J. Phys. Chem. 1993,97, 12789-12792
12789
Temperature Dependence of the Rate of Reaction of C2H with H2 S. K. Farhat, C. L. Morter, and Graham P. Glass' Chemistry Department and Rice Quantum Institute, Rice University, Houston, Texas 77251 Received: July 26, 1993; In Final Form: September 27, 1993.
The rates of reaction of C2H with H2 and C2H2 have been measured over the temperature range 295-854 K. The C2H radical was produced by excimer laser photolysis of C2H2 at 193 nm, and its transient absorption was monitored throughout the reaction by using a tunable infrared color-center laser. The temperature dependence of the rate constant for the reaction with H2 exhibited a non-Arrhenius form that could be well represented by the following expression: k = (9.44 f 0.24) X 10-14P9exp(-1003 f 20/T) cm3 molecule-' s-l. The rate constant for the reaction with C2H2 - - disDlaved no definite temperature dependence. It was measured as (1.6 k 0.3) X 10-lo cm3 molecule-' s-l.
Introduction Theethynyl radical, C2H, plays an important role in combustion processes. It is a dominant chain carrier in the pyrolysis of acetylene at temperatures in excess of 1800 K1,and has been proposed as both a precursor2 and an aid to the reactivation of stable polycyclic molecules3 in the sequence of reactions that leads to soot formation in rich hydrocarbon flames. It has also been found to be one of the more abundant species in interstellar space4and has been detected in the atmospheres of several of the outer planets.Jv6 High-temperature rate measurements on the reaction between CzH and molecular hydrogen are crucial to a critical evaluation of the mechanism of acetylene pyr0lysis,1.~which, of course, is an essential part of any more general hydrocarbon combustion mechanism. Since C2H formation in such systems occurs primarily via thereverseof reaction 1 and since no experimental measurements of reaction -1 exist, it is usual, when modeling either acetylenepyrolysis or combustion, to estimate the rate of reaction -1 from the equilibrium constant Kl, and the rate constant, kl, for the forward reaction. There have been several previous measurements of the roomtemperature rate constant for reaction 1.&l3 Substantial agreement exists between the values obtained in the four most recent studies (4.8,IO 4.4,11 7.1,12 and 5.113 X 1613cm3 molecule-' s-1). However, all of these values are a factor of 3 higher than those reported by Lange and Wagner8and by Laufer and BassagLange and Wagner produced C2H by microwavedischarge of a mixture of bromoacetylene and helium in a fast discharge flow apparatus. Because mixing was judged to be incomplete in their observation zone, their measured rate coefficient was reported as only a lower bound to the true rate constant. Laufer and Bass estimated kl by measuring the effect of added H2 on the rate of butadiyne production, which was itself produced by the reaction of ethynyl with acetylene, which was used as a precursor of C2H. Therefore, they actually determined the ratio of kl to k2, the rate constant for reaction of CZHwith acetylene. When their ratio is combined with an average of more recently measured values for k2,12-15kl is calculated as 6.8 X 10-13 cm3 moleculcl, a value well within the range of the other measurements. The only direct experimental investigation13 of the reaction between CZHand H2 at temperatures in excess of 300 K suffers ~
~~
~
~~
'Abstract published in Aduunce ACS Absfrucfs, November 1, 1993.
0022-365419312097-12789$04.00/0
from twolimitations: (1) only a limited temperature range (298438 K) was investigated and (2) no direct measurements were made in as much as only the ratio of kl to k2 was determined. At combustion temperatures, the only information concerning the rate of reaction 1 comes from a TST calculation by Harding etal.,16whichutilizedabinitiomethods(POL-CI) for determining the properties of the potential energy surface in the saddle point region. The rate of reaction 2 has been measured by a numbe+8-10.12-15 of different investigators at temperatures ranging from 170 to 2177 K. Substantial agreement exists in the more recently published work regarding both the magnitude of the rateconstant and its lackof significanttemperature dependence. In the present study, we report direct measurements at temperatures between 295 and 854 K. No previous measurements have been made over a significant portion of this range. In addition, the greatest experimental uncertainties in the earlier measurements exist at temperatures in excess of 440 K.
Experimental Technique The experimental apparatus, the arrangement of the infrared optics, and the diagnostic measurements nectssary to monitor the operation of the color-center laser have been described previ0usly;1~ therefore, only a brief description will be given here. The infrared absorption cell is a standard multipass ("White") cell with a mirror spacing of 2 m. The UV photolysis beam enters the cell through a window just below the "D" mirrors and rises as it traverses the cell until it strikes a beam block just above the row of infrared spots on the notched mirror. The ArFexcimer photolysis beam and the color-centerinfrared probe beams overlap over approximately the central 30 cm of the cell. For measurements requiring elevated temperatures, the middle portion of the 54 mm i.d. multipasscell was heated with a 1 m long tube furnace. Due to the slant of the photolysis beam, the region probed lies entirely within the oven. The temperature variation within this region was measured with a thermocouple probe as less than 5 K. The ethynyl radical was produced by 193-nm photolysis of acetylene, which was purified prior to its introduction into the photolysis cell by passing it through an activated charcoal filter (Matheson Model 454). The photolysis laser was operated with a pulse energy of approximately 70 mJ and at a repetition rate of 1 Hz. Since the absorption cross section of CzHz at 193 nm is 1.35 X 10-19 cm2.18 with a quantum yield of approximately 0.26 for production of C2H,18J9the concentration of CIH can be calculated to be no more than 1.4 X loL2cm-3 when using the highest acetylene pressures employed ( I 7 mTorr) in experiments 0 1993 American Chemical Society
Farhat et al.
12790 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993
designed to measure k l . In such experiments, less than 2% of the incident UV laser power was absorbed within the entire photolysis cell, and only 1% of the acetylene was decomposed by each laser pulse. With typical linear flow rates of 50 cm/s, the volume in the overlap region was completely replaced between excimer laser pulses. The concentration of C2H was monitored by measuring the absorption of the Q11(9) line of the 3600-cm-l band of the A-X transition at 3593.684 cm-1. To observe the time decay of the radical concentration, the laser was locked to the peak of the absorption line, and the transient signal was averaged over 40 excimer flashes. Reaction mixture contained 4-140 mTorr of C2H2, 18 Torr of He, and 0-7 Torr of H2. The helium was added to ensure thermal equilibrium and to moderate the temperature rise following photolysis. In a previous study,IO SF6was added to ensure rapid vibrational relaxation of the C2H, but it was omitted from this study because it was found to have no effect on the measured ground-state decay rates.10 Gases were obtained commercially and, with the exception of C2H2, were used without further purification. The specified purities of these commercial gases areas follows: He (99.995%), H2 (99.9995%), and C2H2 (99%). All flow rates were measured using calibrated MKS flow meters. Partial pressures for individual components were calculated from the relative flow rate and the measured total pressure.
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Because of improvements to the apparatus and the installation of a "White" cell, it was possible to monitor C2H decays using significantly lower pressures of precursor then were used in our earlier room-temperature studies.I0 However, even at the lowest pressure used (4 mTorr), reaction of C2H with acetylene was rapid, and it was necessary to correct each measored decay for the contribution to the overall reaction from the precursor. In order to do this, the rate constant for the reaction of C2H with C2H2 was first measured a t each of the four temperatures investigated. Absorption-time traces, similar to that shown in Figure 1, were recorded for a number of C2H2/He mixtures. All such traces were found to exhibit single exponential decays, and decay constants were estimated by fitting all points between 80% and 10% of the maximum signal size, weighting each point according to its magnitude. Since experiments were performed under pseudo first-order conditions with [ C ~ H Z>> ] [ C ~ H Zby ] a factor of at least 400, [C~HZ] remains essentially constant, and the rate equation for reaction 2 integrates to [C,HI, = [C,HlO exp(-ko,t)
(3)
with
ko, = k,[C,H21 (4) Figure 2 shows a plot of kob vs [C2H2] a t 854 K. Typically, measurements were taken over a time interval of approximately OS, with kob varying between 3 X 104 and 2.5 X 105 s-1. Table I lists values of k2 determined a t four different temperatures by linear least-squares fits of plots similar to that shown in Figure 2. The relative error in k2 was determined as 17%. This value was calculated from the accumulated uncertainties in the instruments used to measure pressure and flow rates, together with the uncertainty in the various least-square fits to the experimental data. In these particular experiments, the principal source of error resulted from difficulties in measuring the extremely low flow rates of acetylene that were used. Rate constants for reaction 1 were determined by adding varying partial pressures of H2 to mixtures containing 17 mTorr or less of acetylene. In the presence of H2, single exponential decays of C2H were again observed. In these mixtures, C2H reacts with
Figure 1. (a) Trace of C2H absorption vs time for a mixture containing 14.8 mTorr of CzH2 at 295 K. The residuals from the fitted curve are shown in part b.
+ C,H,
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(T = 854 K)
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40 60 80 100 120 140 C,H, Pressure (mtorr) Figure 2. Plot of kob vs [ C Z H ~atJ 854 K. kob is defined by eq 4 and has units of s-1. 20
TABLE I: Rate Constants for tbe CZH+ CZHZReaction 1/ T, 1P3K-I k l / 1PIo,cm3 s-l no. of measurements T, K 295 464 660 854
3.39 2.16 1.52 1.17
1.9 1.5 1.3 1.3
11 6 6 6
both C2H2and H2 according to reactions 1 and 2, and theobserved decay constant is given by
ko, = k,[H21 + k,[C,H,I
(5)
Figure 3 shows a plot of the "corrected" decay constant (k- = kob - kz[C,H,]) vs [Hz] a t 464 K, and Table I1 lists values of kl determined from such plots by using eq 5 . Since the amount of acetylene used was small and since it remained relatively constant from experiment to experiment, the calculated values for kl were not significantly affected (less than 2%) by the large estimated error in kz, and the relative error in kl was determined to be only 12%.
Reaction of C2H with H2
The Journal of Physical Chemistry, Vol. 97,No. 49, 1993 12791 C,H+H,
2.0 10;
0
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Figure 3. Plot of koDnvs [H2] at 464 K. k,, has units of s-1.
is defined in the text and
-Wagner 0 Koshi 0 Our Data m
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2 2.5 3 3.5 1 OOOIT Figure 4. Measured temperature dependence of kl. Koshi's data (ref 13) is represented by the open circles. The line represents the results of a TST calculation performed by Wagner.
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TABLE II: Rate Constants for the C2H + H2 Reaction T,K
1/T, 10-3 K-1
kl/lO-l2, cm3 s-I
no. of measurements
295 464 660 8 54
3.39 2.16 1.52 1.17
0.47 2.8 7.1 12.7
17 9 9 11
Discussion Because we observed the X(O,O,O) state directly, all rate constants reported in this paper are for reactions of the ground state of C2H. However, for the measurements to be valid, it is necessary that the upper state of the infrared transition be fully relaxed. Previous worklo has shown that, under the conditions of this study, relaxation of the C2H (X(O,O,l)) state occurs in approximately1 ps. Thus, completevibrational relaxation should have occurredbefore any ground-state measurementswere made. In addition, the measurements should not have been significantly influenced by reactions of C2H with any photolysis product, or any other radical formed from them, because the average time between collisions of such species can be roughly estimated as 1 ms, and our experiments lasted for no more than 50 p . Wall reactionsshould not have interferedwith our observations because the characteristic time for diffusion of C2H out of the probe beam was several milliseconds. The temperature dependence of the rate constant for reaction 1 is shown in Figure 4. The data can be fit reasonably well by a simple Arrhenius equation. However, it is better fit by the following equation: kl = (9.44 f 0.20) X 0.20) x 10-14P.9 exp(-1003 f 20/ T ) cm3molecule-' s-1, also shown in this figure are recent data by Koshi et a1.13and the results of a TST calculation. This calculation is based upon the original PES of Harding et a1.,16 with the classical barrier height reduced to 1.55 kcal/mol in order to fit the room-temperature data." Our measurements are in excellent agreement with those determined in previous room-temperature studies but exhibit a
slightly steeper temperature dependence than predicted by the TST study or measured by Koshi et al.13 However, the differences are not large. For example, at 438 K, the highest temperature explored by Koshi et al., our rate constant is only 25% greater than their value, a difference that is smaller than the combined error of the two studies. When comparing our data to the results of the transition-state calculation, it should be noted that the PES used in this calculation was determined in 1982, and that significant revisions have been made in the last two or three years to the standard enthalpy and entropy of the ethynyl radical. These revisions have arisen as a result of new measurements of the bond dissociation energy of acetylene2I and the frequency of the bending fundamental vibration of C Z H . ~It ~will be interesting to see whether the extreme non-Arrhenius behavior of the TST rate constant is reproduced when calculations are performed using the newer thermochemical data and a higher level of theory. At combustion temperatures, our measurements of kl extrapolate to values close to those predicted by the modified TST calculations16g2'Jand used in recent modeling studies.' When making an extrapolation to combustion temperatures it should be borne in mind that although the present measurements only cover the limited temperature range 295-854 K, they do cover a considerablespan of 1/ Tspace. One measure of the uncertainty introduced by the extrapolation can be obtained by comparing the value of the rate constant calculated at 2000 K by using the best fit to our experimental data (5.3 X 10-11cm3 molecule-' s-1) to that estimated by forcing a fit of our data to a simpleArrhenius expression. When this later procedurewas followed, an Arrhenius equationofthe form kl= 6.9 X 10-l1exp(-l480/T) wasobtained, which at 2000 K yielded a rate constant of 3.3 X 10-11 cm3 molecule-' s-1. Thorough discussions of the reaction of the ethynyl radical with acetylene have been provided by Shin and Michael14and by Pedersen et d . 1 5 These authors have summarizedall of the earlier measurements referenced herein and have concluded that the rate coefficientdisplays no definite temperature dependence. On the basis of their own work and other accumulated evidence, they have suggested that the reaction occursvia an addition mechanism to form a short-lived C4H3 complex which, under all of the conditions so far studied, dissociates prior to collision, overwhelmingly by CH bond fission, to form H and C4H2. These conclusionsare not affected by the work presented here. However this study does report data in the temperature range between 450 and 850 K that had not previously been investigated. In addition, the results tend to lend support to the earlier observation15 of a small negative temperature dependence of the rate coefficient. Acknowledgment. This work was supported by the Department of Energy under Grant DE-FG05-85ER 13439 and by the Robert A. Welch Foundation. C.L.M. wishes to thank the Robert A. Welch Foundation for a postdoctoral fellowship. References and Notes (1) Kiefer, J. H.; Von Drasek, W. A. Int. J . Chem. Klnet. 1990,22,747. (2) (a) Homann, K. H.; Wagner, H. G.Proc. R. Soc. London 1967, A307,141. (b) Warnartz, J. A,; Bockham, H.; Moser, A,; Wenz, H. W. 19th International Symposium on Combustion; The Combustion Institute: Pittsburgh, 1982; p 197. (3) Frenklach, M.; Clary, D. C.; Gardiner, W. C., Jr.; Stein, S.E. 21st International Svmoosium on Combustion; The Combustion Institute: Pittsburgh, 1986; p-lOh7. (4) Tucker, K. D.; Kutner, M. L.; Thaddeus, P. Astrophys. J . 1974, L115, 193. (5) Atreya, S. K.; Romani, R. N. Recent Adoances in Planetary Meteorology, Hunt, G . E., Ed.; Cambridge Uniuersity Press: New York, 1985; p 17. (6) Strobel, D. F. Planet. Space Sci. 1982, 30, 839. (7) Kern, R. D.; Xie, K.; Chen, H.; Kiefer, J. H. 23rd Inremarional Symposium on Combustion; The Combustion Institute: Pittsburgh, 1990; p 69. (8) Lange, W.; Wagner, H. G. Ber. Bunsen.-Ges.Phys. Chem. 1975,79, 165.
12792 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993 (9) Laufer, A. H.; Bass, A. M. J. Phys. Chcm. 1979,83, 310.
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(16) Harding, L. B.; Schatz, G. C.; Chiles, R.A.J . Chrm. Phys. 1982, 76, 5172. Glass, G. P. J. Phys. Chem. 1987, 91, 5740. (17) Morter, C. L.; Domingo, C.; Farhat, S.K.; Cartwright, E.; Glass,0. (11) Lander, D. R.;Unfried, K. G.; Glass, G. P.; Curl, R. F. J . Phys. P.; Curl, R. F. Chrm. Phys. Lett. 1992,195, 316. Chem. 1990, 94, 7759. (18) Satyapel, S.;Bersohn, R.J. Phys. Chcm. 1991,95, 8004. (12) Koshi, M.;Nishida, N.;Matsui, H. J. Phys. Chem. 1992,96, 5875. (19) Selri, K.; Okabe, H.J. Phys. Chrm. 1993,97, 5284. (13) Koshi.M.:Fukuda.K.:Kamiva,K.;Matsui,H.J.Phys.Chcm.1992, (20) Wagner, A. F. Private communication. 96,'9839. . (21) See: Balko, B. A.; Zhang, J.; Let, Y. T. J. Chcm. Phys. 1991,91, (14) Shin, K. S.;Michael, J. V. J. Phys. Chem. 1992, 95, 5875. 7958 and references therein. (15) Pedersen, J. 0.P.;Opansky, B. J.; Leone, S . R.J. Phys. Chcm. 1993, 97, 6822. (22) Kannamori, H.; Hirota, E. 1. Chrm. Phys. 1989,89, 3962.
(IO) Stephens, J. W.; Hall, J. L.; Solka, H.;Yan, W.-B.; Curl, R. F.;
