Rate Coefficients of C2H with C2H4, C2H6, and H2 from 150 to 359 K

Article abstract of DOI:10.1021/jp9619604

Rate coefficients for the reactions C2H with C2H4, C2H6, and H2 are measured over the temperature range 150-359 K using transient infrared laser absorption spectroscopy.The ethynyl radical is formed by photolysis of C2H2 with a pulsed excimer laser at 193 nm, and its transient absorption is monitored with a color center laser on the Q₁₁(9) line of the Α²Π-Χ²Σ transition at 3593.68 cm^-1.Over the experimental temperature range 150-359 K the rate constants of C2H with C2H4, C2H6, and H2 can be fit to the Arrhenius expressions k_C2H4 = (7.8 +/- 0.6)E-11 exp<(134 +/- 44)/T>, k_C2H6 = (3.5 +/- 0.3) E-11 exp<(2.9 +/- 16)/T>, and k_H2 = (1.2 +/- 0.3)E-11 exp<(-998 +/- 57)>/T cm³ molecule^-1 s^-1, respectively.The data for C2H with C2H4 and C2H6 indicate a negligible activation energy to product formation shown by the mild negative temperature dependence of both reactions.When the H2 data are plotted together with the most recent high-temperature results from 295 to 854 K, a slight curvature is observed.The H2 data can be fit to the non-Arrhenius form k_H2 = 9.2E-18 T^2.17+/-0.50 exp<(-478 +/- 165)/T> cm³ molecule^-1 s^-1.The curvature in the Arrhenius plot is discussed in terms of both quantum mechanical tunneling of the H atom from H2 to the C2H radical and bending mode contributions to the partition function.

Full text of DOI:10.1021/jp9619604

1
9904
J. Phys. Chem. 1996, 100, 19904-19910
Rate Coefficients of C2H with C2H4, C2H6, and H2 from 150 to 359 K
Brian J. Opansky and Stephen R. Leone*,†
JILA, National Institute of Standards and Technology and UniVersity of Colorado,
Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309-0440
X
ReceiVed: July 2, 1996; In Final Form: October 3, 1996
Rate coefficients for the reactions C
50-359 K using transient infrared laser absorption spectroscopy. The ethynyl radical is formed by photolysis
of C with a pulsed excimer laser at 193 nm, and its transient absorption is monitored with a color center
laser on the Q11(9) line of the A Π-X Σ transition at 3593.68 cm . Over the experimental temperature
H with C , C , and H can be fit to the Arrhenius expressions
2 2 4 2 6 2
H with C H , C H , and H are measured over the temperature range
1
2 2
H
2
2
-1
range 150-359 K the rate constants of C
2
2
H
4
2
H
6
2
-
11
-11
k
C H ) (7.8 ( 0.6) × 10 exp[(134 ( 44)/T], kC H ) (3.5 ( 0.3) × 10 exp[(2.9 ( 16)/T], and kH2 ) (1.2
2
4
2 6
-
11
3
-1 -1
(
0.3) × 10 exp[(-998 ( 57)]/T cm molecule s , respectively. The data for C
2 2 4 2 6
H with C H and C H
indicate a negligible activation energy to product formation shown by the mild negative temperature dependence
of both reactions. When the H
2
data are plotted together with the most recent high-temperature results from
95 to 854 K, a slight curvature is observed. The H
data can be fit to the non-Arrhenius form kH2 ) 9.2 ×
exp[(-478 ( 165)/T] cm molecule s . The curvature in the Arrhenius plot is discussed in
2
1
2
-
18 2.17(0.50
3
-1 -1
0
T
terms of both quantum mechanical tunneling of the H atom from H
contributions to the partition function.
2 2
to the C H radical and bending mode
Introduction
vinyl radicals can undergo a disproportionation reaction to form
acetylene and ethylene, scavenge a hydrogen atom, or act as a
source of C3 compounds:
The ethynyl radical, C2H, is of fundamental importance in
combustion chemistry and in planetary atmospheres.
1
-3
The
ethynyl radical is a reactive intermediate in the pyrolysis of
acetylene at temperatures in excess of 1800 K. It is also a
reactive species on Titan, a moon of Saturn, where the
atmospheric temperature is altitude-dependent (94 K at the
2
C H f C H + C H
4
(4)
(5)
(6)
2
3
2
2
2
C H + H f C H + H
2
2
3
2
2
2
surface and 160 K at 300 km above the surface). To understand
C H + CH + M f C H + M
2
3
3
3
6
the importance of various ethynyl reactions in the two drastically
different environments, it is desirable to know the rate coef-
ficients for C2H with such species as C2H4, C2H6, and H2 over
an extremely broad temperature range. In this work we are able
to provide the first experimental data on low-temperature rate
coefficients of the reactions
The vinyl radical, like the ethynyl radical, is one of many
species responsible for the synthesis of higher hydrocarbons in
Titan’s atmosphere through reactions with other molecules
(
C2H2, CH4, C2H6, and C2H4 just to name a few). Reactions 4
and 6 are just a few examples of the hundreds of possible
combinations of radical-radical reactions for which low-
temperature rate coefficients are not known.
The reaction of C2H + C2H6 leads to the production of
ethyl radicals, C2H5, which opens pathways for the production
of propane, C3H8, in Titan’s atmosphere via the following
C H + C H f products
(1)
(2)
(3)
2
2
4
C H + C H f C H + C H
2
2
2
6
2
5
2
C H + H f C H + H
2,6
2
2
2
2
scheme:
using transient infrared laser absorption spectroscopy.
2
(C H + hν f C H + H)
(7)
(8)
2
2
2
The exothermicity of reaction 1 is such that there are two
different thermodynamically accessible product channels
C H + CH f C H + CH
3
2
4
2
2
3
-5
available
C H + C H f C H + C H
5
(2)
-
1
2
2
6
2
2
2
C H + C H f C H + H
∆H ) -95.4 kJ mol
∆H ) -90.4 kJ mol
2
2
4
4
4
(1a)
CH + C H + M f C H + M
(9)
3
2
5
3
8
-1
f C H + C H
2
3
2
2
net: CH + C H f C H + 2H
(10)
4
2
6
3
8
(1b)
In addition, a pressure-dependent study by Lander et al.7
indicated a slight increase in kC H (C2H + C2H6) with increasing
The C4H4 species in reaction 1a is the vinyl acetylene isomer.
Reaction 1b is a possible source of vinyl radicals, C2H3, in
Titan’s atmosphere. It has been proposed by Yung et al. that
2
6
helium number density. If this finding is valid, it raises new
questions as to the mechanism involved, which may include
the formation of an addition complex.
Since the room temperature rate constant for C2H + H2 is
very slow and difficult to measure accurately, scientists
interested in modeling planetary atmospheres have had to rely
2
*
To whom correspondence should be addressed.
†
Staff Member, Quantum Physics Division, National Institute of
Standards and Technology.
X
Abstract published in AdVance ACS Abstracts, November 15, 1996.
S0022-3654(96)01960-0 CCC: $12.00 © 1996 American Chemical Society

Rate Coefficients of C2H with C2H4, C2H6, and H2
J. Phys. Chem., Vol. 100, No. 51, 1996 19905
on theoretical calculations or extrapolations from high-temper-
ature data. For example, the reaction of
C H + H f C H + H
(3)
2
2
2
2
is listed in the proposed scheme of Yung et al. as contributing
to the production of C2H6 in the atmospheres of both Jupiter
2
,3,6
and Saturn.
The reaction of C2H + H2 has been studied theoretically by
8
9
both Harding et al. and Herbst. Harding and co-workers
calculated kH , with Wigner tunneling corrections, from 300 to
2
-
19 2.39
3
2
000 K for reaction 3 as 6.8 × 10
T
exp[-435/T] cm
-
1 -1
molecule s . The calculated fit shows significant curvature
in the Arrhenius plot. Herbst calculated low-temperature rate
coefficients for reaction 3 from 10 to 300 K using statistical
phase space theory. The rate coefficients, kH , are calculated
2
with and without tunneling contributions. There is a steady
decrease in kH from 300 to 40 K, but the calculation with
2
Figure 1. Schematic of experimental setup.
tunneling contributions shows that kH begins to increase from
2
-
15
3
-1 -1
-15
3
∼
1.2 × 10
cm molecule
s
at 40 K to 2.2 × 10
cm
through a series of transverse inlets and outlets. The transverse
flow arrangement allows high laser repetition rates with minimal
photolysis of the same gas volume. With a typical flow rate of
molecule s-1 at 10 K. For the nontunneling contribution
-
1
-13
3
-1
calculation, kH decreases rapidly from 1 × 10 cm molecule
2
-
1
-16
3
-1 -1
s
at 300 K to ∼6 × 10
cm molecule
s
at 150 K.
20
-1
2
.7 × 10 molecules s , the photolysis volume is replenished
Clearly, more theoretical and experimental work is needed to
determine whether or not tunneling plays a large enough role
every 12 laser pulses. After accounting for UV laser loss on
the Brewster windows of the cell, the C2H concentration was
to “see” its effect on kH with temperature. The goal in studying
10
-3
2
estimated to be no greater than 7.5 × 10 cm for the highest
C2H + H2 reaches beyond measuring accurate rate coefficients
for photochemical models. The objective is to distinguish any
experimental evidence for tunneling at low temperatures and
provide a basis for more theoretical work on this fundamental
reaction.
acetylene pressures. (The acetylene number density ranges from
14
14
-3
1
.3 × 10 to 4.8 × 10 cm .) This estimation is based on
-19 -2
using 1.35 × 10
cm for the absorption cross section at
22
23
1
93 nm and 0.26 for the quantum yield for C2H production.
A 1500-6000-fold excess of C2H4, C2H6, or H2 with respect
to C2H is always present in these experiments. Contributions
from radical-radical or secondary reactions can be neglected
since the time between collisions for C2H and C2H4, C2H6, or
H2 is 1000 times shorter than the time between collisions of
two C2H radicals. Rate coefficients are measured at various
Extrapolations of rate coefficients from high-temperature data
can lead to significant errors at low temperatures due to a
negative temperature dependence in certain reactions, as was
shown for C2H + C2H2.10 Several groups have measured rate
coefficients for C2H with C2H4, C2H6, and H2 at 300 K or at
higher temperatures.7
,11-19
Up to this point, there have been
15
-3
ethene/ethane densities of (0.2-5.2) × 10 cm and hydrogen
no temperature-dependent rate coefficient measurements of C2H
with C2H4 and C2H6, and despite the importance of C2H + H2,
there remains no experimental rate coefficient data for this
reaction at low temperature.
17
-3
densities of (0.6-9.0) × 10 cm . The helium density is
18
-3
varied over the range (0.5-2.7) × 10 cm to test for a
pressure dependence in the rate coefficients of C2H with C2H4,
C2H6, or H2.
The Arrhenius plot for reaction 1 shows a mild negative
temperature dependence from 150 to 359 K. In addition,
reaction 2 shows little or no temperature dependence of its rate
coefficients over 153-357 K. Both sets of data are fit to
In the outer jacket either cooled pentane or isopentane is
circulated by a micropump to achieve temperatures as low as
1
50 K. (It should be noted that not every rate coefficient can
be measured down to 150 K because of the low C2H2
Arrhenius expressions in which kC H and kC H are given by
2
4
2
6
concentrations required to keep kC H [C2H2] contributions below
2
2
-
11
-11
(
7.8 ( 0.6) × 10 exp[(134 ( 44)/T] and (3.5 ( 0.3) × 10
4
0%.) In experiments performed above room temperature,
3 -1 -1
exp[(2.9 ( 16)/T] cm molecule s , respectively. The data
for C2H + H2 show a positive temperature dependence from
78 to 359 K which can be fit to the Arrhenius expression kH
heated water was circulated around the inner cell.
The C2H radical is probed in absorption by a high-resolution
1
)
-1
2
color center laser tuned to the Q11(9) line at 3593.68 cm of
-
11
3
-1
(1.2 ( 0.3) × 10
exp[(-998 ( 57)/T] cm molecule
2
2
11
the A Π-X Σ transition. A scanning Fabry-Perot spectrum
analyzer is used to ensure the color center is running on one
longitudinal mode, and a home-built scanning Michelson
interferometer wavenumber is used to monitor the color center’s
wavelength.
-1
s , but when combined with previous high-temperature mea-
surements, there is evidence for curvature in the Arrhenius plot.
Experimental Section
The rate coefficients for C2H with C2H4, C2H6, and H2 are
measured using transient infrared laser absorption spectroscopy.
A schematic of the experimental setup is shown in Figure 1.
The details of this setup have been described in numerous papers
The probe beam, after three to five multipasses, is directed
onto a 50 MHz Ge:Au detector which has a 20 mm sensitive
2
area. Transient decay traces typically have a signal-to-noise
ratio of 10-15 and are amplified and then coadded by a 100
MHz digital oscilloscope. Typical data collection consists of
averaging the transient signal for 1500-2000 excimer pulses.
All gases used in this experiment flow through a mixing cell
before entering the low-temperature cell. Helium is used to
thermally equilibrate the gas mixture with the cell walls. All
gases are obtained commercially with the following purities:
He, 99.99%; C2H2, 99.6%; H2, 99.9999%. The acetone is
1
0,20,21
by this group so only a brief outline will be given here.
Ethynyl radicals are produced in the meter long, temperature
variable flow cell at 193 nm by a pulsed excimer laser which
was run at 55 mJ/pulse at 10 Hz. The absorption cell is
constructed from quartz with Brewster windows for a multipass
setup. The cell consists of an inner zone and an outer volume.
In the inner jacket, the gases flow across the photolysis region

1
9906 J. Phys. Chem., Vol. 100, No. 51, 1996
Opansky and Leone
removed from the acetylene by an activated charcoal filter. The
temperature of the gas mixture is measured by a series of three
type K thermocouples along the length of the cell. One thermo-
couple is inserted at each end of the cell, and the other is placed
in the middle of the cell. This configuration is chosen to ensure
that there are no thermal gradients along the length of the cell.
Partial pressures of each gas are determined by calibrated mass
flow meters and the measured total pressure inside the cell.
Analysis of Kinetic Data
The ethynyl radical is monitored directly from its ground state
2
+
C2H(X Σ (0,0,0)). In addition, it is necessary that the upper
states of C2H are fully quenched before the reaction of C2H-
2
+
(
X Σ (0,0,0)) with C2H4, C2H6, and H2 occurs. Previous
7
11
experiments by Lander et al. and Farhat et al., performed
under similar conditions, have shown that relaxation of the C2H-
(
X(0,0,1)) state occurs in approximately 1 µs. In this study, as
2
+
well as in theirs, the reaction of C2H(X Σ (0,0,0)) with C2H4,
C2H6, and H2 takes place over tens of microseconds. Therefore,
complete vibrational relaxation should have occurred before any
ground state measurements were made. To further ensure
complete vibrational relaxation of C2H, the fits only include
data for t > 3τrise.
2 2 4
Figure 2. C H decay and fit due to reaction with C H (upper curve).
The lower plot is the residuals to the single-exponential decay.
The rate coefficients measured in this study are done under
pseudo-first-order conditions in which [X] (where X ) C2H4,
C2H6, or H2) and [C2H2] . [C2H]. The rate of change of [C2H]
can be expressed as
d[C H]/dt ) -[C H](k [X] + k [C H ])
(11)
2
2
X
C H
2
2
2
2
After integration, this yields
C H] ) [C H] exp[-kobst]
[
(12)
2
t
2
0
where
kobs ) k [X] + k [C H ]
(13)
(14)
X
C H
2
2
2
2
kobs - k [C H ] ) k [X] ) k′
X
C H
2
2
X
2
2
The observed decay rates, kobs, are obtained by fitting the
averaged transient signal to a single-exponential decay plus a
constant, eq 15, to fit the arbitrary offset of the base line; see
Figure 2.
2 6
Figure 3. Plot of k′C2H versus [C H ] at 198 K. The rate coefficient
6
-11
3
-1 -1
k
C2H6 is equal to (3.9 ( 0.6) × 10 cm molecule
s .
which can be fit to the Arrhenius expression kH ) (1.2 ( 0.3)
2
-
11
3
-1 -1
×
10
exp[(-998 ( 57)/T] cm molecule s ; see Figure
y ) A exp(-kobst) + constant
(15)
6
. In addition, no pressure dependence is found for the reactions
of C2H with C2H4, C2H6, or H2 over the experimental conditions
at 300 K.
The values of kobs are corrected for the C2H + C2H2 contribution
taken from our own work10 by subtraction in eq 14. The
resulting k′X values are plotted against their respective X
concentrations, and a linear least-squares fit is used to determine
kX; see Figures 3 and 4. Errors in kX are calculated by
combining the accumulated uncertainties in the corrected decay
fits, which includes errors in kC H , with the uncertainties in
Discussion
C2H + C2H4 and C2H6. In the case of C2H + C2H4, the
negative temperature dependence and lack of a pressure
dependence is attributed to a short-lived addition complex which
undergoes unimolecular dissociation to products before it can
be stabilized. The rate coefficient measured at 150 K is lower
than the one measured at 173 K, but the difficulty in measuring
kC H at 150 K, due to the low C2H2 concentrations required,
2
2
temperature and in measuring the X concentration. The error
in kX is typically 15-25%.
Table 1 summarizes the measured rate coefficients for C2H
with C2H4, C2H6, and H2 from 150 to 359 K. The data for
C2H with C2H4 and C2H6 are plotted in Figure 5 and indicate a
slight negative temperature dependence for kC H and almost no
2
4
degrades the transient absorption signal. One cannot say with
confidence that the measured rate coefficient at 150 K for C2H
+ C2H4 is significant, for example, representing a small barrier
to a C4H5 complex.
2
4
temperature dependence for kC H over the temperature range
2
6
1
50-357 K. Both sets of data are fit to Arrhenius expressions
-11
in which kC H and kC H are given by (7.8 ( 0.6) × 10
exp-
The rate coefficient kC H exhibits no temperature dependence
2
4
2
6
2 6
-
11
3
[
(134 ( 44)/T] and (3.5 ( 0.3) × 10 exp[(2.9 ( 16)/T] cm
from 153 to 357 K, comparable to that of kCN+C H from 75 to
2 6
-1
-1
24
molecule s , respectively. The rate coefficients for C2H +
H2 show a positive temperature dependence from 178 to 359 K
300 K, and no pressure dependence with varying helium
densities. Since the current experimental setup prevents reach-

Rate Coefficients of C2H with C2H4, C2H6, and H2
J. Phys. Chem., Vol. 100, No. 51, 1996 19907
2
Figure 4. Plot of k′H2 versus [H ] at 355 K. The slope of this plot is
-
13
3
-1 -1
equal to (6.7 ( 0.9) × 10 cm molecule
s .
Figure 6. Arrhenius plot of C
2
2
H + H : b, this work; O, Farhat et al.;
0, Koshi et al.; 9, Lange et al.; 2, Laufer et al.; 1, Renlund et al.; 4,
Okabe; [, Peeters et al.; 3, Stephens et al.; ], Herbst calculation.
The solid line is the Arrhenius fit to this work and is equal to (1.2 (
-
11
3
-1 -1
0
.3) × 10
exp[(-998 ( 57)/T] cm molecule
s . The dotted
line is the non-Arrhenius fit to all the data points and is equal to 9.2 ×
-
18 2.17(0.50
3
-1 -1
1
0
T
exp[(-478 ( 165)/T] cm molecule
s
. The dash-
dotted line is the ab initio calculation by Harding et al.
7
addition complex. It is worth noting that Lander et al. did see
a slight pressure dependence for reaction 2 at room temperature
over the same helium number densities. There is no obvious
explanation for why their pressure dependence result for reac-
tion 2 contradicts our findings for the same reaction.
The reactions of the C2H radical with C2H4 and C2H6 exhibit
similar temperature and pressure dependencies as the CN radical
24,25
does with C2H4 and C2H6.
Reactions of the CN radical have
been studied down to temperatures reaching 25 K using a pulsed
laser photolysis, time-resolved laser-induced fluorescence tech-
2
4
nique by Sims and co-workers. The reaction of CN + C2H4
is found to show a mild negative temperature dependence (see
Figure 7). However, the rate coefficient shows a sharp decrease
from 44 to 25 K. The Arrhenius plot for the reaction of CN +
C2H4 in Figure 7 shows that the measured value of kCN+C H at
Figure 5. Arrhenius plot of C
for C H + C ; b, this work for C
H + C ; 0, Lander et al. for C
2 6
Arrhenius fit to C H with C and C H
2
H with C
H + C
H + C
is (7.8 ( 0.6) × 10 exp-
3
2
H
4
and C
; 2, Lander et al. for
; 9, Laufer. The
2 6
H : O, this work
2
4
2
2
H
4
2
2
H
6
25 K is less than kCN+C H at 44 K. Sims et al. indicated that
2 4
C
2
2
H
4
2
2 6
H
this could signal a small potential barrier along the path leading
to CH2CH2CN formation. This reaction also exhibits no
dependence on total pressure. Sims et al. rationalized their
observations by stating that the reaction proceeds through an
addition-elimination mechanism, resulting in an exothermic
displacement of an H atom by the CN radical.
-11
2
2
H
4
-
11
[
(134 ( 44)/T] and (3.5 ( 0.3) × 10
exp[(2.9 ( 16)/T] cm
-
1
-1
molecule
s , respectively.
ing temperatures lower than ∼140 K, one cannot predict whether
kC H will increase as does kCN+C H . The lack of temperature
2
6
2 6
and pressure dependences is attributed to an addition-elimina-
tion mechanism with little or no barrier to formation of the
The rate coefficient kCN+C2H6 for CN + C2H6 displays a
pronounced curvature in its Arrhenius plot; see Figure 7. From
TABLE 1: Summary of Rate Coefficients of C
2
H with H
2
, C
2
H
4
and C
2
H
6
from 150 to 359 K
C2H4 (cm molecule s-1
3
-1
)
temp (K)
k
C2H6 (cm molecule s-1
3
-1
)
temp (K)
k
H2 (cm molecule s-1
)
3
-1
temp (K)
k
-
-
-
-
-
-
-
-
-
-
10
10
10
10
10
10
10
10
10
10
-11
-13
357
357
356
298
298
298
216
197
173
150
(0.9 ( 0.2) × 10
(1.2 ( 0.2) × 10
(1.1 ( 0.2) × 10
(1.4 ( 0.2) × 10
(1.3 ( 0.2) × 10
(1.1 ( 0.2) × 10
(1.6 ( 0.1) × 10
(1.8 ( 0.2) × 10
(2.1 ( 0.3) × 10
(1.4 ( 1.0) × 10
357
355
355
298
298
298
298
198
180
173
(3.2 ( 0.5) × 10
359
355
300
228
215
213
191
178
(7.5 ( 0.8) × 10
-11
-13
(3.6 ( 0.5) × 10
(6.7 ( 0.9) × 10
-11
-13
(3.5 ( 0.5) × 10
(4.6 ( 0.7) × 10
-11
-13
(3.4 ( 0.5) × 10
(2.1 ( 0.4) × 10
-11
-13
(3.9 ( 0.6) × 10
(0.9 ( 0.3) × 10
-11
-13
(3.4 ( 0.5) × 10
(1.1 ( 0.2) × 10
-11
-14
(3.5 ( 0.6) × 10
(5.3 ( 0.9) × 10
-11
-14
(3.9 ( 0.6) × 10
(5.0 ( 1.1) × 10
-11
(3.3 ( 0.4) × 10
-11
(4.0 ( 0.6) × 10
-11
11
1
1
63
53
(3.4 ( 0.8) × 10
(3.3 ( 0.6) × 10
-

1
9908 J. Phys. Chem., Vol. 100, No. 51, 1996
Opansky and Leone
C2H radical were to attack the C-C bond in C2H6, the two
methyl groups would provide some steric hindrance which could
account for kC2H4 > kC2H6 at room temperature. The same
argument can be stated for kC H in the reaction of C2H + C2H2.
2
2
The π electrons in acetylene are exposed for the C2H radical to
capture, and the room temperature rate coefficient kC H is an
2
2
order of magnitude faster than kC H .
2
6
C2H + H2. A summary of all the current rate coefficients
measured for C2H + H2 is given in Table 3. The data for C2H
+
)
H2 from 178 to 359 K can be fit to an Arrhenius plot of kH
2
-1
-11
3
(1.2 ( 0.3) × 10
exp[(-998 ( 57)/T] cm molecule
represented by the solid line in Figure 6. Upon closer
-
1
s
1
1
examination of the combined data from Farhat et al., Koshi
et al., and this work, a slight curvature is observed from 178
1
2
to 854 K. The combined data are best fit to a non-Arrhenius
-
18 2.17(0.50
3
form of kH ) 9.2 × 10
T
exp[(-478 ( 165)/T] cm
2
molecule- s , represented by the dashed line in Figure 6. The
question as to whether or not the curvature in Figure 6 is real
or simply due to experimental error must be addressed.
Farhat et al. did a similar set of experiments as described
in this work over a temperature range 295-854 K. The ethynyl
radical was produced by acetylene photolysis at 193 nm and
detected in absorption with a color center laser. Their data can
1 -1
1
1
Figure 7. Arrhenius plot of CN with C
Herbert et al. and Sims et al. for CN + C
al. and Sims et al. for CN + C
2
H
4
and C
2 6
H : b, work of
2
H ; 0, work of Herbert et
6
2
H
4
.
-11
be fit to an Arrhenius expression of the form kH ) 6.9 × 10
2
3
-1 -1
exp[-1480/T] cm molecule s , but they chose to fit their
3
00 to 1000 K, kCN+C H shows a positive temperature depen-
2 6
data to a non-Arrhenius expression of the form k ) (9.44 (
H2
dence and from 300 down to 25 K, and kCN+C H exhibits a
-14 0.9
3
-1 -1
2
6
0.24) × 10
T
exp[(-1003 ( 20)/T] cm molecule s .
negative temperature dependence. However, from approxi-
The room temperature values of kH for this work and Farhat et
2
mately 75 to 300 K, kCN+C H remains constant just as kC H does
2
6
2
6
al. calculated from the fits shown in Table 3 agree within
for the reaction of C2H + C2H6; see Figure 7. Sims and co-
experimental error.
workers have no suitable explanation for the sharp increase in
12
Koshi et al., using laser photolysis time-resolved mass
24
kCN+C H below 75 K. They have ruled out the formation of
2
6
spectrometry, measured kH2 over the temperature range 298-
a stabilized CN-C2H6 van der Waals complex contributing to
the increase in kCN+C H but state that weak, long-range attractive
4
38 K and found an Arrhenius dependence of kH ) (1.8 (
2
-11
3
-1 -1
2
6
1.0) × 10
exp[(-1090 ( 299)/T] cm molecule s . In
forces between CN and C2H6 assist in increasing kCN+C H at
2
6
4 2
their experiment, the concentration of C H is monitored and
very low temperatures. Sims et al. theorize that a “transient
van der Waals” complex could be formed when the energy of
the colliding CN and C2H6 species is lower than the van der
Waals potential well. This would allow the reactants to find a
favorable orientation for a reaction to occur.
first used to measure the rate coefficients of C2H + C2H2. When
H2 is added to the gas flow, the concentration of C4H2 decreases
due to reaction 1. The ratio of kC H /kH is measured based on
2
2
2
the C4H2 concentration and reported in their work. The room
temperature value of kH in the work by Koshi et al., (5.1 (
2
-
13
3
-1 -1
In addition to comparing reactions 1 and 2 to their CN
counterparts, it is beneficial to relate them to other C2H
reactions. Table 2 lists several rate coefficients at room
temperature of the C2H reactions with hydrocarbons and H2 and
various thermodynamic properties. All of these reactions are
very exothermic, but their rate coefficients vary by 3 orders of
magnitude from C2H + C2H2 to C2H + H2. Interestingly, of
the five reactions listed in Table 2, the fastest are those with
the largest C-H bond dissociation energies: C2H with C2H2
and C2H4. Since the measured energy of activation is negative
in these reactions, there is little or no barrier to form the addition
complex. Therefore, the rate-determining step in each of these
reactions, and C2H + C2H6, is most likely the formation of the
addition complex. The last two reactions listed in Table 2, C2H
with CH4 and H2, have a positive energy of activation, sug-
gesting that the rate-determining step is the direct H atom ab-
straction by the ethynyl radical. Since the mechanism involves
a direct abstraction rather than one of complex formation, it is
inherent that the measured rate coefficients at room temperature
are the slowest of the five and decrease sharply as the
temperature decreases. The factor of 3-4 difference between
kC H and kC H at room temperature can possibly be traced to
2.0) × 10
cm molecule s , agrees within error with the
averaged measured value from this work and Farhat et al., which
-13
-13
3
-1
are (4.6 ( 0.8) × 10 and (4.7 ( 0.5) × 10 cm molecule
-1
s , respectively. Due to the differences in the methods, the
curvature in Figure 6 should be regarded with some caution;
nevertheless, in the discussion that follows we consider some
possible sources of the curvature.
The latest high temperature work was done by Peeters et al.19
using laser photodissociation/chemiluminescence. Ethynyl radi-
cals were generated from C H or C HCF photodissociation
2
2
2
3
by 193 nm light from an excimer. The pseudo-first-order decay
of C H was monitored by depletion of the chemiluminescence
2
2
of CH(A ∆) produced by the radical reaction with O . They
2
measured kH2 from 295 to 440 K and fit their data to the
-
18 2.39
3
-1
expression k ) 1.31 × 10
H2
T
exp(-174/T) cm molecule
-1
s . In conjunction with measurements taken by Koshi et al.
and Farhat et al., the measurements made by Peeters et al. for
reaction 3 follow the trend of kH2 increasing with temperature;
see Figure 6.
When analyzing reaction 3, it is again useful to consult a
similar reaction such as
2
4
2 6
the radical’s attraction to the electron-rich double bond in C2H4.
Compared to ethene, ethane does not possess the π electrons
for C2H to attack. In order to form a complex with C2H6, the
C2H must attack either the C-H or C-C σ electrons. If the
CN + H f H + HCN
(16)
2
Although CN is a diatomic radical, it is isoelectronic with C2H,
and the measured rate coefficients with C2H2, C2H4, C2H6, O2,

Rate Coefficients of C2H with C2H4, C2H6, and H2
J. Phys. Chem., Vol. 100, No. 51, 1996 19909
TABLE 2: Comparison of Various C
2
H Reactions
∆Ha
E
b
D
0
c,d
ke
reaction
a
-
-
-
-
-
10
10
11
12
13
C
C
C
C
C
2
2
2
2
2
H + C
H + C
H + C
2
2
2
H
H
H
2
4
6
f C
f products
f C + C
+ C
+ H
4
H
2
+ H
-102
f
-133
-117
-116
-0.7 ( 0.1
-1.1 ( 0.4
-0.02 ( 0.10
4.3 ( 0.1
HC
2
-H 549.3
(1.3 ( 0.2) × 10
(1.3 ( 0.2) × 10
(3.6 ( 0.6) × 10
(2.3 ( 0.1) × 10
(4.6 ( 0.7) × 10
H
2
H
3
H
3
C
C
2
-H 465.2
-H 410
2
H
5
2
H
2
2
2
H + CH
4
f CH
3
2
H
C-H 438
H + H
2
f C
2
H
2
8.3 ( 0.5
H-H 436
a
Units of kJ mol , ref 31. b Units of kJ mol-1. c Units of kJ mol-1, ref 32. d Reference 33. e Rate coefficients measured at 300 K and in units
-1
of cm molecule s-1. References 3-5, C
3
-1
f
H + C
H
f C H
2 2
+ C
H
3
, ∆H ) -90.4 kJ mol-1; C
-1
2
2
4
2
2
2 4 4 4
H + C H f C H + H, ∆H ) -95.4 kJ mol
for the vinyl acetylene isomer.
TABLE 3: Summary of Rate Coefficients for C
2
H + H
2
The middle two reactions display noticeable curvature in their
Arrhenius plots and have at least one bending frequency below
H2 (cm molecule s-1
3
-1
reference
this work
k
)
temp (K)
-1
5
00 cm . The final two reactions, C2H + H2 and CN + H2,
-
11
(1.2 ( 0.3) × 10
178-359
‡
have the lowest barriers, V , and the lowest bending frequencies
in the group. Their rate coefficients show substantial curvature
in their respective Arrhenius plots.
exp[(-998 ( 57)/T]
Farhat et al.11
-14
0.9
(9.44 ( 0.24) × 10
T
295-854
298-438
exp[(-1003 ( 20)/T]
Koshi et al.12
(1.8 ( 1.0) × 10
-11
8
9
Both Harding et al. and Herbst have performed theoretical
calculations on the reaction C2H + H2, Harding from 300 to
>2000 K and Herbst from 10 to 300 K; see Figures 6 and 8.
Harding and co-workers calculate that reaction 3 has an early
saddle point with the Ha-Hb bond distance in the Ha-Hb-
exp[(-1090 ( 299)/T]
1
3
-13
Lange and Wagner
1.7 × 10
320
298
300
298
298
295-440
1
4
-13
Laufer and Bass
1.5 × 10
1
5
-11
Renlund et al.
(1.2 ( 0.3) × 10
1
6
-13 a
Okabe
Stephens et al.
9.7 × 10
1
7
-13
(4.8 ( 0.3) × 10
‡
Cc-Cd-Hc transition state only 6% larger than in the H2
1
9
-18 2.39
Peeters et al.
1.31 × 10
T
reactant and the Hb-Cc bond 52% greater than in the C2H2
product. This calculation also confirms Hammond’s postulate
that more exothermic reactions have reactant-like transition
states. The fit by Harding et al., including Wigner tunneling
corrections, is for a barrier height of 9.6 kJ mol- and shows
significant curvature. Harding and co-workers performed this
exp(-174/T)
a
Recalculated using the measured ratio and the present-day C H +
2
2
-
10
3
-1 -1
C
2
H
rate constant of (1.3 ( 0.2) × 10 cm molecule
s .
1
TABLE 4: Reactions Involving H Atom Abstractionsa
reaction
V‡ (kJ mol-1)b
∆E (kJ mol-1)c
ν‡ (cm-1)d
‡
calculation at different barrier heights, V . When the barrier is
3
O( P) + H
2
52.3
56.4
44.7
20.5
25.9
17.1
9.6
12.1
10.8
-10.8
59.4
-67.3
-105.8
-129.7
736, 736
592, 592
592, 592
325, 590
440, 686
165, 165
139, 139
decreased, their calculated rate coefficients increase with respect
to the Arrhenius plot in Figure 6, and the fit shows more
curvature. Conversely, when the barrier is increased, the rate
coefficients decrease with respect to their Arrhenius plot in
Figure 6, and the fit shows less curvature. Although the
calculated rate coefficients are lower than the values measured
CH
CH
H + H
OH + H
CN + H
H + H
4
+ H
+ H
3
2
2
CO
2
2
C
2
2
6
7
a
Table 4 is taken from ref 27. b V‡ Classical barrier at the saddle
here and those by Farhat et al. and Koshi et al., the general
point. c ∆E The difference in internal energy between products and
trend of kH and curvature is followed.
2
d
‡
reactants. ν The two lowest bending frequencies at the saddle point.
Herbst, using statistical phase space theory and the vibrational
‡
V and ∆E, taken from Wagner and Bair, do not include zero-point
8
frequencies and rotational constants from Harding et al.,
corrections.
calculated rate coefficients from 300 to 10 K for reaction 3. At
room temperature, Herbst reports that the tunneling contribution
to kH2 is ∼40%, and then kH2 starts to decrease as the temperature
is lowered. The rate coefficients for kH2 decrease to a minimum
and CH4 show similar temperature dependencies as their C2H
24
counterparts. Reaction 16 has been studied by several groups
over the combined temperature range 209-1000 K.26-29 The
measured rate coefficients of reaction 16 exhibit a positive temp-
erature dependence in addition to a mild curvature in the
Arrhenius plot. One study, by Sims and Smith, gives the modi-
fied Arrhenius fit to reaction 16 CN(V)0) as (2.4 ( 0.7) ×
-
15
3
-1
value at ∼40 K of approximately 1.2 × 10
cm molecule
-1
-15
cm3
s . Afterward, kH2 increases to a value of 2.2 × 10
molecule-
1
s
-1
at 10 K; see Figure 8. For clarity, only four of
his calculated points are shown in Figure 6 due to the range of
“1/T space” the calculation spans. Herbst claims that the
increase in kH2 is due to a decrease in the density of reactant
states which control the redissociation rate instead of an increase
in the tunneling rate. However, Herbst is quick to note that his
model is highly sensitive to several undefined parameters such
-
12
1.6(0.2
3
-1 -1
1
0
(T/298)
exp[(-1340 ( 90)/T] cm molecule
s
2
6
27
from 295 to 768 K. A theoretical study by Wagner and Bair
has shown that the H2CN transition state closely resembles the
‡
separated reactants, which is consistent with Hammond’s postu-
late for exothermic reactions.30 The H-H bond distance is
increased only by 0.07 Å at the saddle point, and the C-N bond
distance remains constant. Both Sims and Smith and Wagner
and Bair have concluded that the curvature in the Arrhenius
plot for reaction 16 is due to the temperature dependence of
the partition function associated with the doubly degenerate low-
‡
as the transition state barrier, V , and the imaginary frequency
‡
of vibration, νi . A “slight” decrease in the transition state
barrier increases kH2 by an order of magnitude at 10 K. A
-1
change in the transition state frequency by (200 cm results
in kH2 fluctuating in both directions by an order of magnitude.
In light of the stated results in the previous paragraphs, one
can make some clarifications on the curvature in the combined
experimental data of Farhat et al., Koshi et al., and this work.
Despite the larger scatter of points in this data below room
temperature, the curvature of the modified Arrhenius fit to kH2
from 178 to 854 K appears to be real. Arguments as to what
is causing it can be traced partly to the CN + H2 studies by
Sims et al. and Wagner et al. Both groups made it clear that
‡
frequency bending mode in the H2CN transition state.
Wagner and Bair also compare their results for CN + H2 to
those of other H atom abstraction reactions; see Table 4. The
first three reactions in Table 4 are close to thermoneutral and
-
1
have barriers exceeding 40 kJ mol and possess bending
degrees of freedom with vibrations greater than 500 cm- . The
rate coefficients for these reactions exhibit a steep positive
temperature dependence, but vary little from Arrhenius form.
1

1
9910 J. Phys. Chem., Vol. 100, No. 51, 1996
Opansky and Leone
no temperature dependence from 153 to 357 K. The Arrhenius
-
11
fit for this reaction is equal to (3.5 ( 0.3) × 10
exp[(2.9 (
3
-1 -1
1
6)/T] cm molecule s .
The Arrhenius fit to the data for C2H and H2 can be expressed
-11
3
as kH2 ) (1.2 ( 0.3) × 10
exp[(-998 ( 57)/T] cm
molecule- s . The positive temperature dependence is
1
-1
consistent with reactions involving a hydrogen abstraction as
the rate-determining step and a positive energy of activation
Ea ) 8.3 ( 0.5 kJ mol- for C2H + H2). The curvature in the
1
(
Arrhenius plot of C2H + H2 can be attributed to a combination
of H atom tunneling and a temperature dependence in the
partition function associated with the low-frequency bending
‡
mode in the H2C2H transition state.
Acknowledgment. We gratefully acknowledge the National
Aeronautics and Space Administration for support of this
research and the Department of Energy for additional support.
References and Notes
Figure 8. Arrhenius plot of C
by Herbst: b, calculation with tunneling corrections; 0, calculation
without tunneling corrections.
2
2
H + H using calculated rate coefficients
(1) Homann, K. H.; Wagner, H. G. Proc. R. Soc. London, A 1968,
3
5
07, 141.
(2) Yung, Y. L.; Allen, M.; Pinto, J. P. Astrophys. J., Suppl. Ser. 1984,
5, 465.
(
(
3) Gladstone, G. R.; Allen, M.; Yung, Y. L. Icarus 1996, 119, 1.
4) Mechanism and Theory in Organic Chemistry; Lowry, T. H.,
the curvature in the Arrhenius plot of CN + H2 is due to the
temperature dependence of the partition function associated with
the doubly degenerate low-frequency bending mode in the
Richardson, K. S., Eds.; Harper and Row: New York, 1987.
5) Ervin, K. M.; Gronert, S.; Barlow, S. E.; Gilles, M. K.; Harrison,
(
‡
H2CN transition state. Pronounced curvature in Arrhenius plots
A. G.; Bierbaum, V. M.; DePuy, C. H.; Lineberger, W. C.; Ellison, G. B.
J. Am. Chem. Soc. 1990, 112, 5750.
is displayed by H atom abstraction reactions in Table 4 that are
highly exothermic, have low barriers, and have low bending
frequencies in the transition state. The reaction of C2H + H2
most likely follows this trend. Therefore, at least part of the
curvature in the experimental data from 178 to 854 K can be
attributed to the temperature dependence of the partition function
(
(
6) Allen, M.; Yung, Y. K.; Gladstone, G. R. Icarus 1992, 100, 527.
7) Lander, D. R.; Unfried, K. G.; Glass, G. P.; Curl, R. F. J. Phys.
Chem. 1990, 94, 7759.
(8) Harding, L. B.; Schatz, G. C.; Chiles, R. A. J. Chem. Phys. 1982,
6, 5172.
7
(9) Herbst, E. Chem. Phys. Lett. 1994, 222, 297.
(
10) Opansky, B. J.; Leone, S. R. J. Phys. Chem. 1996, 100, 4448.
‡
linked to the low-frequency bending mode in the H2C2H
(11) Farhat, S. K.; Morter, C. L.; Glass, G. P. J. Chem. Phys. 1993, 97,
2789.
12) Koshi, M.; Fukada, K.; Kamiya, K.; Matsui, H. J. Phys. Chem.
992, 96, 9839.
13) Lange, W.; Wagner, H. G. Ber. Bunsen-Ges. Phys. Chem. 1975,
79, 165.
14) Laufer, A. H.; Bass, A. M. J. Phys. Chem. 1981, 85, 3828.
15) Renlund, A. M.; Shokoohi, F.; Reisler, H.; Wittig, C. J. Phys. Chem.
982, 86, 4165.
1
transition state.
(
However, one must consider how much tunneling plays a
role in this reaction, especially since the fit by Harding and
co-workers, although low compared to the data, displays the
same curvature that the experimental data exhibits. The ab
initio calculation by Harding et al. includes Wigner tunneling
corrections and is conceivably offset from the experimental
data because the barrier height used in the calculation is too
1
(
(
(
1
(16) Okabe, H. J. Phys. Chem. 1982, 78, 1312.
(
17) Stephens, J. W.; Hall, J. L.; Solka, H.; Yan, Y. B.; Curl, R. F.;
Glass, G. P. J. Phys. Chem. 1987, 91, 5740.
18) Peeters, J.; Van Look, H.; Ceursters, B. J. Phys. Chem. 1996, 100,
5124.
(19) Laufer, A. H. J. Phys. Chem. 1981, 85, 3828.
20) Opansky, B. J.; Seakins, P. W.; Pedersen, J. O. P.; Leone, S. R. J.
Phys. Chem. 1993, 97, 8583.
21) Pedersen, J. O. P.; Opansky, B. J.; Leone, S. R. J. Phys. Chem.
1993, 97, 6822.
(22) Satyapal, S.; Bersohn, R. J. Phys. Chem. 1991, 95, 8004.
23) Shin, K. S.; Michael, J. V. J. Phys. Chem. 1991, 95, 5864.
24) Sims, I. R.; Queffelec, J. L.; Travers, D.; Rowe, B. R.; Herbert, L.
B.; Karthauser, J.; Smith, I. W. M. Chem. Phys. Lett. 1993, 461, 211.
(25) Herbert, L.; Smith, I. W. M.; Spencer-Smith, R. D. Int. J. Chem.
Kinet. 1992, 24, 791.
-1
high. If the barrier height was lowered below 9.6 kJ mol ,
then the fit by Harding et al. would overlap the combined
experimental results from 178 to 854 K by Farhat et al., Koshi
et al., and this work. Taking this into account, H atom tunneling
could also contribute to the curvature in the Arrhenius plot of
C2H + H2.
(
1
(
(
One cannot conclusively state whether the curvature in the
Arrhenius plot of C2H + H2 is due solely to either tunneling or
to the partition function associated the low-frequency bending
(
(
‡
modes in the H2C2H transition state. Advanced theories will
need to take into account both explanations.
(
(
(
26) Sims, I. R.; Smith, I. W. M. Chem. Phys. Lett. 1988, 149, 565.
27) Wagner, A. F.; Bair, R. A. Int. J. Chem. Kinet. 1986, 18, 473.
28) Atakan, b.; Jacobs, A.; Wahl, M.; Weller, R.; Wolfrum, J. Chem.
Conclusion
Phys. Lett. 1989, 154, 449.
29) Sun, Q.; Yang, D. L.; Wang, N. S.; Bowman, J. M.; Lin, M. C. J.
Chem. Phys. 1990, 93, 4730.
The rate coefficients of C2H with C2H4, C2H6, and H2 have
been measured from 150 to 359 K. The reaction of C2H +
C2H4 displays a mild negative temperature dependence similar
to that of CN + C2H4 which is characteristic of an addition-
elimination mechanism. The C2H data are fit to an Arrhenius
(
(30) Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 334.
(31) ∆H taken from JANAF: J. Chem. Ref. Data 1992, 21 (Suppl. No.
3
).
(32) Organic Chemistry, 4th ed.; Morrison, R. T., Boyd, R. N., Eds.;
-11
3
expression equal to (7.8 ( 0.6) × 10 exp[(134 ( 44)/T] cm
Allyn and Bacon: Boston, MA, 1983.
(33) Physical Chemistry, 3rd ed.; Atkins, P. W., Ed.; Oxford University
Press: London, 1986.
molecule- s . Likewise, the reaction mechanism of C2H +
C2H6 also consists of an addition-elimination step. Within the
calculated error bars, the rate coefficients of reaction 3 display
1
-1
JP9619604