J. Phys. Chem. 1986, 90, 5941-5945 effect at the secondary-reaction site in n-butane and have showed it to be very similar to the corresponding isotope effect found in our earlier study of the reaction OH propane products.
+
-
Acknowledgment. This research was supported by the Division of Chemical Sciences, the Office of Basic Energy Sciences, the
5941
U.S. Department of Energy. We thank Dr. R. Atkinson for communicating his work prior to its publication. Registry No. H2, 1333-74-0; D2,7782-39-0; N20, 10024-97-2;0, 17778-80-2; H20, 7732-18-5;hydroxyl, 3352-57-6;n-butane, 106-97-8; n-butane-d,o,7582-04-9.
-
Rate Constant for the O('P) 4- CH, OH 4- CH, Reaction Obtained by the Flash Photolysis-shock Tube Technique over the Temperature Range 763 5 T I1755 K J. W. Sutherland,* J. V. Michael, and R. B. Klemm Department of Applied Science, Brookhaven National Laboratory, Upton, New York I 1 973 (Received: February 10, 1986; In Final Form: May 7, 1986)
The rate constant for the reaction of O(jP) with methane was measured over the temperature range 763 I T I 1755 K by the flash photolysis-shock tube technique. The results, k (cm3 molecule-' s-') = 9.2 X 10-'9p.40exp(-2838/T), agree with those of previous workers who employed different experimental methods and thus endorse the flash photolysisshock tube technique as an important method for measuring rate constants in the temperature range -800 K I T I 2000 K. A recommended rate expression for the reaction of O('P) with CH4, k(cm3 molecule-' s-I) = 1.15 X 10-15T'.s6exp(-4270/T) over the temperature range 400 K I T I 2250 K, was derived from an evaluation of the combined results of the present study and those of selected previous investigations.
Introduction The flash photolysis-shock tube technique (FP-ST) is a uniquely powerful method for measuring directly the rate constants of elementary reactions at high temperature^.'-^ It is necessary, of course, that the temperature, pressure, and density of the gas in the reaction zone (i.e., the stagnant gas behind the reflected shock wave) can be confidently deduced from the initial values of temperature and pressure and the incident Mach number. It is well-known that the outward development of the boundary layer from the wall into the flowing gas behind an incident shock wave can result in appreciable errors in the values of these thermodynamic properties when calculated with ideal shock Two approaches were used to correct for such nonideal behavior in the (1) Ernst, J.; Wagner, H. Gg.; Zellner, R. Ber. Bunsen-Ges. Phys. Chem. 1978,82, 409. Niemitz, K. J.; Wagner, H. Gg.; Zellner, R. Z . Phys. Chem. NF 1981, 124, 155. (2) (a) Michael, J. V.;Sutherland, J. W.; Klemm, R. B. Int. J . Chem. Kinet. 1985, 17, 315. (b) Michael, J. V.;Sutherland, J. W.; Klemm, R. B. J. Phys. Chem. 1986, 90, 497. (3) Maki, R. G.; Michael, J. V.;Sutherland, J. W. J. Phys. Chem. 1985, 89, 4815. (4) Bradley, J. N. Shock Waves in Chemistry and Physics; Wiley: New York, 1962.
(5) Mirels, H. Mod. Dev. Shock Tube Res., Proc. Int. Shock Tube Symp., 8th 1971, paper 6; Phys. Fluids 1966,9, 1907; Am. Inst. Aeronaut. Astronaut. J . 1964, 2,84; Phys. Fluids 1963,6, 1201 and references and reports (particularly those from NACA) therein. (6) Strehlow, R. A.; Belford, R. L. Aeronautical and Astronautical Engineering Department Technical Report No. 69- 1, University of Illinois, Urbana, IL, 1969. Belford, R. L.; Strehlow, R. A. Annu. Rev. Phys. Chem. 1969, 20, 247. (7) Bertin, J. J.; Ehrhardt, E. S.;Gardiner, W. C., Jr.; Tanzawa, T. Mod. Deu. Shock Tube Res., Proc. Int. Shock Tube Symp., 10th 1975, 595. (8) Strehlow, R. A.; Cohen, A. J . Chem. Phys. 1959, 30, 257. (9) Skinner, G. B. J. Chem. Phys. 1959, 31, 268. Skinner, G. B.; Sweet, R. C.; Davis, S. K. J . Phys. Chem. 1971,75, 1. Skinner, G. B.; Rogers, D.; Patel, K. B. Int. J. Chem. Kinet. 1981, 13, 481. Bernfeld, D.; Skinner, G. B. J. Phys. Chem. 1983,87, 3732. (10) Brabbs, T. A.; Zlatarich, S. A.; Belles, F. A. J . Chem. Phys. 1960, 33, 307. Belles, F. A.; Brabbs, T. A. Symp. (Int.) Combust. [Proc.],13th 1971, 165. (11) (a) Gardiner, W. C., Jr.; Kistiakowsky, G. B. J . Chem. Phys. 1961, 34, 1080. (b) Tsuchiya, S.; Kuratani, K. J . Chem. Phys. 1965, 42, 2986. (12) Dyner, H. B. Phys. Fluids 1966, 9, 879. (13) Strehlow, R. A.; Case, C. T. J. Chem. Phys. 1961, 35, 1506. (14) Tschuikow-Roux, E.; Simmie, J. M.; Quiring, W. J. Astronaut. Acta 1970, 15, 5 11. (15) Fujii, N.; Koshi, M.; Ando, H.; Asaba, T. Int. J. Chem. Kinet. 1979, 11, 285.
0022-3654/86/2090-5941$01.50/0
present shock tube:2J6 a theoretical method based on the wellknown boundary-layer theory of Mirelss and an experimental procedure in which the final reactant temperature is calculated with the adiabatic equation of state from experimental pressure measurements made at the observation distance from the end plate. Corrections were significant only for temperatures of less than 1400 K in the reflected shock regime. For temperatures 11400 K, ideal shock theory was adequate. A further test of the corrective procedures is to measure the kinetics of a reaction for which there is available a reliable data set that consists of results from several laboratories and one that extends over the experimentally accessible temperature range. The reaction chosen for such a study is17-21 O(3P)
+ CH4
-
OH + CH3
(1) This paper reports new measurements of k l ( T ) over the temperature range 763 I T I 1755 K by the FP-ST technique. The results are compared to those obtained previously by other A critical reevaluation of the rate constant for reaction 1 is made and a recommended expression for k,( T ) is derived.
Experimental Section The FP-ST apparatus has been fully described elsewhere* and only those modifications that are specific to the present study will be given. In the present FP-ST apparatus, a gas sample containing an appropriate absorber, in this instance NO, is shock-heated to high temperatures in the shock tube and is then flash photolyzed in the reflected wave regime to produce measurable amounts of atoms. The change in concentration of these atoms is monitored by the sensitive technique of atomic resonance absorption over time periods of up to about 2 ms following the flash. The pro(16) Michael. J. V.:Sutherland. J. w. Int. J. Chem. Kinet. 1986.18.409. (17) (a) Westenberg, A. A.; deHaas, N. J. Chem. Phys. 1%7,46; 490; (b) 1969, 50, 2512. (18) Brabbs, T. A.; Brokaw, R. S. Symp. (Int.) Combusr. [Proc.],15th 1975. 893. (19) Roth, P.; Just, Th. Ber. Bunsen-Ges. Phys. Chem. 1977, 81, 572. (20) (a) Felder, W.; Fontijn, A. Chem. Phys. Lett. 1979, 67, 53. (b) Aerochem TN-227, Aerochem Research Laboratories Inc., Princeton, NJ, 1982. (c) Fontijn, A. Symp. (Int.) Combust. [Proc.],18th 1981, 797. (d) Felder, W.; Fontijn, A., private communication. (21) Klemm, R. B.; Tanzawa, T.; Skolnik, E. G.; Michael, J. V. Symp. (Int.) Combust. [Proc.],18th 1981, 785. ~
0 1986 American Chemical Society
5942 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
cedure used for measuring H-atom concentrations has already been and, in this paper, the extension of the technique to studying the reactivity of O(3P) atoms is discussed. Oxygen atoms were produced by the flash photolysis of nitric oxide, which has been shown to generate O(3P) efficiently on irradiation in the vacuum ultravioletzz NO
+ hv
+
O(3P) + N
(2)
A sapphire window, placed in the path of the emission from the nitrogen-filled flash lamp, only allows light of X > 145 nm to enter the shock tube. The N atoms that are produced in either the 4S or zPstates react rapidly with the The mole fraction of resulting in [NO] of to 2.5 X N O ranged from 1.2 X -(l-2) X lOI5 molecules cm-3 in the reflected shock regime. Since the rate constant for the reaction of N atoms (either 4S or 2P) with NO is >3 X lo-" cm3 molecule-' s-I, the N atoms are 1 1 ps) in the elapsed converted rapidly to O(3P) atoms (tip time between initiation of the flash and before kinetic measurements can be made (- 150 ps). Hence, all the N atoms are converted to O(3P) atoms prior to making any kinetic measurements.2z The concentration of the 0 atoms is monitored by resonance a b s o r p t i o r ~ . ~The ~ resonance lamp is a microwave discharge in a flowing mixture of 0.1% Oz in H e maintained at a pressure of 1.7 Torr. The operating power level of the lamp is 40 W. A vacuum UV CaFz window in the optical path transmits the resonance triplet lines centered at 130.4nm but effectively blocks the lower lying resonance line emissions from H and/or N atoms. The photomultiplier housing is purged by a steady flow of dry N2. Because extraneous radiation at nonresonant wavelengths is always present, an 0-atom filterz4 was placed in front of the resonance lamp. This filter, which is simply a microwave discharge in a flow system that operates at 0.2 Torr of 02,allows the fraction of the incident intensity that is 0-atom resonance radiation to be measured routinely. The photometer system used here was the same as the one that has been extensively studied by Skinner and co-worker~.~~ In the present experiments the transmittance ranged the corfrom 0.85 to 0.99. From the known curve of responding range in the concentration of 0 atoms is 1.0 X 10" I [O] I2.0X 10l2 atoms ~ m - ~This . level of sensitivity is less than that for H atoms2 (8 X 1O'O I[HI I 2 X 1Ol2atoms ~ m - ~ ) , as was expected since the 0-atom source is self-reversed to some degree. It is important to emphasize that it was not necessary to know the absolute concentrations of O(3P) in this study. The methane concentration was always maintained in large excess ( [CH4]/[O] > 100)and hence the decay of 0 atoms followed pseudc-first-order kinetics. Since the loss of atomic oxygen occurs only by reaction 1 and diffusion into or out of the observation zone is negligible2
-
-
and For 0-atom absorbance values of less than -0.15, [O], was directly proportional to the absorbance, and hence it follows that In [ABS], = -kobdt c (111)
+
The experimental first-order rate constants, kobsd,were obtained from linear least-squares fits to eq 111. The Mach number of each incident shock wave was calculated from incident velocity measurements. The temperature, density, and pressure in the reflected shock regime were then calculated from ideal shock theory. Corrections for nonideal shock behavior, due to boundary-layer effects in the present shock tube, were made by a method based on experimentally measured pressures and the (22) (a) Stuhl, F.;Niki, H.Chem. Phys. Len. 1970, 7 , 197 and references therein. (b) Stuhl, F.; Niki, H. J. Chem. Phys. 1971, 55, 3943. (23) Pamidimukkala, K. M.; Lifshitz, A,; Skinner, G. B.; Wood, D. R. J . Chem. Phys. 1981, 75, 1116. (24) Lee, J. H.; Michael, J. V.;Payne, W. A,; Stief, L. J. J. Chem. Phys.
1978,69, 3069.
Sutherland et al. adiabatic equation of state. This procedure has been fully described elsewhere.16 Except for NO, all the gases employed were obtained from M. G. Industries. He, (Scientific Grade, 99.9999% stated purity) was used both in the driver section of the shock tube and in the resonance lamp. The Ar was also Scientific Grade (99.9999% stated purity) as was the Oz (99.999% stated purity) used in the operation of the 0-atom filter. The CH4 (Scientific Grade, 99.995% stated purity) was thoroughly outgassed at -196 "C prior to preparation of the gas mixtures. Nitric oxide (Matheson Co., 99.0% stated purity) was outgassed and distilled under vacuum at -175 "C, the middle third fraction being retained.
Results A major advantage of the resonance absorption technique is that its high sensitivity permits the use of concentrations that are so low that secondary reactions can be neglected. The possibility that secondary reactions might complicate the measurement of the rate constant of the 0 + CH4 reaction in the present experiment was investigated by simulating the 0-atom decay in the following complex system:
O(3P)
+ CH4 +
-
o(3~)OH
+ CH, O(3P) + C H 3 OH
H2O
-
-+
+ CH3 oz+ H
OH
+ CH3
HCHO
+H
(1) (3)
(4)
(5)
The rate constants were obtained from a recent evaluationz5and the initial concentrations of 0 atoms were taken to be within the range of the experimental values of [O], as estimated from initial values of absorbance and the curve of growth in a lamp of similar design.23 For the worst case with [O], = 2.0 X 1OIz atoms cm-3 cm3 molecule-I s-I, the simulation gave and with k5 N 1.0 X a pseudo-first-order rate constant, as determined from analyzing the simulated data according to first-order kinetics, that was only 10% higher than that obtained when all secondary reactions were neglected. Under most experimental conditions these reactions were found to perturb the measurement of k l (7') by much less than 10%. N o evidence of kinetic complications was apparent in the first-order plots of the experimental data. First-order rate constants were obtained over two to three half-lives and were found to be independent of [CH,] (factor of 7, viz. Table I) and flash energy, i.e., initial 0-atom concentrations. The experimental results are listed in Table I. The errors in the individual rate constants listed in Table I are at the one standard deviation level as determined from the least-squares line. However, the overall errors, estimated from the reproducibility of kl(7') values, range from 8% to 20%. This is easily seen by simply averaging the rate constant values listed in Table I over specific temperature intervals of about fl5 K.
-
Discussion There have been five extensive investigations of the kinetics of reaction 1: two were carried out by the discharge flow technione by the high-temperature flash photolysis-resonance fluorescence technique,20and two by shock tube procedures that employed kinetic modeling to analyze their data.'*J9 The results from these experiments are summarized in Table I1 along with the temperature range over which the derived Arrhenius rate expressions are valid; they are among the most extensive for any bimolecular reaction and thus provide an excellent data base with which to examine the procedures previously adopted in this laboratory to correct for nonideal shock behavior in the present apparatus.2.'6 The data set, with which our experimental results are to be compared, was constructed as follows for the temperature range 400-2250 K. Rate constants were generated from the (25) Tsang, W.; Hampson, R. F. "Chemical Kinetic Data Base for CH4 Combustion", NBS IR 842913, National Bureau of Standards, U S . Department of Commerce, 1985.
Rate Constant for the O(3P)
+ CH4 Reaction
TABLE I: Rate Data for the Reaction 0 + CHI Pl
OH + C H 3 kl/(
P C d
/
Torr
-
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5943
Ms"**
kobda/s-l
(1015 molecule cm-')
T5/ cm3 molecule-' K
S-1)
PCH,/
PI/ Torr
Ms",~
koMa/s-'
(1015 molecule cm-3)
kl/( T 5 / cm3 molecule" K S-I)
~~
A. XCH, = 1.4788 X 4526 f 54 2.578 3322 f 51 2.524 2.523 3707 f 60 2603 f 22 2.403 1471 f 20 2.164 862 f 26 2.058 1002 f 13 2.193
1227 1130 1146 1065 964 904 948
1.76 1.32 1.47 1.08 0.68 0.42 0.46
B. XcH, 7.675 X lo4 1.325 2.179 f d.006 3441 f 44 2.035 f 0.010 1929 f 31 1.255 1.954 f 0.011 1066 f 6 1.191 1.424 2.231 f 0.018 4187 f 92 2.120 f 0.007 2748 f 33 1.293 1.443 2.369 f 0.019 5595 f 123 1.484 2.366 f 0.010 6221 f 86 1.563 2.494 f 0.029 7734 f 204 1.622 2.627 f 0.017 13212 f 624
1249 1114 1038 1295 1184 1424 1420 1554 1699
2.60 1.54 0.90 2.94 2.13 3.88 4.19 4.95 8.15
15.28 15.04 15.35 15.13 15.51 15.30 15.31 15.16 15.54 15.28 15.40 15.86 15.58 15.10 15.60 15.12 15.05 15.18 15.39 15.16 15.30
C. XCH, = 1.0080 X 10" 2.394 2.050 f 0.020 3160 f 60 2.505 2.172 f 0.011 5654 f 78 2.488 2.116 f 0.009 4680 f 111 2.398 2.072 f 0.007 3502 f 76 2.136 1.843 f 0.011 1426 f 52 2.315 1.988 f 0.007 3002 f 80 2.430 2.062 f 0.025 3484 f 73 2.484 2.131 f 0.020 5426 f 130 2.653 2.216 f 0.009 7038 f 206 2.199 f 0.024 6281 f 149 2.602 2.507 2.104 f 0.010 4702 f 104 2.772 2.259 f 0.009 7414 f 170 2.759 2.291 f 0.012 9449 f 169 2.802 2.416 f 0.014 12865 f 479 2.288 1.932 f 0.010 2128 f 40 2.229 1.940 f 0.011 1974 f 54 2.155 1.895 f 0.014 2005 f 30 2.127 1.863 f 0.008 1812 f 63 2.379 2.020 f 0.013 3013 f 50 2.249 1.950 f 0.013 2364 f 108 2.156 1.871 f 0.009 1555 f 28
1132 1247 1193 1152 949 1076 1135 1203 1283 1260 1170 1318 1350 1478 1023 1030 990 963 1101 1038 970
1.32 2.26 1.88 1.46 0.67 1.30 1.44 2.18 2.65 2.41 1.88 2.68 3.43 4.59 0.93 0.89 0.93 0.85 1.27 1.05 0.72
15.03 15.19 15.18 15.04 15.28 15.38 15.20 15.22 15.83 15.09 15.21 15.76 15.24 15.53 15.88 15.60 15.08
2.347 f 0.007 2.471 f 0.028 2.502 f 0.008 2.593 f 0.016 2.045 f 0.018 1.951 & 0.013 2.119 f 0.006 2.186 f 0.015 2.262 f 0.017 2.348 f 0.030 2.321 f 0.014 2.213 f 0.010 2.439 f 0.014 2.463 f 0.026 2.660 f 0.031 2.492 f 0.035 2.506 f 0.025
D. XCHa = 4.907 X lo4 1.324 4696 f 90 6719 f 93 1.398 1.410 7619 f 174 1.436 10838 f 143 2135 f 61 1.166 1.111 1294 f 26 1.205 2333 f 33 1.246 2952 f 45 3771 f 39 1.340 1.321 6381 f 119 1.318 5016 f 71 1.310 3685 f 105 1.383 7642 f 118 1.416 10403 f 141 1.533 18701 f 260 1.435 12120 f 139 1.394 10893 f 158
1407 1536 1569 1668 1123 1039 1192 1256 1330 1417 1390 1278 1507 1537 1755 1568 1584
3.55 4.81 5.40 7.55 1.83 1.16 1.94 2.37 2.82 4.83 3.81 2.81 5.53 7.35 12.20 8.44 7.82
10.45 10.78 10.68 10.69 10.37 10.38 10.65
2.161 f 0.013 2.057 f 0.006 2.074 f 0.001 1.985 i 0.012 1.8K8 f 0.006 1.797 f 0.007 1.849 f 0.010
10.30 10.49 10.40 10.78 10.27 10.27 10.57 10.66 10.64
Errors are one standard deviation.
15.65 15.20 15.19 15.28 15.68 15.70 15.06 15.19 15.43 15.10 15.44
E. XcH, = 2.8063 X lo4 2.574 f 0.022 91 12 f 66 0.844 2.552 f 0.030 6579 f 61 0.817 2.575 f 0.011 10133 f 180 0.825 2.477 f 0.010 4653 f 76 0.806 2.533 f 0.008 6272 f 67 0.834 2.404 f 0.025 4711 f 52 0.802 0.747 2.315 f 0.020 3392 f 48 2.229 f 0.011 2006 f 21 0.728 0.792 2.397 f 0.024 3623 f 41 2.143 f 0.016 1852 f 45 0.695 1.991 f 0.007 866 f 30 0.658
15.50 15.86 15.48 15.15 15.84 15.45 15.38 15.34 15.81 15.24 15.40 15.38 15.22
1.815 f 0.016 1.759 f 0.012 1.868 f 0.011 1.953 f 0.007 1.861 f 0.010 1.717 f 0.012 2.032 f 0.013 1.889 f 0.014 1.992 f 0.010 2.098 f 0.014 1.959 f 0.012 2.033 f 0.019 2.105 f 0.008
15.53 15.62 15.57 15.51 15.84 15.11 15.41 15.74 15.26
2.020 f 0.010 1.918 f 0.007 1.995 f 0.025 2.099 f 0.016 1.937 f 0.006 1.801 f 0.011 1.737 f 0.015 1.614 f 0.008 1.742 f 0.009
30.31 30.30 30.34 30.53 30.78 30.86 30.71 30.54 30.24 30.24 30.67 30.54 30.14 30.67 30.18 30.58 30.82 30.52 30.60 30.53 30.89 30.12 30.61 30.76 30.74 30.48
1.891 f 0.007 1.988 f 0.013 1.993 f 0.011 2.081 f 0.021 2.126 f 0.01 1 2.143 f 0.007 2.401 f 0.018 2.307 f 0.022 2.366 0.018 2.400 f 0.022 2.391 f 0.015
1658 1628 1648 1542 1616 1475 1379 1293 1458 1211 1067
10.80 8.05 12.28 5.78 7.52 5.87 4.54 2.76 4.58 2.66 1.32
F. XCH, = 1.9813 X 1479 f 71 4.139 1537 f 40 4.043 2515 f 57 4.307 3697 f 50 4.470 2330 f 40 4.401 697 f 14 3.843 4948 f 59 4.752 2725 f 59 4.344 4434 f 57 4.759 7413 f 76 4.877 3914 f 64 4.576 5975 f 87 4.755 7802 f 245 4.888
920 877 96 1 1031 952 835 1100 975 1068 1161 1032 1101 1167
0.36 0.38 0.58 0.83 0.53 0.18 1.04 0.63 0.93 1.52 0.86 1.26 1.60
G. XcH, = 1.4788 X 4307 f 75 3.522 2603 f 37 3.331 2902 f 51 3.481 6407 f 73 3.670 3.419 2798 f 79 1416 f 24 2.970 1171 f 30 2.880 382 f 5 2.634 11 19 f 38 2.864
1101 1010 1078 1173 1027 911 859 763 863
1.22 0.78 0.84 1.75 0.82 0.48 0.41 0.15 0.39
H. Xc,, = 5.188 X lo4 1.988 f 0.007 2129 f 18 2.255 2.417 2.121 f 0.006 3890 f 63 2.426 2.126 f 0.015 4316 f 62 2.575 2.247 f 0.013 6473 f 66 2.605 2.264 f 0.007 8650 f 128 2.331 f 0.013 9301 f 78 2.680 2.370 f 0.013 14027 f 157 2.705 1.996 f 0.008 2503 f 20 2.275 1.937 0.010 2201 f 26 2.176 1.887 f 0.006 1890 f 16 2.108 1.821 f 0.008 1178 f 33 2.044 1.772 f 0.007 1022 f 35 1.963 1.826 f 0.006 1293 f 41 2.016 1.910 f 0.009 2128 f 27 2.170 1.946 f 0.003 2266 f 27 2.183
1036 1152 1156 1268 1288 1352 1390 1046 996 954 90 1 862 905 973 1003
0.94 1.61 1.78 2.52 3.32 3.47 5.19 1.10 1.01 0.90 0.58 0.52 0.64 0.98 1.04
I. XCH, = 2.400 X lo4 953 f 10 0.985 1363 f 39 1.057 1174 f 10 1.057 2344 f 40 1.111 2460 f 36 1.133 2402 f 47 1.148 5570 f 82 1.244 3909 f 54 1.223 5457 80 1.256 1.270 5831 f 109 5796 f 92 1.255
96 1 1039 1036 1112 1152 1176 1416 1325 1382 1415 1407
0.97 1.29 1.11 2.11 2.17 2.09 4.48 3.20 4.35 4.59 4.62
*
*
Ms is the measured Mach number of the incident shock wave.
expressions shown in Table I1 for temperature intervals corresponding to A(l/T) values of 3.0 X l V 5 K-' over the temperature range covered by each investigation except for the study of Westenberg and deHaas," for which the interval chosen was 1.O X lo4 K-'. All the points (total of 138) were then combined to
obtain one data set that was fitted by the least-squares method to a three-parameter equation to give k , ( T ) = 2.67 X 10-16T1.7s exp(-4117/T) (IV) Equation IV holds over-the temperature range 400-2250 K and
Sutherland et al.
5944 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 TABLE II: Sources of Data Base for the Reaction O(3P) + CHI OH + CH, source
Arrhenius expression'
k , ( ~=) 3.3
ref 17; temp range: 400-900 K ref 18; temp range: 1300-2000 K ref 19; temp range: 1500-2230 K ref 20; temp range: 420-1670 K ref 21; temp range: 474-1 156 K
X'IO-11
exp(-4170/~)
k , ( T ) = 3.15 X 10-'oexp(-5900/T)
k,(n= 6.8 X
exp(-7030/T)
k,(o= 8.7 X 10-19T249exp(-3566/T) k l ( T ) = 2.01
"Units for k l ( T ) are cm3 molecule-'
-
-
x
exp(-5435/T)
s-I
. I
O
4
0
c
-
0
. . , . . . . . " . . . . . .-~ .
.
. .
, ^ \
.
aata obtainea oy tne riasn pnotoiysis-snoclc tube metnoa; (0) aata obtained by the flash photolysis-resonance fluorescence (FP-RF)method; (0) data obtained by the discharge flow-resonance fluorescence (DF-RF)method.
than 8%, over the temperature range 400-2250 K, further corroborating the validity of the correction procedures adopted to correct for boundary-layer effects in the present shock tube. It can be argued that, because of the uncertainty in the temperature independence of the stoichiometric factor used to extract the rate constant from their experimental data, the results of Westenberg and deHaas" should be omitted from the data base along with those of Brabbs and Brokaw,I8 who also obtained their rate constants by an indirect method. When this was done, the three-parameter expressions eq IV and VI1 became
- I40
0.2
0.4
0.6
0.8
1.0
1.2
k , ( T ) = 7.06
X
10-16T1.63f0.10 exp[(-4214 f 7 8 ) / q
10' KIT
A In A = f0.76
Figure 1. Arrhenius plot of the rate data: ( e ) this data; (+) estimated experimental error; dashed line, fit to this data, eq VI; solid line, fit to previously reported data, eq IV.
is in good agreement with a recent independent evaluation by Hamp~on~~ k , ( T ) = 1.7 X lO-I5Tl5exp(-4330/T)
(VI
(stated temperature range, 300 5 T I 2000 K; given estimated error, f25%). Rate constants, when evaluated by eq IV and V agree within 9-14% over the entire temperature range. The experimental data, given in Table I, are plotted in Arrhenius form in Figure 1 along with the evaluation of previous experimental studies, eq IV. These new shock tube data were also analyzed by the least-squares method to obtain the following three-parameter fit:
k , ( T ) = 9.20
X
10-19T2~40f0~90 exp[(-2838 f 9 9 8 ) / q
(VI)
k , ( T ) = 3.16
X
10-1sT1.44*0.10 exp[(-4362 f 7 7 ) / q
(IX)
A In A = f0.74
Values for k,( r ) calculated from eq VI11 and IX do not differ significantly from those evaluated from eq IV and VII. Therefore, we recommend eq VI1 as the best expression to represent the experimental rate constant data for reaction 1. The overall error in k l ( T ) is estimated to be f 2 0 % over the temperature range 400-2250 K. Careful examination of the present shock tube data listed in Table I showed that the Arrhenius plot is nonlinear. The curvature is more pronounced at the higher temperatures and is only clearly evident when the data is considered over the entire temperature range. Indeed, if only the data below 1 6 0 0 K is analyzed, an excellent fit to the two-parameter Arrhenius expression is obtained
k , ( T ) = 2.09
X
exp[(-5521 f 105)/T]
(X)
In A = 22.2880 f 0.0929
A In A = f6.88
Equation VI is not much different from eq IV as is shown in Figure 1. Adding our results (derived from eq VI in the same manner as described earlier for the previous data) to the combined data base resulted in the following three-parameter least-squares fit: k , ( T ) = 1.15 X 10-15T1.56exp(-4270/T)
(VIII)
(VII)
Rate constants generated from eq IV and VI1 agree to within less
These values for AArrhand EAmh are in excellent agreement with those k , ( T ) = (2.01 f 0.34)
X
exp[(-5435 f 112)/T]
(XI)
obtained over the temperature range 474-1 156 K in an earlier study from this laboratory with the flash photolysis-resonance fluorescence (FP-RF) and discharge flow-resonance fluorescence (DF-RF)techniques.21 The experimental data, which are shown in Figure 2, clearly demonstrate the excellent agreement between
Rate Constant for the O(3P)
+ CHI Reaction
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5945
TABLE III: Comparison of Theoretical Calculations and Experimental Observations of k 2')
theor values'
exptl values" T/K 2000 1667 1429 1250 1111 1000 909 833 769 667 588 526 476 435 400
ki(T)' 1.92 (-1 1) 9.43 (-12) 4.83 (-12) 2.56 (-12) 1.39 (-12) 7.70 (-13) 4.32 (-13) 2.46 (-13) 1.42 (-13) 4.85 (-14) 1.69 (-14) 6.02 (-15) 2.20 (-15) 8.20 (-16) 3.05 (-16)
ki(V 2.30 (-1 1) 1.13 (-11) 5.10 (-12) 2.60 (-12) 1.35 (-12) 7.66 (-13) 4.00 (-13) 2.30 (-13) 1.30 (-13) 4.50 (-14) 1.60 (-14) 6.10 (-15) 2.30 (-15) 8.69 (-16) 3.30 (-16)
ki (
nd
1.66 (-11) 7.57 (-12) 3.70 (-12) 1.89 (-12) 1.01 (-13) 5.54 (-13) 3.11 (-13) 1.78 (-13) 1.04 (-13) 3.71 (-14) 1.36 (-14) 5.20 (-15) 2.05 (-15) 8.29 (-16) 3.37 (-16)
ki(V 1.37 6.61 3.39 1.82 1.01 5.79 3.38 2.01 1.22 4.65 1.82 7.41
(-1 1) (-12) (-12) (-12) (-12) (-13) (-13) (-13) (-13) (-14) (-14) (-15)
'Units for k , ( T ) are cm3 molecule-I s-l; (-x) E 10". 'Calculated with k , ( T ) = 1.15 X 10-1ST1.'6exp(-4270/T); from the present evaluation, eq VII. CCalculationsof A. Wagner et a1.26b"Calculated with k,(T) = 1.12 X-10-18p." exp(-3470/T); ref 27. 'Calculated with k , ( T ) = 3.54
X
10-'8p*21exp(-32610T); ref 28.
the sets of data obtained from these three different techniques. The experimental results from eq VI1 are compared in Table I11 with the results from activated complex theory calculations.2628 The valueszb for the rate constants, derived from the barrier height and transition-state geometry with the use of the appropriate Pol-CI wave functions, are given in the table. The experimental data, as described by eq VII, are generally in excellent agreement with the best theory26bbut are not as well described by the less sophisticated theoretical models of Cohen2' and Michael et aL2* This is clearly seen in Table 111, where the experimental rate constants are compared with those from the three theoretical (26) (a) Walch, S. P.; Dunning, T. H., Jr. J . Chem. Phys. 1980,72, 3221.
(b) Wagner, A. F.; Dunning, T. H., Jr.; Walch, S.P.; Schatz, G. S.,private
communication.
(27) (a) Cohen, N. Aerospace Report No. ATR-84(7073)-1, The Aerospace Corp., El Segundo, CA 90265, 1984. (b) Cohen, N. Znr. J . Chem. Kiner. 1986, 18, 59. (28) Michael, J. V.; Keil, D. G.; Klemm, R. B. Znr. J . Chem. Kinet. 1983, 15, 705.
models over the temperature range 400-2000 K. The predictions of Wagner et a1.26bagree within 10% with the experimental values, those of Cohen" are generally lower than experiment by 15-30%, and those of Michael et a1.,*" which are lower by about 30% a t high temperatures, cross the experimental values at T N 700 K and are then higher by about 20% at 526 K. In conclusion, the excellent agreement between the data obtained by the FP-ST method and that from previous studies demonstrates the accuracy of the procedures16developed to correct for the small but significant deviations from ideal shock behavior at temperatures below 1300-1400 K. Appropriate rate constants are now measured routinely by this technique in the temperature range -800-2500 K. The recommended rate constant that is derived from all the available experimental data for the reaction O(3P) with CHI is kl(T) (cm3 molecule-' s-l) = 1.15 X 10-15T',56 exp(-4270/ T). It is important to reiterate that, as used here, the expression
k(T) = A F exp(-B/T)
(XW
is simply an empirical equation used to express the experimentally observed, non-Arrhenius dependence of the rate constant over a specific range of t e m p e r a t ~ r e . We ~ ~ note that Wagner et have calculated the rate constant for the reaction of O(3P) with CH, from activated complex theory over the temperature range 400-2000 K and that their data can be fitted by the least-squares method to give the expression
kl(Qth= 3.44
X
10-18P.32*0.07exp[(-3713
f
53)/q
(XIII)
A In A = f0.52 Values of k,( T ) calculated from eq XIII agree within a few percent with the original data listed in Table I11 and with those calculated from eq VII. This excellent agreement between the values of k,()'2 derived from the two expressions holds over the entire range in temperature, even though very different values for A , n, and B are used (Table 111). Acknowledgment. This work was supported by the Division of Chemical Sciences, U S . Department of Energy, Washington, DC, under Contract No. AC02-76CH00016. Registry No. CH4, 74-82-8; 0, 17778-80-2. (29) Cvetanovic, R. J.; Singleton, D. L.; Paraskevopoulos, G. J . Phys. Chem. 1979,83, 50.
