J . Phys. Chem. 1991, 95, 674-681
674
coefficients of HCI. This is attributedg9 to deficiencies in the short-range repulsion potential. We are not aware of comparisons between HNC equations and transient kinetic data. We hope that our results will motivate a more comprehensive effort of comparing the statistical mechanics theories with experiment. At large salt concentrations, the salt effect is not merely "physical" screening of the Coulombic interaction. When the interionic separation is small, "chemical" bond strengths (of the RO-H bond in HPTS, for example) are modified. In this limit the kinetic parameters Kd and K, are no longer independent of salt concentrations, as assumed above. In fact, it has been showngsd that Kd decreases with increasing salt concentration, in proportion to the solvent activity to some power. It would be interesting to extend the present measurements to higher concentrations. Another aspect is the (weak) dependence of the diffusion coefficient on salt concentration. Such effects would modify our model in the direction of an even weaker dependence of QY on salt concentration. We have already reportedZoa preliminary investigation of salt effects in time-resolved measurements. A more extended com-
Direct Rate Constant Measurements for H Flash Photolysis-Shock Tube Technique
parison between theory and transient measurements is deferred to subsequent publications. Finally, extension of the results obtained in this paper to spatially limited reactions, such as those in inverse micelles,34could provide an important tool for understanding similar processes in biological systems.42
Note Added in Proof. A recently published investigation (Suwaiyah, A,; AI-Adel, F.; Hamdan, A,; Klein, U. K.A. J. Phys. Chem. 1990, 94, 7423) finds that the absolute QY of HPTS in water is about 0.75. This contrasts with earlier report^'^,^^ of an absolute QY of about unity. If substantiated, this would slightly affect the quantitative assessment of the relative QY data. Acknowledgment. We are grateful to Peter Rentzepis and Attila Szabo for discussions and suggestions. E.P. thanks the Landau Foundation for support. This work was supported in part by Grants 88-00125 and 86-00197 from the US.-Israel Binational Science Foundation (BSF), Jerusalem, Israel. (42) Gutman, M.; Nachliel, E. Eiochim. Eiophys. Acta 1990,1015, 391.
+ CH4
---*
CH,
+ Hp, 897-1729
K, Using the
Martin J. Rabinowitz,? James W. Sutherland,* Patricia M. Patterson, and R. Bruce Klemm* Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11 973 (Received: November 27, 1989; In Final Form: August 15, 1990)
A kinetic study of the reaction of hydrogen atoms with methane was performed using the Brookhaven flash photolysis-shock tube (FP-ST) facility. Experiments were conducted in the reflected shock regime over the temperature range 897-1729 K under pseudo-first-order conditions ( [CH4]/[H] 1 200). Hydrogen atoms were monitored by using atomic resonance absorption and rate constants were derived directly from decays of absorbance signals. Separate experiments, in which the initial H-atom and radical concentrations were varied, demonstrated the absence of kinetic complications due to secondary reactions. This observation was further verified by the results of a computer modeling study. The rate constant values obtained in this research may be fitted with equal uncertainty to either a two-parameter expression, k , ( T ) = (1.78 f 0.12) X exp[-(6440 f 80) KIT)], or a three-parameter expression, kl(T) = 1.6 X 10-'9T2.57fo.76 exp[-(3340 f 920) K/U. Units are cm3 molecule-' s-l with uncertainties quoted at the one standard deviation level. The preexponential term for the three-parameter expression and its uncertainty are given in logarithmic form: In (A) = -43.3 f 6.2. The mean deviation of the data from either expression is about *lo% over the entire temperature range. Rate constants for the reverse reaction, k-,(T),were computed from our measured k l ( T )values, using the equilibrium constant for reaction 1, at each experimental temperature. These data were also fitted to both two-parameter and three-parameter expressions with equal uncertainty. Combining the present FP-ST data with those obtained in flow tube experiments (by Kurylo, Hollinder, and Timmons), expressions for kl(T)and k-,(T)are evaluated for the temperature span 400 K S T 5 1800 K k,(T) = 6.4 X 10-187Q.11M.18 exp[-(3900 f 140) K/U cm3 molecule-' s-' and k-,(7') = 6.6 X 10-20~~24*.18 exp[-(3220 f 140) K / q cm3 molecule-l s-l. The data of this study are compared with previous experimental and theoretical results. For example, good agreement is found between the data reported here for k l ( T ) and the calculated values reported by Truhlar and co-workers; but there is a discrepancy between the present results and the values recommended by Warnatz.
Introduction The reaction of atomic hydrogen with methane H(2S) + CH4 H2 + CH3 (1) is an important process in methane pyrolysis and in methane combustion as an inhibitor in ignition.' Numerous kinetic studies2-8 of reaction 1 and the reverse reactione" CH3 + H2 .-c CH4 + H (-1) have been reported and extensive review articles have been published.IJ2-l4 Previous experimental results for reaction 1 are graphically represented in Figure 1. Of the four studies performed at high temperatures, where accurate kinetic data are needed, only
-
*Authors to whom correspondence should be addressed. 'Permanent address: NASA/Lewis Research Center, Cleveland, OH.
one5 employed direct methods. In the other three studies?-" rate data for reaction 1 were derived indirectly by comparing simu(1) (a) Warnatz, J. In Combustion Chemistry;Gardner, Jr. W. C., Ed.; Springer-Verlag: New York, 1984, and references therein. (b) Tang, W.
Combust. Flame 1989, 78, 71.
(2) Fenimore, C. P.; Jones, G. W. J. Phys. Chem. 1961, 65, 200. ( 3 ) Pccters, J.; Mahnen. G. Symp. (Inr.) Combusr. [Proc.]l l r h 1973, 133. (4) Biordi, J. C.; Lazzara, C. P.; Papp. J. F. Combust. Flame 1976, 26, 57. (5) Roth, P.; Just, Th. Ber Bunsen-Ges. Phys. Chem. 1975, 79, 682. (6) Kurylo, M. J.; Hollinder, G. A.; Timmons, R. B.J. Chem. Phys. 1970, 52, 1773. (7) Sepehrad, A.; Marshall, R. M.; Purnell, H . J. Chem. Soc., Faraday Trans. 1 1979, 75, 835. (8) (a) Clark, T. C.; Dove, J. E . Can. J. Chem. 1973, 51, 2147. (b) Johnston, H. S.Ado. Chem. Phys. 1960, 3, 131. (c) Johnston, H.S.;Parr, C. J. Am. Chem. SOC.1963, 85, 2544. (d) Johnston. H. S. Gas Phase Reaction Rate Theory; Ronald: New York, 1966.
0022-3654/91/2095-0674$02.50/00 1991 American Chemical Society
+ CH4
Rate Constants for H -10
'
-
+ H2 Reaction
CH3
I
'
I
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 675
I
\
-1 1 CI r
lm
I s
-12
0
',
A
60 -
> E
50 -
0
-13
40
\
2
\
Y
51 -14
-15
'r
\ \
\
\
\
\
\
-18
1.o
2.0
-
--1.6,
4.5
3.0
6.0
Time, ms
F i 2. Typical transmission change observed following flash photolysis of CH, in the reflected shock regime. Steps result from incident and reflected shocks traversing the observation window. Upper inset: firstorder plot obtained from the raw data; ka = 1832 f 8 s-', kl = 3.97 x IO-I3 cm3 molecule-' s-l. Lower inset: plot of deviations of experimental data from the fitted line. Experimental conditions: PI = 3 1.34 Torr, T5= 1073 K, ps = 4.615 X IO1* molecules cm", and [CH,]= 4.619 X lo1' molecules ~ m - ~ .
1o3 KIT
are now routinely determined to be 12 X 10" Torr L s-' (about 10 times lower than before'"). An IBM pS/2, Model 80, computer is now used for data analysis. In this experiment, methane (XCH, ranged from 5 X lo-" to 3 X lCr3 in argon) was photolyzed by UV light from a nitrogen-fillixl flash lamp.20 Emission from the discharge passed through a MgF2 window (A 1 115 nm). Depending on the concentration of CH4 used, electrical energies ranging from 450 to 1200 J were discharged through the lamp to produce initial yields of H and CH3 lations with measured species profiles obtained from flames. Thus, of (2-5) X l o r 2particles ~ m - ~The . concentration of H atoms a gap exists between about 800 and 1700 K in directly determined was monitored by atomic resonance absorption spectrophotometry rate constants for reaction 1. Indeed, in the absence of sufficient (ARAS).'sv21The resonance lamp used in this study was operated experimental data at high temperatures, two recent reviews of with a microwave discharge in a flowing mixture of 0.1% H2 in reaction 1 recommended the rate constant expression derived from He maintained at a constant pressure of 4 Torr. The fraction of the bond energy-bond order (BEBO) calculation of Clark and Lyman-a emission was determined by using an H-atom filter (a Dove.* microwave discharge in a flowing gas mixture of 10% H2 in He), In the present study, the Brookhaven flash photolysisshock located between the resonance lamp and the shock tube. The tube15 was used to perform direct rate constant measurements of Lyman-a fraction ranged from 0.75 to 0.85. k,(T) at high temperatures that covers the important range beThe Mach numbers of incident shock waves were calculated tween 800 and 1700 K. from incident shock velocity measurements. The temperature, density, and pressure in the reflected shock regime were then Experimental Section calculated from ideal shock theory. Corrections for nonideal shock The flash photolysisshock tube (FP-ST) technique,16 as imbehavior, due to boundary-layer effects in the present shock tube, plemented in this laboratory, has been described p r e v i o u ~ l y . ~ ~ * ~were ~ made by using a procedure based on experimentally measured Details of recent modifications that upgrade the performance of pressures and the adiabatic equation of ~ t a t e . ' ~ JThe ' methane the apparatus are given elsewhere: improved vacuum seals;18 concentration at each experimental temperature ( T5)was dereplacement of oil diffusion pumps with turbomolecular pumps;'* termined from the initial mole fraction and the calculated density and redesign of the diaphragm rupture mechanism.19 Leak rates in the reflected shock regime. Since [CH,] was always maintained in large excess ([CH4]/[H] 2 200), the reaction followed pseudo-first-order kinetics. Diffusion (9) Clark, T. C.; Dove, J. E. Can. J. Chem. 1973, 51, 2155. of H atoms out of the reaction zone is negligible.ls Thus (IO) MBlla, W.; Mozzhukhin, E.;Wagner, H. Gg. Ber. Bunsen-Ges.fhys. Chcm. 1986, 90,854. In [HI, = -K,,t + In [HI, (1) ( I I ) Marshall, R. M.; Shahkar, G. J. Chem. Soc. Faraday Trans. I 1981, 77, 227 1. where KO, = kl[CH4]. For H-atom-absorbance values less than (12) Walker, R. W. J . Chem. Soc. ( A ) 1968, 2391. about 0.5, Beer's law holds and experimental first-order rate (13) (a) Shaw, R. J. fhys. Chem. Ref. Data 1978,7, 1179. (b) Allara, D. L.; Shaw, R. J. Phys. Chem. Ref. Data 1980, 9(3), 523. constants, KO,, were obtained from linear least-squares fits using (14) Tsang. W.; Hampson, R. F. J. fhys. Chem. ReJ Data 1986, IS, 1087. eq 11. Helium, argon, and hydrogen/helium mixtures were ( I 5) Sutherland, J. W.; Klemm, R. B. Symp. (fnr.) Shock Waues Shock Figure 1. Summary of previous experimental results (emphasis on high-temperature studies). (---) Roth and Just:' k , ( T ) = 1.20 x IO" exp(-7578/T), 1700-2000 K. (-) Biordi et al.:' k l ( T ) = 2.49 x 10-'9?'.0 exp(-8300/T), 1300-1700 K. (-.-.) Fenimore and Jones? k l ( T ) = 1.87 X 10-ioexp(-6026/T), 1100-1900 K. (-) Sepehrad et al.:' k , ( T ) 2.99 X exp(-6628/T), 640-818 K. (--) Kurylo et ai? kl(T) = 1.04 X 10-10exp(-5338/T),424-732 K (0)Peeters and Mahnen? 5.3 X 1600 K. Units of kl(T) are cm3 molecule-1 s-l.
~
Tubes [froc.] l6rh 1988, 395, and references therein. (16) (a) Ernst, J.; Wagner, H.Gg.; Zellner, R. Err. Bunsen-Ges. fhys. Chem. 1978, 82, 409,and references therein. (b) Niemitz, K. J.; Wagner, H.0s.;Zellner, R. Z . Phys. Chcm. 1981, NFI24, 155. (17) (a) Michael, J. V.; Sutherland, J. W.; Klemm, R. B. Int. J . Chem. Kfner. 1985, 17, 315. (b) Michael, J. V.; Sutherland, J. W. Inr. J. Chem. Kinel. 1986,18, 904. (c) Maki, R. 0.; Michael, J. V.;Sutherland, J. W. J. fhys. Chem. 1985,89,4185. (18) Sutherland, J. W.; Patterson, P. M.; Klemm, R. B. J . fhys. Chem. 1990, 94,2471.
(19) Patterson, P. M.; Sutherland, J. W.; Klemm, R. B. Symp. (fnr.) Shock Wows Shock Tubes [froc.]17th; American institute of Physics: New York, 1990; p 444. (20) (a) Klemm, R.B.; Stief, L. J. J. Chem. fhys. 1974,61,4900. (b) Koyano, 1.; Welge, K. H. Private communication. (21) (a) Myerson, A. L.; Watt, W. S . J . Chem. fhys. 1968,19,425. (b) Myerson, A. L.; Thompson, H.M.; Joseph, P. J. J. Chem. fhys. 1965, 42, 3331.
Rabinowitz et al.
676 The Journal of Physical Chemistry, Vol. 95, No. 2, 1991
In (ABS), = -Kobst + In (ABSlo
(11)
I
I
I
I
0.6
0.8
1.0
1.2
obtained from MG Industries. He and Ar were scientific grade (99.9999% stated purity) and in the HJHe mixtures the H, purity was 99.999%. The methane (LINDE research grade, 99.99% or MG scientific grade, 99.9995%) was thoroughly outgassed at 77 K prior to preparation of the gas mixtures.
Results Rate constants were measured over the temperature range 897-1729 K and the experimental data are listed in Table I. Errors in the Mach number measurements were typically 0.6%-0.8%, leading to a corresponding error of about 1.5% in the temperature of the reflected shock regime. Figure 2 illustrates data obtained from a typical FP-ST experiment. The main part of the figure shows the trace resulting from the change in Lyman-a transmission following flash photolysis of the test gas mixture in the reflected shock regime. The steps in the trace, on the left side of the figure, are due to density changes associated with the incident and reflected shock front traversing the observation window. The first-order plot of In (ABS), vs time obtained from the raw data is also shown (upper inset). The bimolecular rate constant ( k , ) was determined from the slope (-Kob). The corresponding percentage deviations of the data points from the linear first-order fit are also depicted in Figure 2 (lower inset). Within the experimental error, no change was observed in the measured k , ( T ) values when the initial pressure was varied by a factor of 3 and the [CH,] varied by a factor of about 6. This is consistent with pseudo-first-order kinetic behavior. Variations in the flash energy, from 461 to 1038 J at -920 K for the mixture XCH,= 2.93 X resulted in no change in the measured values of k , ( T ) . In separate experiments at 1600 K 5 T I1700 K, H atoms were not observed either in photolysis runs using only pure argon or in thermal runs (no flash) performed on CH4/Ar mixtures. These experiments confirmed that H-atom production due either to photolysis/pyrolysis of possible system contaminants or to methane thermal decomposition was negligible even at the highest temperatures of this study. In a preliminary study that is reported the rate constant for CH, thermal decomposition was measured under low-pressure-limit conditions in the present shock tube (without using the flash lamp). Five experiments were evaluated that cover the temperature range 1742 K IT I 2126 K. Two experiments (at 1742 and 1803 K) were performed with mole fractions of CH4 of 800-IO00 ppm and these were analyzed by assuming rapid establishment of [HI steady state (due only to reactions 1 and 3; see Table 11 and ref 22). Three experiments (at 1983,2122, and 2126 K) were performed with mole fractions of CH4 of 30-lo00 ppm and, for these the initial formation rates (d[H]/dt) were used to determine k3(T ) directly from the linear absorbance and from a simulation of the data with the mechanism in Table I1 (see ref 22). The results of these experiments (given in Table 111) display a large discrepancy with those recommended by Warnatzla and by Tsang.Ib Of the reported investigations, that of Roth and Just5 is the most direct. Even though a similar technique was used in both st~dies.~f2 the rate constant for thermal decomposition obtained in this laboratory22is about a factor of 5 smaller than that reported previ~usly.~ The rate constant data for reaction 1 are plotted, according to the Arrhenius equation, in Figure 3. A linear least-squares fit to the data results in the expression (897 K I T I 1729 K) kl(T)
(1.78
* 0.12) X 1O-Io exp[(-6440 f 40) K / T I
(111)
(The units of kl(7') are cm3 molecule-' s-l and the uncertainties are given at the one standard deviation level. These units for bimolecular rate constants and levels for uncertainties will apply throughout.) The mean deviation of the experimental data from this linear fit is f10.3%. Because of slight curvature apparent (22) Sutherland, J. W.;Patterson, P. M.; Rabinowitz. M.J.; Klemm, R. B. 'Preliminary Shock Tube Kinetic Study of Methane Thermal
Decomposition". BNL Informal Report 44699, May, 1990.
-13
0.4
4
l o 3 KIT Figure 3. Arrhenius plot of k , ( T ) data of Table I. The line is the exp(-6440 f 8 0 / n cm3 expression k , ( T ) = (1.78 i 0.12) X
molecule-'
s-l.
-1 1
I
I
I
I
I
1
I
I
- 1 1.5 n 3-
lY)
-a -
'0 @
-12
5 .
0
c
Y
Y
5!
d
5
-12.e
-13
I
103 KIT Figure 4. Modified Arrhenius plot of &,( 7')data of Table 1. The line is the expression k l ( r ) = 1.60 X I 0-'9'1(2.5'M,'6) exp(-3340 f 920/ r ) cm3 molecule-! s-l. (In ( A ) = -43.3 & 6.2).
in Figure 3, a three-parameter fit was applied to the rate constant data (see Figure 4) to obtain the following expression (897 K I T 5 1729 K): k , ( T ) = 1.6 X 10-'9T2.57M.76 exp[-(3340 f 920) K/TI
(IV)
The preexponential factor and its uncertainty are given in logarithmic form: In ( A ) = -43.3 f 6.2. The mean deviation of the experimental data from this nonlinear fit is 19.6%. Discussion
In the work reported here, first-order kinetic behavior was observed over two to three decay lifetimes (tile) and in no case
Rate Constants for H
+ CH4
-
CH3
+ H2 Reaction
TABLE I: Rate Constant Data for the Reaction H + CHI PI
kobdrb
9
Torr
h4,"
s-l
pCC
Tq,K
kid
-
K1'
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 677 CHI + H1 k-j
PI, Torr
M.a
Pf
Tc.K
kId
Ki'
k-/
4901 5790 4590 4456 5078 5462 6347 604 1
2.859 2.888 2.839 2.904 2.872 2.907 2.902 2.961
1589 1593 1600 1610 1614 1660 1661 1729
3.323 3.887 3.135 2.969 3.427 3.642 4.240 3.955
24.543 24.551 24.565 24.583 24.590 24.660 24.66 1 24.729
13.54 15.83 12.76 12.08 13.94 14.77 17.19 15.99
2.275 2.312 2.355 2.403 2.463 2.488 2.486 2.507 2.520
2717 1796 2543 2622 4187 5086 4237 5067 5508
2.606 2.642 2.680 2.730 2.817 2.818 2.810 2.829 2.846
1335 1372 1415 1465 1528 I549 1552 1574 1588
2.021 1.318 1.839 1.862 2.882 3.499 2.922 3.472 3.751
23.609 23.805 24.005 24.201 24.399 24.454 24.461 24.512 24.541
XcH4 = 5.159 X IO4 8.560 15.28 5.537 15.34 7.661 15.05 7.694 15.30 11.81 15.09 14.31 15.16 11.95 15.13 14.16 15.10 15.28
3251 2391 3206 4294 3267 5516 5247 5523 5422 6716
2.594 2.580 2.653 2.627 2.662 2.666 2.658 2.688 2.733 2.813
1352 1353 1373 1385 1388 1433 1444 1480 1480 1525
1.575 1.166 1.521 2.057 1.544 2.604 2.159 2.585 2.497 3.004
23.702 23.708 23.810 23.869 23.883 24.080 24.123 24.253 24.253 24.391
XCH, 7.947 x Io4 6.645 15.09 4.918 15.20 6.388 15.37 8.618 15.25 6.465 15.34 10.81 30.30 8.950 30.29 10.66 30.72 10.30 30.38 12.32
2.469 2.495 2.534 2.536 2.638 2.138 2.259 2.366 2.387
5648 7241 8233 7358 10750 2732 4358 6952 10112
2.801 2.844 2.883 2.862 2.995 4.703 4.945 5.227 5.273
1529 1556 1614 1616 1712 1 I64 1279 1382 1414
2.538 3.204 3.594 3.235 4.516 0.73 1 1.109 1.674 2.413
24.402 24.47 1 24.590 24.594 24.715 22.376 23.267 23.854 24.001
10.40 13.09 14.62 13.15 18.27 3.267 4.766 7.018 10.05
15.18
2.283 2.285 2.304 2.311 2.324 2.363 2.369 2.408 2.413 2.465
15.52 30.16 30.61 30.47 30.70 30.85 30.00 30.38
2.352 1.966 1.999 2.010 2.016 2.057 2.058 2.062
4918 1422 1683 1642 1793 1855 2130 2107
2.742 4.238 4.386 4.393 4.442 4.581 4.457 4.523
1416 1020 1048 1058 1063 1096 1096
24.009 20.853 21.188 21.303 21.359 21.717 21.717 21.759
Xc+, 9.827 X lo4 7.601 30.32 1.635 30.06 1.841 30.74 1.784 30.54 1.924 30.06 1.897 30.17 2.238 30.03 2.178
2.074 2.146 2.175 2.241 2.256 2.273 2.494
2169 3167 4285 5162 4353 5941 11701
4.527 4.652 4.823 4.932 4.902 4.938 5.383
1114 1I79 1205 1266 1277 1297 1525
0.487 0.693 0.904 1.065 0.904 1.224 2.212
21.902 22.508 22.725 23.180 23.254 23.384 24.391
2.224 3.079 3.978 4.595 3.887 5.217 9.069
1100
1.825 0.341 0.390 0.380 0.41 1 0.412 0.486 0.474
15.56 31.02 3 1.70 3 1.64 31.87 3 I .34 31.78 31.32
2.255 1.853 1.934 1.998 2.008 2.035 2.037 2.067
3472 736 1330 1884 1685 1832 1935 2292
2.664 4.082 4.399 4.561 4.622 4.614 4.684 4.690
1311 92 1 987 1041 1049 1073 1074 I100
1.302 0.180 0.302 0.413 0.364 0.397 0.413 0.488
23.470 19.508 20.433 21.106 21.199 21.470 21.481 21.759
= 1.001x 10-3 5.548 30.21 2.099 0.923 31.70 2.104 1.478 31.20 2.123 30.60 2.129 1.957 1.717 30.67 2.138 30.85 2.137 1.849 1.923 30.81 2.170 2.243 30.77 2.181
261 1 2909 3349 3118 3531 2970 3784 4072
4.599 4.840 4.808 4.730 4.778 4.787 4.856 4.872
1129 1134 1151 1156 1 I60 1163 1193 1202
0.567 0.601 0.696 0.658 0.738 0.620 0.778 0.835
22.050 22.098 22.258 22.304 22.340 22.367 22.626 22.700
2.571 2.720 3.127 2.950 3.303 2.772 3.438 3.678
30.48
2.114
3884
4.706
1 I74
0.806
22.464
2.263
5463
4.935
1283
1.08 1
23.294
4.641
30.84 30.67 30.62 30.66 30.04 30.59 30.41
1.833 1.875 1.894 1.904 1.923 1.938 1.936
1366 1846 2072 1993 2723 2199 2634
3.960 4.024 4.086 4.132 4.085 4.214 4.168
913 951 966 972 99 1 1000 1001
0.164 0.216 0.240 0.229 0.330 0.247 0.299
19.387 19.943 20.151 20.233 20.486 20.602 20.615
1.941 1.958 1.967 1.997 2.055 2.064 2.075
2524 2932 3607 3993 6151 5359 4729
4.153 4.229 4.262 4.348 4.450 4.500 4.492
I002 1017 1024 1050 1101 1 IO9 1119
0.288 0.329 0.401 0.435 0.655 0.564 0.499
20.628 20.8 16 20.902 21.21 1 21.769 21.851 21.952
1.396 1.581 1.918 2.05 1 3.009 2.581 2.273
30.59 30.40 33.03 30.84 30.99
1.819 1.829 1.840 1.850 1.860
1583 1601 1656 1687 1698
3.916 3.920 4.292 4.035 4.084
897 905 91 3 921 930
0.149 0.143 0.155 0.154
19.142 19.265 19.387 19.508 19.641
XCH, = 2.704 X IO-' 0.778 29.99 0.784 30.48 0.738 31.86 0.795 31.95 0.784 31.71
1.865 1.889 1.894 1.904 1.924
2206 2194 2283 2701 3564
3.953 4.096 4.296 4.337 4.359
937 953 957 966 982
0.206 0.198 0.197 0.230 0.302
19.743 19.971 20.027 20.151 20.367
1.043 0.991 0.984 1.141 1.483
10.26 10.13 10.16 15.85 15.06 15.03 15.05 15.23
2.169 2.346 2.421 2.034 2.079 2.098 2.128 2.133
4108 8451 11905 3024 4195 3832 5326 5558
1.689 1.811 1.861 2.404 2.333 2.384 2.407 2.433
1248 1414 1497 1118 1163 1166 1201 1209
0.830 1.593 2.184 0.429 0.614 0.549 0.755 0.780
23.053 24.001 24.308 21.942 22.367 22.394 22.692 22.757
XcH, = 2.930 X IO-' 3.600 15.07 6.637 15.04 8.985 15.07 1.955 15.27 2.745 15.07 2.452 30.36 3.327 30.58 3.428 30.52
2.140 2.164 2.178 2.309 2.313 1.837 1.851 1.872
5238 6417 7762 10936 10699 2300 2109 2093
2.416 2.431 2.452 2.648 2.600 3.924 3.977 4.040
1216 1243 1257 1378 1391 914 925 942
0.740 0.901 1.080 1.410 1.405
22.812 23.017 23.117 23.835 23.897 19.403 19.567 19.815
3.244 3.915 4.672 5.916 5.879 1.031 0.925 0.893
15.14 15.12 15.09 15.10 15.26 15.09 15.11 15.11
15.14 15.15
15.03 15.34 15.19 15.22 15.06 15.03 14.94 15.11
2.515 2.524 2.531 2.545 2.549 2.586 2.586 2.653
xCH,
XCH, = 1.024 X 3.588 30.18 x~H,
0.151
= 2.110 x 10-3
0.846 1.083 1.191 1.132 1.611 1.199 1.450
30.10 30.32 30.40 30.48 30.20 30.39 30.17
0.200
0.181 0.177
OThe error in measuring the Mach number is typically about &0.7% a t the one standard deviation level. bThe mean error from the linear cm3 least-squares fit ranged from 0.4% to 1.4% at the one standard deviation level. 1000 K) between the calculated rate constants and the present results. Truhlar and c o - w ~ r k e r performed s ~ ~ ~ ~ ~calculations on reactions 1 and -1 using variational transition state theory. In their first paper,31 they reviewed the theoretical literature extensively and investigated the efficacy of two potential energy surfaces (PES'S). This work provided calculated rate constants that agreed rather poorly with experimental ones. But the "reaction-path analysis" used by the authors pointed the way toward modifications in the barriers for the semiempirical PES'S. In their subsequent calculated results using four improved PES'S (termed J1, et^.)^^ were tabulated and compared with experimental values for kl( T), k 1 (T), and kinetic isotope effects (rate constant ratios). The calculated rate constants for reaction 1 included in this second report32are compared with the combined experimental results, eq V, in Table V. All of the surfaces give values for k l ( T ) that are smaller than the experimental results at T < 667 K and larger than the experimental results a t T > 1000 K. Even so, three of the surfaces give rate constants that agree equally well (f30%) with the experimental result at high temperatures, 667 K I T I 1500 K. At low temperatures, T < 600 K, the J2A surface gives values for kl(T) that are in somewhat better agreement with experiment than the values computed from the other surfaces. MBIler et all0 have measured k-,(T) in a shock tube over the temperature range 1066-2 166 K using pyrolysis of azomethane or tetramethyltin to generate methyl radicals. Their data were fit to the Arrhenius expression
+
k _ , ( T ) = 3.31
X
lo-" exp(-7200 K/T)
(XI)
The quoted uncertainties1° in the A factor and E, terms combine to predict 3 5 0 % precision. The agreement of these results with those derived from eq X, however, is not good. At 1200 K, the k 1 ( T ) value of Moller et al.IOis about 100% larger than ours and at 1700 K it is more than 150% larger. This discrepancy is shown clearly in Figure 6. Also shown in this figure are calculated values for k-,(T) reported by Schatz et aL30 and by Truhlar and cow o r k e r ~ . The ~ ~ ?values ~ ~ of Schatz et al. agree reasonably well with the present results (900-1700 K) but the temperature dependence is too steep, suggesting that the 13.5 kcal mol-' barrier may be too large. The calculated values for k-,(T), reported by Truhlar and c o - ~ o r k e r son ~ ~the , other hand, are in very good agreement with the present results in both absolute value and in
681
J . Phys. Chem. 1991,95, 681-683
Figure 6. The data used to derive this expression were derived primarily from low-temperature experiments (300K IT I700 K) and thus there is a lack of curvature. Of more interest and import, however, is the rather large discrepancy between this evaluated expression and the values derived from eq X and those reported by Truhlar and c o - w ~ r k e r s . ~Assuming ~ that the equilibrium constant K I is well established, either our derived values (eq X)and Truhlar's calculated ones are in error or there is a problem with the low-temperature measurements of k-! as evaluated by Allara and Shaw.13b*33 In conclusion, we have reported rate constants for reaction 1 that were derived from experimental H-atom decays obtained under kinetically isolated conditions. The calculated rate constants of Truhlar and c o - w ~ r k e r are s ~ ~in excellent agreement with these experimental results. However, our k , ( T ) data are not in agreement with those of Roth and JustS or with those recommended by Warnatz' (the present results are smaller at 1700 K by about a factor of 3.5). In addition, we report a discrepancy with previous determinations of kI( T)13band with the recommended value for the (low pressure) thermal decomposition rate constant of methane.! In order to resolve these disagreements, further kinetic studies on reactions 1, -1, and 3 are indicated. 1(-16) 0.4
I
0.6
0.8
,
I
1.0
, 1.2
I
I
1.4
I
I
1.6
1.8
1.000/1 (K-')
Figure 6. Comparison of k-,(T)data. (0-0) this study; (---) MBller Clarke and Dove;9 (@-e) Allara and S h a ~ ; "(@.-e) ~ et al.;1° (0) Schatz et al.;M@---a)Truhlar and co-workers3*(J2A).
general temperature dependence. Interestingly, the value for k-! reported by Clark and Dove9 a t 1340 K (7.6 X cm3 molecule-' s-!) is in reasonably good agreement (see Figure 6) with the value calculated by using expression VI11 at the same temperature (5.9 X cm3 molecule-' s-l). The expression for k-,(T) recommended by Allara and is also shown in
Acknowledgment. We thank two referees for pointing out the potential kinetic complication associated with singlet methylene. We also acknowledge the contributions of Dr. W. Tao and Mr. J. Quartemont in the computer simulations. This work was supported by the Division of Chemical Sciences, US.Department of Energy, Washington, DC, under Contract No. DE-ACO276CH00016. ~
~
~~
~
~~
(33) It is interesting to note that an expression for k-,(T)derived from the k , ( T ) evaluation of Shawl3' (via k-, = k , / K , ) is in better agreement with eq
X and the calculated values of Truhlar and co-workers32than it is with the k-,(T) expression recommended by Allara and S h a ~ . " ~
Kinetics of the Reaction of Chlorine with Formic Acid in Aqueous Sulfuric Acid M. Fazlul Hoq, Bhart Indu, W.R. Emst,* School of Chemical Engineering, Georgia Institute of Technology, Atlanta. Georgia 30332
and H.M. Neumann School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332 (Received: December 12, 1989; In Final Form: July 26, 1990)
In sulfuric acid solution, the rate of reaction of chlorine with formic acid is proportional to formic acid and chlorine concentrations and is inversely proportional to the acidity function h-. The kinetic parameters are nearly identical with those for the reduction of bromine to bromide ions by formic acid. The two reactions appear to follow similar mechanisms-equilibrium ionization of formic acid followed by direct reaction of a formate ion with a halogen molecule.
Introduction
ne
of formic acid by &lofine in sulfuric acid solution may be an important reaction in the commercial production of chlorine dioxide based on the methanol-chlorate Kinetic information on this reaction has not been reported.
Previous work4 on the bromine-formic acid reaction has demonstrated that the stoichiometry involves equilibrium ionization Of formic acid HCOOH HC02and the bromine-formate reaction
(1) Masachelein, W.J. Chlorine D h f & Ann Arbor Science: Ann Arbor,
Br2
(2) Norell, M.US. Patent No. 4,770,868, Sept 13, 1988. (3) Swindells, R.;Fredette, M.C. J. US.Patent No. 4,325,934, Apr 20, 1982.
(4) Hammick, D. 127, 2715.
MI, 1979.
0022-3654/91/2095-0681%02.50/0
+ HC02-
-
+ H+
H+ + 2Br-
+ C02
(1)
(2)
L.;Hutchison, W. K.;Snell, F. R.1.Chem. Sm. 1925,
0 1991 American Chemical Society
