J . Phys. Chem. 1991, 95, 2390-2394
2390
halogen substitutents (see Figures 1 and 2). With increasing halogen substitution, that orbital lies increasingly lower in energy. If the orbital interacts substantially in the reactive transition state, then its lower energy will suppress the rate constant. It is clear that this orbital must contribute to the transition-state wave function since it comprises part of the carbon-carbon A bond that is broken in the reaction as the plane of symmetry of the haloethene is twisted. The extent to which it contributes is difficult to estimate. The wave functions for all the haloethenes in reactions 1-10 have been studied at the UHF/3-21G//UHF/3-12G level, and those for reactions 1 and 8 have been studied a t the UHF/631G**//UHF/6-31G** level. For these two cases, there is no qualitative difference between the results of the two basis sets. From these calculations, it can be generally concluded that (i) the HOMO in all cases contains lone-pair contributions from both the halogen atoms and the carbon-carbon double bond, (ii) the fewer the halogen substituents, the more the orbital resembles the bare ethene A bond, and (iii) the electrons in the lowest lying occupied valence A orbital are delocalized in a bonding manner over the carbon and halogen substituents. There is no systematic change in bonding structures at the S C F level from molecule to molecule, e.g., the CCI2 entity has the same general shape in CH2CC12as it does in CC12CC12. At this level of theory, no accurate statements can be made about orbital energetics. Conclusions
The high-pressure discharge flow kinetics results for the gasphase reactions of the hydroxyl radical with five halogenated
ethenes have been measured from 297 to 368 K. For a large number of small radical/molecule systems, rate constants within homologous series have been shown to correlate quantitatively with the electron-donating and electron-accpeting abilities of the reactants. In this manner we have confidence that frontier orbital analysis can be used to examine the character of the rate-determining transition state. For the haloethenes studied in this work, the highest occupied molecular orbital is composed of carboncarbon r-bonding and halogen atom lone-pair contributions. The attacking OH radical experiences greater nonbonding interactions in the transition state than it does in the OH/alkene reactions, where the HOMO is solely carbon-carbon ?r bonding. In addition, the electron density originally localized in the alkene A bond is more delocalized in the haloethene, particularly in the lowest lying valence A orbital which is bonding between the carbon and halogen substituents. As a result, the rate constants for these reactions do not correlate in a simple manner with the energy of the HOMO (the experimental ionization potential), as is the case in the OH/alkene reactions, and the rate constants are suppressed relative to the OH/alkene trend by a barrier for O H insertion into the carbon-carbon ?r bond.
Acknowledgment. We thank Michelle Sprengnether for instigating this study by suggesting we measure the rate constant for reaction 5 . This work is supported by the National Science Foundation under Grant CHE-860143 1. Registry No. HO, 3352-57-6; CI2C=CH2, 75-35-4; (Z)-CICH= CHCI, 156-59-2;(E)-CICH=CHCI, 156-60-5; FCIC=CF2, 79-38-9; F2C=CC12, 79-35-6; H2C=CH>, 74-85-1.
Temperature and Pressure Dependence of the Reaction CH
+ H,
K. H. Becker,* R. Kurtenbach, and P. Wiesen Physikalische ChemielFachbereich 9, Bergische Universitat-Gesamthochschule Wuppertal, Postfach 1001 27, 0-5600 Wuppertal 1, FRG (Received: July 3, 1990; In Final Form: October IO, 1990) The reaction CH(X211) + H2 was studied as a function of temperature in the range 200-400 K at 4 Torr total pressure and as a function of total pressure in the range 2-591 Torr at 298 K. CH radicals were generated by excimer laser photolysis of CHCIBr2/Ar mixtures and were detected by laser-induced fluorescence. The reaction proceeds along two pathways: Above 300 K, production of CH2 + H dominates with an activation energy of 13.82 4.19 kJ.mol-’, whereas below 300 K, the rate constants exhibit a negative temperature dependence with an activation energy of -6.12 f 1.93 kEmol-’ consistent with an adduct formation followed by collisional stabilization. The limiting rate constants ko and k , and the broadening factor F, were determined from the pressure dependence. A transition-state-theory model was applied to analyze the experimental results.
*
Introduction
The methylidyne radical in different electronic states is an important reactive intermediate in hydrocarbon combustion and planetary atmospheres.’ Therefore, the investigation of its chemical reactivity has been the subject of a number of studies during the past years. The knowledge of CH kinetics has recently been reviewed.2 The reaction C H + H2 is of particular interest since it is the simplest example of a carbyne reaction allowing to carry out ab initio calculations which can be compared with experimental results. Berman and Lin3 investigated the C H H2 reaction at 100 Torr total pressure in the temperature range 159-658 K and proposed a mechanism with two reaction channels, abstraction and addition, as shown in reaction 1:
+
CH(X2n) + Hz
* CH:
CH2(k3B,) + H
(la)
CH3
(W
To whom correspondence should be addressed.
Under their experimental conditions they found that the abstraction channel dominates above 500 K, whereas addition followed by collisional stabilization of the adduct becomes more important below 400 K. In addition, these authors found the rate constant to be pressure dependent as expected from reaction 1b. However, they were not able to extrapolate the pressure limiting rate constants ko and k , from their experimental results. More recently, Xiang and Guillory4 studied the CH + Hz reaction with C H in the ground and first excited vibrational state. They concluded that the kinetic behavior of CH(u”=l) is even more complex than that of CH(v”=O) because of the contribution from vibrational relaxation to the measured rate constants. Brooks and SchaefeP calculated potential energy surfaces for the C H H2reaction and found a high geometric selectivity. For
+
(1) Bccker, K. H.; Engelhardt, B.;Wiesen, P. Chem. Phys. Lett. 1989,154, 342 and references therein. (2) Sanders, W. A.; Lin, M. C. In Chemical Kinetics of Small Organic Rudicals; Alfassi, Z . , Ed.; CRC Press: h a Raton, FL, 1988; Vol. 3, p 103. (3) Berman, M. R.; Lin, M. C. J . Chem. Phys. 1984,81, 5743. (4) Xiang, T.-X.; Guillory, W. A. Chem. Phys. 1989, 130, 299. ( 5 ) Brooks, B. R.; Schaefer, H. F. J . Chem. Phys. 1977, 67, 5146.
0022-3654/91/2095-2390%02.50/0 0 1991 American Chemical Society
CH t H2 Reaction
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2391
the least-motion path with the CH perpendicular to the H2 molecule, they calculated a barrier of about 314 kl-mol-’, whereas they found nearly no barrier for the non-least-motion or parallel approach. In the present study, the reaction of CH(X211) radicals with molecular hydrogen has been investigated for the first time at 4 Torr total pressure in the range 200-400 K by using a pulsed UV laser photolysis (LP)-laser-induced fluorescence (LIF) technique. Because of the low total pressure, the collisional stabilization of the adduct, reaction 1b, was of minor importance and, therefore, it was possible to study the abstraction, reaction la, without any significant influence by the addition channel. The present results were analyzed by use of the transition state theory and were compared with literature data. The pressure dependence of the reaction in the range 2-591 Torr a t 298 K was also investigated. From these measurements the pressure limiting rate constants ko and k , were extrapolated by a method described by Troe.6
Experimental Section A standard photolysis-probe laser technique was used to examine the C H H2 reaction. C H radicals were generated by pulsed excimer laser photolysis of CHClBr2 a t 248 nm. The photolysis laser was a Questek 2640 with a typical pulse energy of 100 mJ. The laser beam was focused with a 1-m focal length quartz lens into the center of the reaction cell. The relative C H concentrations were measured by LIF from the integrated intensity of the Q branch of the A2A X211(0,0) transition at 431.5 nm. The probe laser was a Lambda Physik system comprising a FL 2002 dye laser pumped by an EMG 102 excimer laser. The dye laser was operated with stilbene 3 in methanol, yielding typical pulse energies of 1-2 mJ. Both lasers were operated at a repetition rate of 10 Hz. The reaction cell consisted of a stainless steel cylinder of 100-mm diameter and 100-mm length through which the photolysis and probe laser beams counterpropagated. The reaction cell was fitted in a second stainless steel cylinder of 170-mm diameter and 220-mm length. The volume between the two cylinders was evacuated in order to reduce heat losses during cooling or heating of the reaction cell. In experiments carried out at elevated temperatures the cell was heated by means of a Ni/Cr (80/20) resistive wire. For studying reactions below room temperature, a coolant fluid was circulated through a jacket surrounding the inner cylinder. The temperature in the reaction cell was measured by a movable thermocouple and kept constant during the experiments to better than f0.5 K. The fluorescence was detected at right angles to the laser propagation by a 1P28 photomultiplier through a lens system and a continuous band filter. The photomultiplier output was integrated by a boxcar averager (PAR Model 162) and digitized and analyzed by a microcomputer. The time delay between the photolysis laser and the probe laser was varied from zero to several hundred microseconds by a digital delay generator (BNC, Model 7010). All reactions were investigated under pseudo-first-order conditions with reactant concentrations at least 100 times larger than that of the C H precursor CHC1Br2. All measurements were carried out in a slowly flowing gas mixture with a flow rate < O S ms-’. The concentrations of the gases were determined from their partial flows measured with calibrated flow meters (Tylan FM 360). All gases employed in this work were supplied by Messer Griesheim and used without further purification. Their stated purities were 99.999% and 99.998% for H2 and Ar, respectively. CHCIBr2 (Alfa, 99% purity) was carefully degassed before use.
+
0
-1 -2
-3
-4
A t (ps) Figure 1. Semilog plot of CH decay after excimer laser photolysis of 3.7 X 10l2molec~les.cm-~ CHCIBr, in the presence of different H2 concenat T = 261 K: 0 , 0; 1.3; 0,3.9; D, mole~ules.cm-~] trations 6.2; 0,8.6; 0 , 1 1 . 1 .
*;
-
Results The measured dependence of the LIF intensity on the photolysis laser power shows that the CH radicals were generated by the absorption of at least two or three 248-nm photons by CHCIBr2, probably leading to the stepwise breaking of the C-Br and C-CI (6) Troe, J. J . Chem. Phys. 1977,66.4758.
c 1015 molecule,cm-’I
c H2
Figure 2. Plot of pseudo-first-orderdecay constants K’of CH radicals vs the concentration of molecular hydrogen: 0 , 2 9 8 K D, 327 K; 0,371 K 0 , 397 K.
bonds. However, the mechanism of the C H formation is not clearly understood. The LIF signal decayed exponentially with the delay time after the photolysis pulse, as shown in Figure 1. In the absence of the reactant, the CH decay was mainly caused by reactions with CHCIBr2 and the photolysis products or by diffusion out of the observation zone. For the typically used CHClBr2 concentrations of 0.1 mTorr the C H decay could be monitored over a time range of about 1 ms or 6 lifetimes. By plotting the In of the relative C H concentration as a function of the reaction time, the pseudo-first-order decay constants K were calculated from the slope of the individual straight line plots which were obtained for different H2 concentrations. The K values increased proportionally with the concentration of added molecular hydrogen. The bimolecular rate constants kCH+H4for a given temperature and pressure were then obtained by plotting corrected pseudo-first-order decay constants K’as a function of the H2 concentration as shown in Figure 2. The K’values were obtained by subtracting the decay constants, which were obtained in the absence of H2, from the corresponding K values. Pressure Dependence. The C H H2reaction was investigated in argon as buffer gas as a function of total pressure in the range 2-591 Torr at 298 K. The obtained bimolecular rate constants are listed in Table I. The given error limits are based on the “Student’s t distribution” and reflect a 90% confidence interval. These values are shown in Figure 3 in comparison with literature data. The solid line in Figure 3 is the result of a fit to Troe’s semiempirical equation? Limiting rate constants ko = (9.0 f 3.0) X c m 6 d and k , = (7.3 f 2.0) X 10-l’ c m 3 d and a broadening factor F, = 0.85 f 0.10 were obtained.
+
Becker et al.
2392 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
-
TABLE 1: Rate Constants for the Reaction CH + HZ Products os a Function of Total Pressure at 298 K kCH+H2, cm3d press., Torr this work literature ref 2 4 8 16 25 32 50 63 100 100 100 127 200 223 323 442 59 1 600
T CKI 400 350
-25.51
CH
U
N 0 r(
V
7.9 f 2.2
3
11.4 f 0.9
3
14.1 f 0.6 23 f 5 26 f 5
3 13 14
TI 0
12.42 f 6.72
-275l2I5
3
19.4 f 0.8
T
45 f 4
37
1/T C
-
f 0.06 f 5.87 f 6.00
'
I'
33
9
f 6.06
'
'
45
41
I
'
4 9 '
K-'I
Figure 4. Arrhenius plot of the bimolecular rate constant ~ C H + H *vs 1/T for the reaction CH + H2 products. The dashed line is a weighted, linear least-squares fit of the rate constants above 300 K.
3
2.12 f 0.10 1.51 f 0.52 1.36 f 0.20 1.02 f 0.41 0.86 f 0.27
T CKI
-26 5 .
'Y)
300 I
+
I
1
H,
-27 0 -
33
1
200
250
I
CH
h z
35
I
40
1
45
50
1/T C K-'I Figure 5. Arrhenius plot of the low-temperature component & & + H ~ of the reaction CH + H2 CH3. The solid line is a weighted, linear least-squares fit to these rate constants.
-
-
U
i I 0
Y
'
'
200 '
I
'
400 I '
'
600 ' '
'
'
800
p r e s s v e CTorrl
Figure 3. Pressure dependence of the bimolecular rate constant ~ C H + H ~ for the CH + H2 reaction at 298 K with Ar as bath gas: this work; 0 , Berman and Lin;' m, Butler et al.13J4 The solid line is the result of a fit of the data listed in Table I to the expression of Troe.6
*,
Temperature Dependence. The bimolecular rate constants for the CH H2reaction were measured in the range 200-400 K at 4 Torr total pressure. These values are shown in Figure 4 and summarized in Table I1 with error limits representing a 90% confidence interval. The Arrhenius plot exhibits regions of positive and negative slopes with a minimum at 300 K. In the 327-397 K range, the rate constant shows a positive temperature dependence. If one uses the simple Arrhenius expression k = A exp(-E,/RT), the rate constant in this "high"-temperature regime is well described by
+
@H+H~
'
'
15.48 f 3.62
t
O F
H,
\
2.24 i 0.09 1.71 f 0.50 1.69 i 0.17 1.67 f 0.34 1.82 f 0.17 1.66 f 0.33 2.37 f 0.63 4.04 f 0.87 5.86 f 1.22
40 50
+
*E
I
E
I
-
TABLE 11: Bimolecular Rate Constants for the Reaction CH + Hz as a Function of Temwrature at 4 Torr Total Pressure T, K kCH+H2, 10-12 cm3.s-l kkH+H2, 10-l~ c m 3 4
0
200
I
v)
5.45 f 1.20
207 22 1 236 26 1 279 298 327 37 1 397
250
I
I
1.74 f 0.13 1.66 f 0.33 2.73 f 0.19 3.97 f 0.63
29.80 32.30 41.88 45.42
300
I
I
=
3.75??#
X
exp[-(13.82 f 4.19)/RT]
cm3d
with Ea in units of kEmol-I. This expression was obtained by a linear least-squares fit to the measured rate constants above 300 K weighted by the inverse square of its experimental error (dashed
line in Figure 4). When the rate constant value of 298 K was included to the fit, the activation energy decreased by 10%. Extrapolating the Arrhenius curve obtained from the 'high"temperature experiments to temperatures below 300 K gives an estimate of the contribution of the "high"-temperature channel in the lower temperature region. The contribution of the lowtemperature reaction channel to the overall rate constant is then obtained by subtracting the value of this contribution from the rate constants measured below 300 K. These values are plotted vs the inverse temperature in Figure 5 and are listed in Table 11. A weighted linear least-squares fit to these values for the lowtemperature channel gives the expression k&.f+H2 =
5.99?/,9,8 x
exp[(6.12
* 1.93)/RT]
Cm3*S-I
The extrapolation of this equation to temperatures above 300 K provides an estimate of the contribution of the addition channel to the overall rate constant. This was found to be less than 5% of the measured total rate constant kCH+H, at 4 Torr total pressure.
Discussion The present results are consistent with the reaction mechanism proposed by Berman and Lin.3 The observed pressure dependence is in accord with the collisional stabilization of the CH3' intermediate (reaction 1b). The broadening factor F, determined in this work, 0.85 f 0.10, is in excellent agreement with the value of 0.8 1 f 0.13 calculated by a method developed by Troe and co-~orkers.~** In the calculation of F,,the vibrational frequencies (7) Luther, K.;Troe, J. Symp. ( I n r . ) Combusr., [Proc.],17th 1979,534.
CH + H2 Reaction
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2393
for the CH3adduct given by Amano and Bernath9 and Yamada and co-workersI0 were used. By comparison with the work of Berman and Lin,) who obtained at 100 Torr total pressure an Arrhenius diagram with a minimum at 400 K, the minimum measured at 4 Torr total pressure is shifted toward lower temperatures, indicating that under our experimental conditions the abstraction channel l a is the dominant reaction path above 300 K whereas the addition channel 1b becomes more important below 300 K. The Arrhenius expressions obtained in the present work show that the rate constants for the abstraction channel were measured without any significant influence from the addition channel. The values obtained for the activation energies and the A factors in the present work can be compared with those from Berman and Lin' and Zabarnick and co-workers," both of whom investigated the reaction at 100 Torr total pressure. For the temperature range 150-300 K Berman and Lin3 reported a negative activation energy of -(4.36 f 0.36) kEmol-' and an A factor of (2.37 f 0.43) X c m 3 d . By subtracting the contribution of this low-temperature component from the overall rate constants in the temperature range above 400 K, they obtained an activation energy of 16.33 f 5.86 kbmol-' and an A factor of 3.6?i,:.5 X c m 3 d for the abstraction channel. Later work by Zabarnick and co-workers" in the temperature range 372-675 K yielded an activation energy of 14.63 f 0.50 kJ-mol-' and an A factor of (2.38 f 0.31) X cm3.s-'. These values were obtained by using the Arrhenius expression for the addition channel of Berman and Lin3 for the correction of the overall rate constants. The activation energies for both reaction channels and the A factor for the abstraction channel obtained in the present work are in good agreement with the literature values. However, the A factor for the addition channel from the present work is significantly smaller than the value of Berman and Lin3 which can be explained by the different total pressures employed in both studies. In addition to our experimental work, a series of calculations were carried out in order to test the experimental results. Rate constants were calculated by using a RRKM-transition-statetheory (TST) model which was developed by Berman and Lin'* for the C H N2 reaction. Briefly, the model is based on the RRKM theory to describe the unimolecular dissociation of the activated CH3* complex whereas the collisional stabilization of the adduct is described by the collisional efficiency pCaccording to a treatment by Tree.* From the proposed reaction mechanism the bimolecular rate constant can be expressed as a function of the reaction probabilities k, and k,' for the decomposition of the CH3' adduct, the rate constant w for the stabilization of the adduct and the sum of vibrational states of the transition state of the entrance channel at energy E+, E:P(E+), and the density of vibrational states of the adduct at energy E, N ( E ) , as follows:
+
~ C H + H=~
exp(-E+/RT) dE+ (I) In this equation E describes the energy of the vibrationally excited CH3' adduct and ?I the energy difference between the transition state of the entrance channel and the CH3* adduct. The rate constants were calculated for a given temperature and pressure by integrating eq I between E+ = 0 and E+ = 6 . 3 kEmol-' in intervals of 0.01 kJ.mo1-' mole, using the molecular parameters ( 8 ) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 161. (9) Amano, T.;Bernath, P. F. J . Chem. Phys. 1982. 77, 5284. (IO) Yamada, C.; Hirota, E.; Kawaguchi, K. J. Chem. Phys. 1981, 75, 5256. (1 1) Zabarnick, S.;Fleming, J. W.; Lin, M. C. J . Chem. Phys. 1986.85, 4373. (12) Berman. M. R.: Lin. M. C. J . Phvs. Chem. 1983. 87. 3933. (13) Butler, J. E.; G&s, L.P.; Lin, M.
