nonlinear least squares procedure. In a typical experiment to
determine k1, the kinetics of the decay of C2H3 radicals was
recorded as a function of the concentration of molecular
hydrogen. When high concentrations of H2 were used, that of

1
1348 J. Phys. Chem., Vol. 100, No. 27, 1996
Knyazev et al.
TABLE 1: Conditions and Results of Experiments To Measure k
1
T/K [M]/(1016 atoms cm-3
)
[C
H
Br]/(1011 molecules cm-3
)
Ia
10
4.1
8.9
5.1
8.9
3.5
10
13
28
8.9
3.5
14
5.6
5.1
4.6
[H
2
]/(1015 molecules cm-3
)
k
/s-1
k
1
b/(10-14 cm molecule s-1
3
-1
)
2
3
4
499
499
500
549
600
600
601
650
650
700
700
747
747
850
851
939
947
18.0
18.0
18.0
18.0
18.0
18.0
18.0
18.0
6.0
18.0
18.0
18.0
18.0
18.0
18.0
6.1
6.1
6.1
5.0
5.7
16.6
16.6
6.2
5.6
3.09
6.0
6.0
6.1
6.1
5.0
5.8
5.7
5.4
36.5-107.4c
35.0
26.8
42.7
97.7
79.9
80.1
62.8
87.0
44.2
37.2
27.2
64.8
62.5
34.9
55.9
103.3
107.8
0.082 ( 0.008
0.081 ( 0.011
0.081 ( 0.012
0.175 ( 0.030
0.325 ( 0.040
0.390 ( 0.051
0.280 ( 0.030
0.522 ( 0.060
0.544 ( 0.064
0.818 ( 0.089
0.820 ( 0.105
1.24 ( 0.15
c
36.5-107.4
38.0-105.3
23.6-83.6
23.1-78.5
23.1-44.4
21.3-95.2
9.96-39.7
11.8-30.7c
5.50-36.4
5.50-26.1
3.29-10.75
3.38-9.99
1.20 ( 0.16
c
1.33-5.28
2.54 ( 0.35
2.36-6.60
0.836-2.92
0.890-3.00
2.43 ( 0.28
d
d
21
12
4.70 ( 0.52
6.0
4.20 ( 0.65
a
Photolyzing laser intensity (mJ cm-2 pulse-1). b All error limits are 1σ with uncertainties in [H]
included. c Research Grade H
2
2
(99.9995%, Air
d
Products) was used. Includes contribution from thermal decomposition.
TABLE 2: Conditions and Results of Experiments To Measure k
2
T/K [M]/(1016 atoms cm-3
)
[(CH
)
CO]/(1011 molecules cm-3
)
Ia [H
]/(1015 molecules cm-3
)
k
wallb/s-1
k
1
c/(10-15 cm molecule s-1
3
-1
)
3
2
2
6
6
6
7
7
8
9
46
46
99
51
51
20
04
18.0
18.0
18.0
18.0
18.0
6.0
18.0
18.0
18.0
6.0
15.5
15.5
9.0
29.0
29.0
32.0
15.2
8.9
35
14
40
10
40
20
40
30
30
30
12
43-140
43-140
34-95
12
8
13
7
13
9
5
7
5
10
11
0.404 ( 0.046
0.407 ( 0.042
0.842 ( 0.101
1.62 ( 0.19
1.57 ( 0.17
3.50 ( 0.37
7.21 ( 0.73
15.7 ( 1.7
18-78
18-78
6.7-32
4.3-13
2.3-8.5
2.4-8.2
0.74-6.0
0.74-6.0
1000
1000
1104
1104
30.2
19.7
19.7
14.2 ( 1.5
32.0 ( 3.4
35.2 ( 3.8
6.0
a
Photolyzing laser intensity (mJ cm-2 pulse-1). b Rate constant of CH
wall reaction. c All error limits are 1σ with uncertainties in [H]
3
2
included.
high experimental temperatures precluded the use of any wall
coating material other than boron oxide, and, therefore, a similar
investigation of potential second-order heterogeneous effects
could not be performed. The agreement of our earlier results
on the kinetics of C2H3 + O2 reaction (ref 13 and references
cited therein) and of our current results on CH3 + H2 with the
literature data (see below) indicates the absence of any such
heterogeneous effects in the cases of these two reactions. While
not being a rigorous proof, this leads us to expect no significant
contributions from a second-order heterogeneous reaction in the
C2H3 + H2 system.
on Arrhenius plots in Figures 2 and 3. The results of the current
study yield the Arrhenius expressions:
-
12
k ) (3.42 ( 0.35) × 10 exp(-(4179 (
1
6
7 K)/T) cm molecule s-1 at T ) 499-947 K
3
-1
-
11
k ) (1.45 ( 0.18) × 10 exp(-(6810 (
2
102 K)/T) cm molecule s-1 at T ) 646-1104 K
3
-1
III. Data Analysis for Reactions (1,-1)
Rate constants of reaction 2 were similarly determined at
In this section we present the development of a model of
reactions (1,-1) which describes both our experimental data
on reaction 1 and permits extrapolation of k1 and k-1 values to
temperatures outside the experimental range. Properties of the
C2H3-H2 transition state (including the width of the potential
energy barriersa parameter important in the treatment of
tunneling) are determined from an ab initio study. These ab
initio results are used in a model of reactions (1,-1), the
parameters of which (energy barrier and lowest vibrational
frequencies of the transition state) are adjusted to reproduce the
experimental data. Rate constant values for reaction -1 are
obtained from those for reaction 1 via equilibrium constants
calculated from the known thermochemistry. The uncertainties
of the extrapolation of rate constants to other temperatures are
evaluated.
temperatures 646-1104 K and bath gas (He) densities (6-18)
1
6
-3
×
10 molecules cm . Photolysis of acetone at 193 nm was
used as a source of CH3 radicals. Variation of laser intensity
and the precursor concentration did not affect the values of k2
obtained.
The gases used were obtained from Aldrich (acetone, 99.9%)
and Matheson (He, >99.995%; H2, >99.99%; C2H3Br, 99.5%).
Precursors were purified by vacuum distillation prior to use.
Helium and hydrogen were used as provided. In order to
eliminate a possible influence of a minor impurity in hydrogen
on the measured rate constants, several experiments on reaction
1
were performed using Research Grade H2 (99.9995%)
obtained from Air Products. No effect of the nominal purity
of the hydrogen used on the values of k1 could be detected.
The sources of ionizing radiation were hydrogen (10.2 eV, MgF2
window, used for the detection of C2H3 and CH3 radicals) and
Ar (11.6-11.9 eV, LiF window, used for the detection of
ethylene) resonance lamps.
III.1. Ab Initio Study of the Transition State of Reactions
(
1,-1) and the Shape of the Potential Energy Profile Along
the Reaction Path. The geometries and harmonic vibrational
frequencies of the C2H3-H2 transition state (C2H3-H2 ) were
q
The values of the bimolecular rate constants k1 and k2
determined in this study are presented in Tables 1 and 2 and
studied using the ab initio UMP2 method with the 6-31G**
basis. Energies were calculated with the UMP4/6-31G** and

Kinetics of C2H3 + H2 and CH3 + H2 Reactions
J. Phys. Chem., Vol. 100, No. 27, 1996 11349
a
TABLE 3: Geometrical Structure and Energies of C
2
H
3
,
C
2
H
3
-H
q, C
H , and H Obtained in the Ab Initio Study
2 2 4 2
property
C2H3b
C2H3-H2q c
C2H4
H2
Bond Distances (Å) and Bond Angles (deg)
C1C2
H11C1
H12C1
H21C2
1.288
1.086
1.082
1.077
1.290
1.082
1.084
1.080
1.335
1.081
1.081
1.081
1.081
121.57
121.57
121.57
121.57
H22C2
1.444
H11C1C2
H12C1C2
H21C2C1
H22C2C1
H5H22
121.63
122.05
136.41
121.85
121.55
131.54
115.70
0.8483
175.58
0.7340
d
H5H22C2
Energies (hartrees)
-77.394 251 -78.487 172 -78.038 334 -1.131 332
E(HF/6-31G**)
E(MP2/6-31G**) -77.627 982 -78.768 569 -78.317 282 -1.157 661
E(MP4/6-31G**) -77.663 531 -78.810 649 -78.353 792 -1.164 566
E(PMP4/6-31G**) -77.671 223 -78.819 911
1
Figure 2. Plot of experimental and calculated rate constants (k ) of
the reaction of C
data: (closed circles) current study; (open squares) ref 7 (as reported);
closed squares) ref 7 shifted to agree with the results of the current
2
H
3
radicals with H
2
vs temperature. Experimental
a
q
have planar structure. b Data for C
C
2 3
H , C
2
H
3
-Hc
2
, and C H H
2
4
2
3
taken from ref 15. UMP2/6-31G** vibrational frequencies (scaled by
.94) are 3129, 3119, 3031, 2061, 1800, 1387, 1144, 1077, 1037, 993,
68, 810, 374, 274, and 1449i. The H5-H22 bond bends toward the
C-C bond.
(
0
9
study (see text); (open circle) ref 6. Calculations: (solid line) current
model (formula IV); (long dash) ref 9; (medium dash) ref 8; (short
d
-1
dash) ref 8 with the energy barrier changed by -5.8 kJ mol (see
text).
sufficiently accurate, the geometrical configuration of the
transition state (Table 3) was used in the model. The calculated
set of vibrational frequencies of the transition state (scaled
2
6
by 0.94, Table 3) was used as a basis for the model. These
frequencies, as expected, are very close to those obtained by
8
Mebel et al. at the UMP2/6-31G* level with the QCISD(T)/
6
-311** geometry optimization.
The shapes of the potential energy surface obtained at
different levels of calculations (UMP2, UMP4, and PMP4) were
used to determine the width of the potential energy barriersan
important parameter required for the modeling of tunneling. The
potential energy profile along the reaction path was fitted with
the Eckart function
Aê
+ ê
Bê
2πx
l
V )
+
2; ê ) exp
(I)
(
)
1
(
1 + ê)
where x is a coordinate along the reaction path, l is a parameter
determining the width of the barrier, and parameters A and B
are related to the barriers for the direct and reverse reactions
E1 and E-1:
Figure 3. Plot of the rate constants of reactions 2 and -2. Experi-
2
mental data: (open circles) k values of the current study; (open squares)
the same data converted to k-2 values; (closed circles) k-2 values from
1
8
19
Marquaire et al.; (heavy lines) k
2
from Baeck et al. and k-2 from
2
1
17
Roth and Just and Rabinowitz et al. Calculated values (thin lines):
2
and k-2 from Marquaire et al.; (dashed line)
recommendation on k
1
8
1/2
1
1/2 2
(solid lines) k
A ) ∆E1,-1 ) E - E ; B ) (E + E-1
)
(II)
1
-1
1
0
2
from Baulch et al.
PMP4/6-31G** methods. For the purpose of obtaining complete
information on the shape of the potential energy surface along
the reaction coordinate, properties of H2 and ethylene were also
calculated at different levels of theory. Properties of the vinyl
radical were taken from ref 15. Structures and energies of these
species are listed in Table 3. The GAUSSIAN 92 system of
The transition probability for such a barrier can be described
2
7
analytically, as shown by Eckart.
In the fitting process,
parameter A was fixed at the value obtained from ab initio
calculations, and B and l were determined from the fitting. Only
points with energy above that of C2H3 + H2 were used (Figure
4). The resultant values of B, l, and E-1 are listed in Table 4
for three levels of calculations used. Although it can clearly
be seen that improvement of the level of theory results in a
significant reduction of the reverse reaction barrier, the barrier
2
2
programs was used in all ab initio calculations.
The shape of the potential energy barrier for reactions (1,-
) was calculated using the method of reaction path following
1
1
/2
in mass-weighted internal coordinates described by Gonzalez
width changes only slightlysfrom 1.64 amu Å at the UMP2
2
3
1/2
1/2
and Schlegel.
For each point along the reaction path,
level to 1.60 amu Å at the UMP4 level and to 1.64 amu
Å
optimization was done at the UMP2/6-31G** level and energy
was calculated at the UMP4/6-31G** level. Spin contamination
was removed by the spin projection (PMP4) method of
at the PMP4 level. In the model of reactions (1,-1) we use
the PMP4 value.
III.2. Transition State Model of Reactions (1,-1). The
2
4,25
28-30
Schlegel.
physical properties of C2H4 and H2 are well-known.
For
The results of this ab initio study of the transition state C2H3-
H2q and the reaction path were used in creating a model of
reactions (1,-1). Although the reaction energy threshold values
calculated at the applied levels of theory are not believed to be
the vinyl radical, we use the set of frequencies and rotational
constants reported by Ervin et al. which is a combination of
31
experimental measurements and ab initio calculations. Proper-
q
ties of the C2H3-H2 transition state were obtained from our

1
1350 J. Phys. Chem., Vol. 100, No. 27, 1996
Knyazev et al.
TABLE 5: Models of the Molecules and Transition State
Used in the Data Analysis
Energy Barriers
-1 ) 63.0 kJ mol
) 35.8 kJ mol-
1
E
-1
∆E1,-1 ) -27.2 kJ mol-1
E
1
Vibrational Frequencies (cm-1)
3265, 3190, 3115, 1670, 1445, 1185, 920, 825, 785
3129, 3119, 3031, 2061, 1800, 1387, 1144,
077, 1037, 993, 968, 810, 508, 372, 981i
3026, 3106, 3103, 2989, 1623, 1444, 1342, 1236,
023, 949, 943, 826
4162
C
C
2
H
H
3
3
:a
q b
2
2
-H :
1
C
H
2 4
:c
1
H
2
:d
Rotational Constants (cm- ) and Symmetry Numbers
1
:a
1.953(1)
1.076(1)
C
H :
2
H
c
1.592(4)
59.34(2)
C
C
2
H
3
H
3
2
4
:
q b
d
2
-H
2
:
a
from ref 31. b Structure and vibrational frequen-
2
from our ab initio study (two lowest frequencies
2 3
Properties of C H
q
cies of C
2
H
3
-H
adjusted). Imaginary frequency calculated from the Eckart potential
parameters of the model. c Ethylene parameters from ref 28. Properties
d
Figure 4. Shapes of potential energy barrier of reactions (1,-1)
obtained at different levels of calculation: (Circles) UMP2; (triangles)
UMP4; (squares) PMP4. Data obtained at each next level of calcula-
2
of H from ref 29.
the Eckart formula27 with the Eckart potential parameters
obtained from our ab initio study (barrier width parameter, see
section III.1), known ∆E1,-1, and the reaction energy barrier
E1.
-1
tions are shifted upward by 20 kJ mol . Lines represent fits to Eckart
function. Energy relative to C + H
2
H
3
2
.
TABLE 4: Eckart Parameters Obtained from Fitting the
Potential Energy Profile Along the Reaction Path
In the current treatment of tunneling, the barrier width (a
geometrical parameter) is determined from ab initio calculations.
The imaginary frequency is determined by the width and the
height of the reaction barrier. Ab initio UHF and UMP2
methods usually overestimate the barrier height and, therefore,
overestimate the curvature of the potential energy surface in
the direction of the reaction coordinate and the imaginary
frequency associated with the barrier. On the other hand,
geometrical parameters are usually determined more accurately
by the same methods. This makes the current method of the
treatment of tunneling more accurate compared to the one where
the imaginary frequency of the transition state obtained from
ab initio calculations is used directly in determining the transition
probability.
UMP2
UMP4
PMP4
Aa/(kJ mol
-1
)
78.4
309.5
1.64
1184i
43.1
62.8
290.0
1.60
1195i
44.5
42.6
243.0
1.64
1087i
41.3
B/(kJ mol-1)
l/(amu Å)
1
/2
b
-1
ν
i
/cm
E
-1b/(kJ mol-1
)
a
2 3
A was fixed at the value obtained from ab initio energies of C H ,
b
C
2
H
4
, H
2
i
, and H. Imaginary frequency ν and potential barrier for
reaction -1 calculated from the fitted values of B and l.
ab initio study with some of its parameters adjusted to achieve
agreement with the experimental results.
Calculation of k1 and k-1 requires knowledge of the thermo-
chemistry of reaction. In this study, we use ∆Hf°298(H) ) 218.0
The experimental values of k presented in Table 1 were
reproduced by calculations using formula III. The two lowest
frequencies of the transition state and E were adjusted to
1
kJ mol-
1 29
and ∆Hf°298(C2H4) ) 52.5 ( 0.3 kJ mol .
-1 29,30
The
heat of formation of the vinyl radical has been a subject of
1
controversy (see reviews in refs 31 and 32). ∆Hf°298(C2H3) )
achieve a good fit. The resultant optimized value of E is 35.8
kJ mol . The sum of squares of deviations between the
experimental and the calculated rate constants was determined
1
-1
-1
3
00.0 ( 3.3 kJ mol , a value obtained using a method based
31
32
on gas-phase acidity, is believed to be the most accurate.
This value is supported by the results obtained in G2 ab initio
as a function of E (E was fixed at some values and the
1
1
3
3a
15
calculations,
in modeling of the C2H3 decomposition
frequencies of the transition state were optimized). From the
3
3b
reaction, and in a recent study of the Cl + C2H4 reaction.
curvature of this dependence the uncertainty of E was
1
3
5
-1
Molecular properties (moments of inertia and vibrational
frequencies) of C2H3, C2H4, and H2 were taken from Ervin et
estimated as (0.8 kJ mol (2σ). The fixed and optimized
parameters of the model are listed in Table 5.
31
28
29
al., Chao and Zwolinski, and JANAF Tables, respectively.
The optimized model of reactions (1,-1) results in the
following expressions for the temperature dependencies of the
rate constants of reactions 1 and -1:
These data result in the heat of reaction ∆H°298(1,-1) ) -29.5
-
1
(
3.6 kJ mol and ∆E1,-1 ) E1 - E-1 ) -27.3 ( 3.6 kJ
-1
mol . Here, E1 and E-1 are the energy barriers for the direct
1) and reverse (-1) reactions, respectively.
k1 is given by
-
20 2.56
(
k1 ) 1.57 × 10
T
×
3
4
exp(-(2529 K)/T) cm molecule s-1 (IV)
3
-1
q
kBT κ(T)Q
h Q
E1
k
-1 ) 8.42 × 10-17T1.93
×
k1(T) )
exp -
(III)
(
)
Q
3
k T
B
C H H2
exp(-(6518 K)/T) cm molecule s-1 (V)
3
-1
2
q
where Q , QC H , and QH are partition functions of the transition
2
3
2
at 200 K e T e 3000 K. These modified Arrhenius expressions
provide a good fit to the calculated rate constants within the
temperature range between 300 and 3000 Ksthe average
deviation is 2% with a maximum deviation of 5%. At lower
temperatures the deviation is highersup to 22% at 200 K. The
significant temperature dependence of the preexponential factor
state, vinyl radical, and H2 molecule, respectively, and κ(T) is
the temperature-dependent tunneling factor:
∞
E/kBT
κ(T) )
∫
P′(E)e-
dE
-E1
9
Here, P′(E) is the first derivative of the energy-dependent
tunneling transition probability P(E). It was calculated using
of reaction 1 is similar to that predicted by Tsang and Hampson
on the basis of a bond energy-bond order analysis.

Kinetics of C2H3 + H2 and CH3 + H2 Reactions
J. Phys. Chem., Vol. 100, No. 27, 1996 11351
The uncertainty of these formulas which provide the extrapo-
lation of our experimental data to higher and lower temperatures
is determined by three factors. First is the scatter of experi-
mental points which results in error limits for the energy barrier
E1 ( 0.8 kJ mol (2σ). Second is the uncertainty resulting
from the treatment of tunneling. Third is the additional
uncertainty factor for the rate constant of the reaction of H atoms
with ethylene resulting from the uncertainties in the enthalpy
of reactions (1,-1).
cally by summation over the rotational states. Experimental
data on k2 determined in the current study were converted via
the calculated equilibrium constants to the rate constants of the
reverse reaction (-2) of H atoms with methane. The values of
k-2 obtained in this manner can be represented by the Arrhenius
dependence
-1
k-2 ) 2.46 × 10 exp(-(6837 K)/T) cm molecule s-1
-
10
3
-1
at T ) 646-1104 K
Among these three factors, the most difficult one to estimate
is that related to the treatment of tunneling. Unfortunately, the
current treatment of tunneling as a one-dimensional motion with
an Eckart potential is only a crude approximation. Better
methods require detailed knowledge of the potential energy
surface, which is not readily available at the current level of
theory. In the absence of any rigorous method of calculating
potential errors associated with the current treatment of tun-
neling, we choose to investigate those resulting from changing
the most important parameter for the treatment of tunnelingsthe
barrier width lsby a factor of 1.5. The fitting of our
experimental results on the rate constant of the reaction of vinyl
radicals with H2 was repeated with the barrier width parameter
l increased or reduced by this factor. Reduction of l resulted
Data on k2 and k-2 obtained in the current study are presented
in Figure 3 together with the recent experimental results of
19
Baeck et al. and the values calculated from the recommenda-
1
0
tions of Baulch et al. for k2 and with those calculated by
1
8
Marquaire et al. from their model of reactions (2,-2). The
2
1
17
data of Roth and Just, Rabinowitz et al., and Marquaire et
al. on k-2 are also shown. As can be seen from the plot, our
results are in good agreement with these data and predictions,
confirming the accuracy of the method used in the current
experiments.
IV.2. C2H3 + H2 a H + C2H4 (1,-1). Although the
literature on reactions 1 and -1 is abundant, no direct
measurements of rate constants are available. The current study
provides the first set of direct determinations of the rate constants
of the reaction of vinyl radical with molecular hydrogen.
-
1
in a more significant change of E1 (by +2.8 kJ mol ) than the
-
1
increase (by -1.1 kJ mol ). The resultant modified models
of reactions (1,-1) were used to calculate rate constants at
temperatures between 200 and 3000 K, and “tunneling”
uncertainty factors were obtained from the comparison of these
rate constants with those obtained with the unmodified (Table
7
C2H3 + H2 f H + C2H4 (1). Callear and Smith investigated
reaction 1 at 300 and 400 K. Vinyl radicals were generated by
attachment of H atoms from the Hg-photosensitized decomposi-
tion of H2 to acetylene. Reaction products were analyzed by
gas chromatography. Although rate constants reported by these
5
) model. The overall uncertainty factors were obtained by
-
17
3
-1 -1
authors (k1 ) 2.5 × 10
cm molecule
s
s
at 300 K and
including additional factors resulting from the uncertainty in
E1 due to the data scattering and from the uncertainty in ∆E1,-1
-16
3
-1 -1
2
.5 × 10 cm molecule
at 400 K) are widely cited as
experimental results, their values were obtained by arbitrarily
choosing the values of the optical density of the reaction vessel
and of the radical termination rate constant. Only the ratio of
the rate constant of reaction 1 at 400 K to that at 300 K was
determined experimentally, thus yielding an activation energy
(
(
for reaction -1). The resultant overall uncertainty factors f1
for reaction 1) and f-1 (for reaction -1) are (listed as f1/f-1) as
follows: 24/220 at 200 K, 2.4/10 at 300 K, 1.3/3.9 at 400 K,
.2/1.6 at 1500 K, and 1.4/1.6 at 3000 K. Potential errors
1
originating in the treatment of all involved species as combina-
tions of rigid rotors and harmonic oscillators (which are likely
to become important at high temperatures) are not included here.
-1
of 23 ( 1 kJ mol .
6
Fahr et al. employed laser photolysis with kinetic absorption
spectroscopy and gas chromatographic product analysis to obtain
the value of the rate constant of reaction 1 at room temperature.
IV. Discussion
-
20
3
-1
These authors’ results (k1 ) (3 ( 2) × 10
cm molecule
-
1
IV.1. CH3 + H2 a H + CH4 (2,-2). Both reactions 2
and -2 have been studied by many groups using a variety of
experimental methods. Reviews are available in refs 9, 10, and
s
from the kinetic absorption spectroscopy experiments and
from the gas chromato-
graphic product analysis experiments) are 3 orders of magnitude
-20
3
-1 -1
k ≈ 1 × 10
1
cm molecule
s
7
1
7-19, and references cited therein. Approximate agreement
lower those reported by Callear and Smith. Vinyl radicals were
has been reached between the results of different groups, with
generated by excimer laser photolysis of divinyl mercury (in
optical absorption experiments) or methyl vinyl ketone (in gas
chromatographic experiments). In the kinetic absorption spec-
troscopy experiments, the formation of 1,3-butadiene (C H )
the exception of the values of k-2 at temperatures above 1700
17
K, where rate constants recently obtained by Rabinowitz et al.
are lower than those of Roth and Just21 by a factor of 3.5. An
earlier controversy due to the disagreement between k2/k-2
values obtained from experimental data and those calculated
from the known thermochemistry of the reaction has been
recently resolved by Marquaire et al.18 who studied reaction
4
6
in the reaction of vinyl-vinyl recombination was monitored.
The values of k were obtained from kinetic modeling of the
1
observed temporal behavior of the C H signal in the presence
4
6
and in the absence of H . In the gas chromatographic experi-
2
-
2 by the ESR/discharge flow method at temperatures 348-
ments, the rate of reaction 1 was compared with that of reaction
4
12 K. These authors reproduced their experimental data and
2 (CH + H f H + CH ). Vinyl and methyl radicals were
3
2
4
3
7
those of other groups on reactions 2 and -2 with transition-
state-theory modeling to provide k2 and k-2 temperature
dependencies consistent with the thermochemistry of reactions
simultaneously produced in equal concentrations by the 193-
nm laser photolysis of methyl vinyl ketone. The ratio of k to
1
k2 rate constants was determined by comparing the increase of
(
2,-2).
Equilibrium constants of reactions (2,-2) were calculated
using the known properties of the species involved. With
C H yield in the presence of H to that of CH .
2
4
2
4
Our extrapolated rate constant at room temperature (k1 ) 7.1
-
18
3
-1 -1
× 10
cm molecule s , uncertainty factor 2.4) is in
3
2
-1
36
∆
Hf°298(CH3) ) 146.4 ( 0.4 kJ mol and ∆Hf°298(CH4)
)
significant disagreement with the results of Fahr et al. (Figure
2). The difference exceeds 2 orders of magnitude. Even if no
tunneling is taken into account and our experimental rate
constants are extrapolated assuming a pure Arrhenius depen-
dence, the disagreement is still at least a factor of 50. In prior
-
1
-
74.6 ( 0.3 kJ mol , we obtain ∆H°298(2,-2) ) -3.0 ( 0.7
-1
-1
kJ mol and ∆E2,-2 ) -0.4 ( 0.7 kJ mol . Models of CH3,
29
CH4, and H2 were taken from JANAF tables, and the rotational
partition function of molecular hydrogen was calculated numeri-

1
1352 J. Phys. Chem., Vol. 100, No. 27, 1996
Knyazev et al.
investigations to determine the rate constant for the reaction of
vinyl radicals with molecular oxygen, the results13 obtained
using a method and apparatus identical with those in this study
were in good agreement with those obtained in optical absorp-
tion measurements of Fahr and Laufer.38 The large disparity
between the results in the case of the C2H3 + H2 reaction
therefore cannot be explained by the difference in the radical
source or detection method used.
One possible reason for such disagreement is that neither of
the two reaction systems used in ref 6 is sufficiently sensitive
to the rate constant of the reaction of vinyl radical with H2. In
6
the kinetic absorption spectroscopy experiments of Fahr et al.,
1
4
in which initial concentrations [C2H3]0 ) (2.3-16) × 10
molecules cm- and [H2] ≈ 2.3 × 10 molecules cm , the
3
19
-3
37
kinetics was dominated by the fast (rate constant ) 1.3 ×
-10
3
-1 -1
1
0
cm molecule s ) self-reaction of vinyl radicals. The
characteristic time of fast C4H6 growth due to the vinyl
recombination was less than 100 µs and the overall time of the
kinetic measurement was 350 µs. If the value of k1 ) 3 ×
Figure 5. Temperature dependence of k-1: (Open circles) the results
of the current study (converted from the k experimental values); (closed
1
square) ref 3; (closed circle) obtained from the data of ref 3 using
different values of the rate constants of reference reactions (see text);
-20
3
-1 -1
1
0
cm molecule
s
reported by Fahr et al. is used, the
2
4
5
first-order effective rate constant of the reaction of C2H3 radicals
(heavy lines) Just et al., Yampol’skii, and Nametkin et al.; (thin solid
line) current model; (thin dashed lines) estimated uncertainty limits of
the current model.
with H2 is 0.7 s-1 which would not affect the fast kinetics of
C4H6 formation during the above measuring time. Even if our
-
18
3
-1 -1
(
high) value of k1 ) 7.1 × 10
cm molecule
s
is used
to calculate transition-state energies. The disagreement between
our experimental results and the prediction of Mebel et al. can
be nearly removed by reducing their energy barrier by 5.8 kJ
instead, this first-order effective rate constant of the C2H3 +
-
1
H2 is still only 163 s .
6
In the gas chromatographic section of Fahr et al., their
conclusion of approximate equality of the rate constants of
reactions 1 and 2 was derived from a comparison of the changes
in C2H4 and CH4 yields due to the substitution of He with H2.
These changes (11-27% for CH4 and 8-21% for C2H4) were,
-1
mol (Figure 2). The remaining minor disagreement reflects
the differences in the transition-state vibrational frequencies
(which were adjusted in our model to fit the experimental data)
and in the treatment of tunneling. Comparison of our model
with the ab initio results of Mebel et al. and with those obtained
in the current study (ab initio frequencies, Table 3) show that
UMP2/6-31G* or UMP2/6-31G** scaled frequencies of the
transition state provide a good approximation for the purpose
of calculating the rate constants of reactions (1,-1). Only a
relatively minor adjustment of our ab initio frequencies (two
lowest frequencies were multiplied by a factor of 1.36) was
required to reproduce the experimental data.
6
on average, a factor of 2 larger than the combined reported
uncertainties (1σ) of the total measured yields of these species.
Most of the methane and ethylene produced in this system
resulted from reactions other than reactions 1 and 2. In addition,
a potential contribution to the formation of CH4 in the presence
of molecular hydrogen due to the fast reaction of H atoms
1
0
-10
formed in reaction 1 with CH3 radicals (rate constant g 10
3
-1 -1
cm molecule s ) was neglected in the analysis in ref 6.
4
H + C2H4 f C2H3 + H2 (-1). Yampol’skii and Nametkin
As can be seen from Figure 2, the activation energy of the
5
et al. studied C2H4 pyrolysis in a fluidized bed of powdered
7
results of Caller and Smith is in reasonable agreement with
4
quartz at 100 Torr over the temperature ranges 1093-1213 K
our extrapolated values of k1. This is illustrated by shifting the
values reported by these authors (which give only a meaningful
measure of activation energy since absolute values of k1 were
not measured but assumed) down by a factor of 2.6 to achieve
agreement with our absolute values of the rate constants.
5
and 1073-1173 K. Values of k-1 were obtained by applying
different methods of product analysis. It is unclear to what
extent these values were affected by heterogeneous reactions,
which could be significant due to a very high surface-to-volume
ratio of the powdered quartz. Although the k-1 values reported
by these authors (Figure 5) are in good agreement with our
k-1(T) dependence represented by formula V, it is, most likely,
a coincidence.
Disagreement between our results and the predictions of
9
8
Tsang and Hampson and Mebel et al. is not surprising. Tsang
and Hampson based their recommendation for k1(T) on the
thermochemistry of reactions (1,-1) and on the bond energy
2
Just et al. used atomic resonance absorption spectrophotom-
2
-
bond order fit to the approximate data of Just et al. for the
etry (ARAS) to monitor H atoms and infrared spectroscopy to
monitor C2H4 concentration behind reflected shock waves at
temperatures 1700-2200 K. The main purpose of these
experiments was to obtain the rate constants of the H-atom-
producing channel in the unimolecular decomposition of eth-
ylene. These rate constants were determined with an accuracy
of a factor of 2 due to the uncertainty in the H atom signal
calibration. Kinetic modeling of the C2H4 concentration profiles
made it possible to calculate approximate values of k-1, which
resulted in the Arrhenius dependence
reverse reaction -1 obtained in a narrow temperature interval
1700-2080 K) by an indirect method. In the calculations of
Tsang and Hampson an earlier value for the heat of formation
(
-
1
of the vinyl radical ∆Hf°298(C2H3) ) 286.2 kJ mol was used
which is 13.8 kJ mol- lower than the one used in our model.
Potential uncertainties involved in the analysis were partially
reflected in these authors providing an uncertainty factor of 10
for their recommendation.
1
8
Mebel et al. calculated the k1(T) dependence based purely
on their ab initio results which included calculating the reaction
barrier height at the G2(PU)//QCISD method, which is a
2
-9
k (Just et al. ) ) 8.3 × 10
×
3
3
-1
modification of the Gaussian-2 (G2) method of Curtiss et al.
exp(-(11500 K)/T) cm molecule s-1 (VI)
3
-1
The G2 method is known to yield heats of formation of small
molecules with an accuracy of a few kilocalories per mole and
can be expected to give similar or lower accuracy when used
shown in Figure 5. As can be seen from the plot, these data

Kinetics of C2H3 + H2 and CH3 + H2 Reactions
J. Phys. Chem., Vol. 100, No. 27, 1996 11353
are higher than those obtained from our model (formula V) by
approximately a factor of 3.
expressions
-
12
The values of k-1 reported by Just et al. depend on the rate
constants of both H-producing and H2-producing channels of
the ethylene thermal decomposition used in the modeling.
k1 ) (3.42 ( 0.35) × 10
×
exp(-(4179 ( 67 K)/T) cm molecule s-1 (VII)
3
-1
2
Although the authors do not provide any estimates of the
-11
k2 ) (1.45 ( 0.18) × 10
×
uncertainties in the values of k-1, they describe their results as
approximate and caution that formula VI should not be
interpreted in physical terms but considered simply as the
expression that best interpolates the experimental data. We,
therefore, believe that the difference between our results and
those of Just et al. is not very large considering the indirect
nature of the values obtained in ref 2.
exp(-(6810 ( 102 K)/T) cm molecule s-1 (VIII)
3
-1
The k2(T) dependence in combination with the known thermo-
chemistry of the reaction provides the following temperature
dependence of the rate constant of the reverse reaction in the
same temperature range:
Our predicted values of k-1 at temperatures between 1000
and 3000 K are, on average, lower by a factor of 3 than earlier
recommendations of Tsang and Hampson.9 This disagreement
is closely related to the difference between our results and those
k-2 ) 2.46 × 10 exp(-(6837 K)/T) cm molecule s-1
-
10
3
-1
(IX)
2
of Just et al., since the recommendation of ref 9 was based on
Both expressions VIII and IX are in good agreement with
previous experimental and theoretical studies of reactions 2 and
2.
The potential energy surface and properties of the transition
state for reactions (1,-1) were studied by ab initio methods.
Experimental and ab initio results of the current study were
analyzed and used to create a transition-state model of the
reaction. Vibrational frequencies and energy of the transition
state were adjusted to reproduce the experimental k1(T) depen-
dence. The resulting model of the reaction provides the rate
constants for both direct (1) and reverse (-1) reactions
a bond energy-bond order fit to the data of ref 2.
3
Jayaweera and Pacey studied the pyrolysis of ethylene with
-
gas chromatographic analysis of products at 900 K and pressures
1
50-580 Torr. The rate constant of reaction -1 was deter-
mined relative to the product K6k7, where K6 is the equilibrium
constant of reaction
H + C H a C H
5
(6)
2
4
2
and k7 is the rate constant of reaction
C H + C H f C H + C H
6
(7)
2
5
2
4
2
3
2
-20 2.56
k1 ) 1.57 × 10
T
×
39
Extrapolating K6 values of Brouard et al. to 900 K and taking
k7 from MacKenzie et al.,40 Jayaweera and Pacey obtain k-1(900
exp(-(2529 K)/T) cm molecule s-1 (IV)
3
-1
-
13
3
-1 -1
K) ) (1.1 ( 0.3) × 10
cm molecule
s
which is 3.6
-
17 1.93
k-1 ) 8.42 × 10
T
×
times higher than our results (Figure 5). K6 values have been
remeasured by Hanning-Lee et al.41 at 800 K and extrapolation
exp(-(6518 K)/T) cm molecule s-1 (V)
3
-1
4
1,42
to other temperatures is available via the modeling
of
reaction 6. These newer values of K6 yield k-1(900 K) ) 8.0
at 200 K e T e 3000 K. Data on reactions 1 and -1 available
in the literature are analyzed and compared with the results of
the current study.
-
13
3
-1 -1
×
10 cm molecule
s
from the results of Jayaweera and
4
0
Pacey if the same k7 is used. Reaction 7 has been studied by
indirect methods only. The values of k7(900 K) that can be
obtained from the literature differ markedly, thus introducing
significant uncertainty into the values of k-1 obtained from the
data of ref 3. For example, if the results of the latest study by
Acknowledgment. This research was supported by the
Division of Chemical Sciences, Office of Basic Energy Sciences,
Office of Energy Research, U.S. Department of Energy under
Grant No. DE-FG02-94ER1446. The authors thank Drs. Askar
Fahr, Louis J. Stief, and R. Bruce Klemm for helpful discussions
and Dr. Philip D. Pacey for the data on the reactions (2,-2).
4
3
Zhang and Back are used in combination with the recom-
mendation of Tsang and Hampson for the rate constant of the
9
C2H5 + H2 f H + C2H6 reaction (reference reaction used by
-
17
3
Zhang and Back), we obtain k7(900 K) ) 4.9 × 10
cm
molecule- s . Using this value in interpreting the results of
1
-1
References and Notes
-
14
3
Jayaweera and Pacey yields k-1(900 K) ) 3.0 × 10
molecule-
which is in agreement with our values (Figure
). We therefore conclude that our results on k-1 and those of
cm
(
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1
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