J. Phys. Chern. 1981, 85, 3126-3129
3126
Resonance Absorption Measurements of Atom Concentratlons In Reacting Gas Mixtures. 7. Pyrolysis of C2Hoand C2D6 Behind Shock Waves Chi-Chang Chlang and Gordon B. Skinner' Depertmenr of Chemlshy, Wrbht State Univershy, Dayton, Ohlo 45435 (Received: March 17, 1981; In Final Form: June 22, 7081)
Measurements have been made of H and D concentrations in dilute mixtures of CzH6 and c2D6, shock-heated to temperatures of 1240-1700 K at 2-3-atm pressure. In the range 1240-1500 K the product klkz has been measured, where reaction 1 is C2H6 2CH3and reaction 2 is CH3 + C2H6 CHI + CzHb When literature values of k2 were used, kl was found to be 2.8 x 1015exp(-84240 cal/RT) s-l. This expression can be correlated well with other literature data on the reaction via a RRKM/energy transfer model. Between 1500 and 1700 K interpretation of the data requires a reaction which forms H atoms from methyl radicals, which we take to be CH3 + CHB C2H6+ H CzH4 + 2H, with a rate constant at 1700 K of 1.5 X 10" mol-' cm3 5-l.
-
-
-
-
Introduction Although the dissociation of ethane has been extensively studied, there is still a good deal of uncertainty about how the rate constant depends on pressure at higher temperatures, and particularly about the efficiency of energy transfer from other gases that are commonly used as diluents in shock tube experiments. In their recent detailed review, Baulch and Duxbury' limit themselves to a recommended expression for kl,- for the reaction
-
C2He
2CH3
(1)
between 750 and 1500 K,and a recommendation for k-' between 250 and 420 K. A few recent paper^^-^ have addressed the energy transfer problem at high temperatures, but the data have not been easy to interpret6and it seemed desirable to carry out further studies. One of the best ways to measure kl is to observe the formation of CH4, which occurs by the reaction CH3 + CzH6
-
CHI + C2H6
(2)
This reaction is quantitative for CH3 at moderate concentrations in the early stages of reaction, before other processes that either produce or use CH3 become important. We have used this approach in a recent paper? in which a single-pulse shock tube was used. However, corrections for other reactions become increasingly important as the temperature (and therefore the extent of reaction in a single-pulse experiment) increases, so we reported data in that study only up to 1240 K. An alternative which is not quite so satisfactory is to measure the concentration of H atoms (and D from CZDe), which are a good measure of the extent of reaction 2 at C2H, concentrations of 200 ppm or less, and small extents of reaction. In the range 1250-1500 K, ethyl radicals decompose very rapidly, so reaction 2 may be written CH3 + C2H6
-
CHI + CzH4 + H
(24
Since the analysis for H atoms by means of resonance ~~
~
(1)D. L. Baulch and J. Duxbury,Combust. Flame, 37, 313 (1980). (2) K.Glanzer, M. Quack, and J. Troe, Syrnp. - - (Int.) Combust., [Roc.], 16, 949 (1976). (3) P. Roth and T. Just, Ber. Bunsenges. Phys. Chem., 83,577(1979). (4)D. B. Olson, T. Tanzawa, and W. C. Gardiner, Jr., Int. J. Chem. Kinet., 11, 23 (1979). ( 5 ) D. B. Olson and W. C. Gardiner, Jr., J. Phys. Chem.,83,922(1979). (6)G.B. Skinner, D. Rogers, and K. B. Patel, Int. J. Chem. Kinet., 13,'481(1981).
absorption spectroscopy is very sensitive, it is possible to follow their appearance near the beginning of the reaction. In this range [HI = klk2[C2H6]2t2
(3)
where [C2H6]is the initial concentration of ethane and t the time. Later in the reaction a more complete kinetic model must be used to interpret the concentration of H atoms, but because of the low concentrations of ethane used, several of the reactions of the conventional ethane decomposition scheme4 have little effect on the H concentration. By using a kinetic model we were able to confirm the conclusion of Roth and Just3 that at least one process not previously considered leads to formation of H atoms.
Experimental Section Our apparatus and techniques have been described in an earlier paper.' To summarize, we used a stainless steel shock tube with a test section 7.5 cm in diameter and 4.5 m long. Concentrations of H and D atoms were measured by resonance absorption behind the reflected shock wave. The microwave discharge lamp used to produce the Lyman-a radiation had been characterized in terms of emitted line shape, and also empirically calibrated by the method of Appel and Appleton.8 Temperatures were calculated from the incident shock speed, while the reflected shock pressure was also monitored. Since the observed pressures were within 2-3% of those calculated, and did not vary more than 2-3% during the measurements, we have estimated that the uncertainty in temperature is no more than 1% or 15-20 K. We have estimated the effect of wall cooling on our experiments using methods described p r e v i o ~ s l y . ~ In J~ typical experiments, the observed H and D concentrations are calculated to be 2 to 3% lower than would be the case without wall cooling. The effect is smaller than in our single-pulse experiments for several reasons: the diameter of the tube is greater, the measurements were made closer to the end plate, the experimental times were shorter, and measurements were made linearly across the tube rather (7)C.-C. Chiang, A. Lifshitz, G. B. Skinner, and D. R. Wood, J.Chem. Phys., 70,5614 (1979). (8) D. Appel and J. P. Appleton, Symp. (Int.)Combust., [ R o c . ] ,15, 7ni . - -(1974). ~
(9)G. B.Skinner, R. C. Sweet, and S. K. Davis, J. Phys. Chem., 75, l(1971). (10)G. B. Skinner, Int. J. Chem. Kinet., 9,863 (1977).
0022-3654/81/2085-3126$01.25/00 1981 Amerlcan Chemical Society
The Journal of Physical Chemistry, Vol. 85, No. 21, 1981 3127
TABLE I: Experimental Data on H and D Concentrations and Dissociation Rate Constants
H or D
P,,
i X
I
7
I
1
Id
B 10 20 30 40
OO
t 2 X 1 0 8 , s2 Figure 1. Measured D concentrations for 50 ppm of CzD, in argon at 1386 K and 1.87 atm.
than on the entire volume. We did not make corrections for either our calibrations7 or these experiments, so the cancellation of error should reduce the overall effect to less than 2%. Gas samples were made from CzH6 obtained from Phillips Petroleum Co. (99.97% pure), CzD6from Merck Sharp and Dohme of Canada, and argon from Airco (Research Grade, 2 ppm totalimpurity, with less than 0.5 ppm hydrocarbons reported as methane).
Results Because ethane absorbs H (and D) Lyman-a rather strongly, all of our gas mixtures were quite dilute-10 and 50 ppm of CzH6 and 10,50, and 200 ppm of CzDe In each experiment the Lyman-a intensity dropped suddenly when the reflected shock wave passed the observation station, because of the absorption due to the ethane. This sudden change was followed by slower changes due to the appearance of H or D atoms; thus the two effects could be distinguished. The CpD6 in the 200ppm mixture absorbed about 30% of the radiation at 1200 K and 2.3 atm, and the absorption was not strongly temperature dependent. In analyzing the absorption curves, we assumed the molecular absorption remained constant throughout. This assumption will be accurate for the lower temperature experiments where only a little of the ethane decomposed, but less dependable at higher temperatures. Fortunately, the most concentrated mixture, which had the highest absorption, was studied in the lower half of the temperature range. We also found, as we had earlier, that a few percent of the radiation from the lamp was not absorbed even by a high concentration of H or D atoms. A correction was made by an adjustment of the base line of our light intensity curve. In reporting the data in Table I, we have given the initial slope of the graph of the H or D concentrations for a given shock tube run vs. the square of the time. By eq 3, this should be equal to lzlItz[CzH6]2or the corresponding equation for C2Ds. Since the concentrations rarely produced a straight line over all the times measured, we have also included a point near the end of the graph so the overall shape of the curve may be estimated. A typical set of data is shown in Figure 1. In calculating klwe have used the Arrhenius parameters for reaction 2 that are given in Table 11, which are a com-
T,K 1392 1458 1480 1572 1578 1622 1654
atm
2.55 2.56 2.43 2.57 2.46 2.35 2.20
1384 1391 1460 1480 1536 1615
2.70 2.55 2.76 2.53 2.48 2.46
1339 1397 1412 1497 1585 1591 1654 1661 1701
2.06 2.03 1.88 2.27 2.37 2.28 2.09 2.21 2.06
1284 1306 1320 1357 1386 1427 1491 1554
2.18 2.09 2.77 2.70 1.87 2.74 2.65 2.42
1238 1259 1293 1320 1324 1343 1366 1371 1376 1421
2.24 2.16 2.79 2.10 2.74 2.00 2.80 2.74 2.58 2.54
later initial slope, time, r n ~ l c r n - ~ s - ~gs
10 ppm of C,H, 2.5 X lo-, 6.5X 8.9 X 1.7 X lo-' 1.6 X lo-' 5.0X 9.8X lo-' 50 ppm of C,H, 2.8X lo-' 2.0X 1.4X loF4 6.0X loF5 1.7 X 1.2X 10ppm of C D 3.7 X lo-' 9.4 X lo-' 1.1 X 6.0 x lo-' 8.6 X lo-, 8.0 X
4.2X 8.0 X
3.8 X
lo-'
concn, mol cm'3 x
10"
kl,s" -
0.14 0.22 0.33 0.70 0.84 1.23 0.43
390 940 1220
in Argon 800 800 800 800 800 800
300
in Argon 800 0.63 800 0.47
300 600 400 180
0.52 1.18 1.82 1.35
150 110 580 240
in Argon
1600 1600 1600 1600 1200 1000 600 600 400
0.09 0.15 0.20 0.62 0.55 0.43 0.62 0.93 1.16
50 ppm of C,D, in Argon 0.30 1.9X lo-, 1600 1.7 X 1600 0.34 6.4X 1200 0.60 1.1 x 10-5 800 0.36 600 0.44 2.3 X 1.1 X 600 0.98 1.9X 400 0.87 3.1 X 400 0.81 200 ppm of C,D, in Argon 1.7X lo-, 1600 0.34 3.4 X 1600 0.72 1.2X lo-' 800 0.67 1.4X lo-' 1600 1.16 3.4 X lo-' 800 0.82 1.9 X 1600 1.10 1.4X 500 1.18 1.6 X 300 0.62 2.0x 10-4 300 0.91 2.2X 300 1.05
180 350 440 1190
36 34 64 100 420 760 1110
2.4 4.7 8.7 8.7 22 21 71 86 120 120
promise based on the data of Clark and hod" and Pacey and PurnellI2 and the activated complex theory (ACT) calculations of Clark and Dove.13 While the last authors pointed out that an Arrhenius curve is not valid for this reaction over a wide temperature range, it should apply over the limited range of our data. We made an ACT calculation to estimate a kinetic isotope effect for reaction 2 of about 0.6, as shown in Table 11. When plotted as in Figure 2, no secondary kinetic isotope effect for reaction 1is apparent. We have recentlfll' carried out single-pulse experiments on the dissociation of both CzH6and C& under very similar conditions of pressure, temperature, and sample concentration in the range of 1000-1240 K, and found that the isotope effect (11)T.C. Clark and T. P. J. Izod, "Dynamic Mass Spectrometry",Vol. 3, Heyden, London, 1972, p 209. (12)P. D. Pacey and J. H. Purnell, J . Chem. Soc., Faraday Trans. 1, 68,1462 (1972). (13)T. C. Clark and J. E. Dove, Can. J. Chem. 51, 2147 (1973). (14)D.Rogers and G. B. Skinner,Int. J. Chem. Kinet., 13,741 (1981).
3128
The Journal of Physical Chemistry, Vol. 85, No.. 2 1, 198 1
Chlang and Sklnner
TABLE 11: Reaction Scheme for Ethane Pyrolysis reaction 1. C,H6 2CH, 1D. C,D, 2CD, 2. CH, t C,H, CH, + C,H5 2a. CH, t C,H, CH, + C,H, + H 2aD. CD, t C,D6 + CD, + C,D, + D 3. G,H. -+ C,H, + Hb 4. H-+'C,H,--+7H, + C,H, 4a. H t C,H, -+ H, t C,H, + H 4aD. D + C,D, D, t C,D, + D C,H, t H 5. C,H, 5a. C,H, --c C,H4 + 2H 5aD. C,D6 C,D4 + 2H 6. CH, -+ CH, + H 6D,CD4--+ CD3 + D 7. CH, + CH, C,H, t H 7a. CH, t CH,+ C,H, + 2H 7aD. CD, + CD, C,D, + 2 D 8. CH, + CH, + C,H4 + H, 8D. CD, + CD, C,D, t D,
A"
E , cal
ref
8 4 240
this work, RRKM
1 9 900
11-13
1 9 900
ACT calcd
-+
-f
-+
-+
19 ACT calcd RRKM calcd, similar to ref 20
9 400 1 0 000 100 400
-+
-+
100 400 9 2 500 100 400
-f
-+
16,17 16,17
26 6 0 0 26 600
3 this work
3 2 000
3, 21, 2 2
--f
-+
a
Units of mol, cm', s.
Very fast, combined with reactions 2, 4, 5, and 7.
is less than a fador of 1.3. A small isotopic effect was noted by Clark and Quinn16at 778-878 K by static studies, the ratio klD/kl varying from 1.07 to 1.17. Extrapolation of their data indicates a ratio of 1.5 at 1400 K, but such a long extrapolation would be hazardous without a theoretical basis and, as they point out, current theories of unimolecular reactions are not sufficiently refined to be of use in dealing with such a small effect. Since the standard deviation of OUT data points is 0.30 in terms of log kl,rather larger than we usually have in this sort of experiment, we can only conclude that under our conditions the ratio is not likely to be greater than 1.5. From Figure 2 the rate constants obtained from low concentrations appear to be consistently higher than those from higher concentrations. We can think of no theoretical reason why this should be so, and consider that the systematic differences are due to limitations of our analytical methods. Because H atoms are not produced directly in ethane dissociation, it was harder to find favorable experimental conditions than in our earlier study of CD4 pyrolysis.lB At low concentrations the extent of reaction had to be large to produce measureable concentrations of atoms, while at high concentrations the absorption due to the atoms had to be measured against a background of molecular absorption. For these reasons we decided to calculate a single Arrhenius curve through all the data. We did not attempt to obtain kl values for the data above 1500 K, since in t,hoseexperiments the slopes quickly decreased, presumably because of depletion of the ethane, and reliable values of the initial slopes could not be obtained. For all of the rate constants given in Table I, the Arrhenius equation k 1 , l D = 2.8 X 10" exp(-84240/RT) s-' with a standard deviation in log k of 0.3, was obtained. This curve is shown in Figure 2 along with the RRKM curve calculated from the model given in ref 6; the agreement is close. In this region, as shown, the observed rate constants appear to be a factor of about 6 below k,.
Discussion Our data can be compared most directly with those of Roth and Just: whose measurements on C2Hsdissociation (15)J. A. Clark and C.P.Quinn, J. Chem. SOC.,Faraday Trans. 1,72, 706 (1976). (16)C.4. Chiang,J. A. Baker, and G.B. Skinner, J. Phys. Chem., 84, 939 (1980).
0
7
8
1 0 ~, 1K ~ Flgure 2. Experimental and calculated rate constants for dlssoclatlon of C&le and CP,: (A)10 ppm of CpH& (0)50 ppm of CpH,; (A)10 ppm of C2De; (0)50 ppm of CpD,; (0) 200 ppm of C2D6. Average pressure 2.5 atm. (-) Least-squares llne through all points; (- -) RRKM calculated lines.
-
were quite similar to ours. They were able to account for the initial slopes of [HI vs. t2at lower temperatures by the equation kl = 2 x 1013exp(-35700/T) s-' taken along with Clark and Dove's13 expression k2 = 0.54F exp(-4200/T) mol-' cms s-' The two equations for kl,while differing considerably in Arrhenius parameters, give rate constanta agreeing within a factor of 1.6 over our experimental temperature range. At 1400 K, the product klk2has the value 1.7 X lOl3 mol-' cm3 s-l from their equations, and 3.7 X 1013from ours, so it seems that our measured H and D concentrations were a little more than a factor of 2 higher than theirs under similar conditions. An almost direct comparison with one of their experiments can be made since they show [HI to (0.27 X lo-'' mol cm-? at 300 ps for an be 1.6 X 10l2 experiment with 50 ppm of C2H6at 1460 K and 2.13 atm. In Table I we show [HI = 0.52 X lo-" mol cm-3 at 300 ps
Pyrolysis of CpHe and CPDe
The Journal of Physical Chemistry, Vol. 85, No. 21, 1981 3129
TABLE 111: Comparison of RRKM Model with Data of Olson, Tanzawa, and Gardiner (OTG)" log k , , s-'
a
T,K
obsd, OTG
1300 1600 2000 2500
0.26 2.98 4.91 5.94
calcd 0.84 3.20 5.01 6.22
p Ar 0.029 0.016 0.009 0.003
Reference 4.
for an experiment with 50 ppm af C2& at 1460 K and 2.76 atm. The results would probably have been closer if the pressures had been the same, so in this case the agreement is within a factor of 2. Perhaps the overall measurements of atom concentrations in the two sets of data are in better agreement than the calculations of the initial slope, which were admittedly difficult since in many experiments the slope began to decrease after a third or less of the total time. The difference is disturbing, particularly since data from the two laboratories were in good agreement concerning the dissociation of CH4 and CDq.16J7 Our experimental data provide support for the RRKM and energy transfer models for ethane dissociation that we described earlier6and which correlates quite well much of the experimental data obtained by many workers from room temperature to 1300 K. This model leads to k, about a factor of 2 higher than that given by Baulch and Duxbury's' consensus equation at 1400 K. The difference is within the error limit assigned by Baulch and Duxbury to their equation, but we still regard the difference as sig- nificant. It is the combination of our RRKM model with a particular energy transfer model, leading to rather low calculated energy transfer efficiencies for argon, that has enabled it to correlate many experimental results. The RRKM model can be extended to higher temperatures to make comparisons with Olson, Tanzawa, and Gardiner's data4from 1300 to 2500 K. For mixtures of 3 to 7% c&6 in argon and atom concentrations of 1.1 X lo* to 4.4 X lo* mol cm", they obtained the expression log [k1/(cm3 mol-' s-')I = 111.29 - 25.26 log T - 34800/T, and if the average concentration of 2.5 X IO* mol is used, the equation becomes log (k1/s-l) = 105.69 - 25.26 log T 34800/ T. Taking an average CzH6percentage of 5%, and using the same RRKM and energy transfer models as before, we obtain the data of Table 111. The agreement is within a factor of 2 except at 1300 K. At that temperature our model is tied to other experimental data rather well, so we suggest that the Olson, Tanzawa, and Gardiner data may be off a little at the lower temperature end of their range. If the 0values are small, as we indicate, the effect of changing the ethane concentration from 3 to 7% should be noticeable, although Olson, Tanzawa, and Gardiner did not observe it. Our model has the same problem in matching chemical activation results18as those developed by Olson, Tanzawa, and Gardiner. Our value of kE at 114.9 kcal of vibrational (17)P. Roth and T. Just, Ber. Bunsenges. Phys. Chem. 79,682 (1975). (18) F. B. Growcock, W. L. Hase, and J. W. Simons, Znt. J. Chem. Kinet., 5, 77 (1973).
energy is 2.9 X 1O'O s-', compared to the experimental value of 4.6 x 109 8-1. To interpret the results at higher temperatures and conversions, numerical integrations of a reaction scheme are needed. The reactions we included are listed in Table 11, although not all of those given had a noticeable effect on the formation of H or D atoms. All of these reactions were considered reversible in principle, although only the first one showed appreciable reverse rates during the calculations. Reactions of ethyl radicals other than dissociation were insignificant at our low concentrations. Reaction 4 has no direct effect on H atom concentrations, since it occurs as the global process 4a with no net change for H. Indirectly, it reduces the concentration of C 2 6 ,and hence the rates of reactions 1and 2. Comparable reactions of H with C2H4would also have no effect on the H concentrations. Reaction 8 was suggested by Gardiner et aL2' in connection with methane pyrolysis studies, and considered significant by Tsuboi22and Roth and Just: but under our conditions it does not affect the atom concentrations significantly. Reaction 7 was also suggested by Gardiner et al. and was considered important by Roth and Just to account for the observed concentrations of H atoms at higher temperatures. We concur with this opinion, while not agreeing exactly with Roth and Just's estimate of the rate constant for reaction 7. From our calculations it is clear that at temperatures above 1500 K the ethane dissociates rapidly, so that reaction 2 ceases to produce H atoms. Nevertheless, at these temperatures H atoms are formed, and it seems clear that they must be formed from methyl radicals since very little else is present. In the calculation for our highest temperature experiment at 1700 K with 10 ppm of C2D6 in argon, if reaction 7 is left out of the calculation the computed D concentration at 400 M S is only 20% of that observed, and nearly all of this would be formed during the first 20% of the reaction time. With reaction 7, the calculated concentration of D atoms continues to rise approximately linearly with time during the later part of the experiment, as observed. Only a few percent of the CH3 needs to react this way to produce the observed atom concentrations. We obtain best agreement with our experimental results by using rate constants for reaction 7 about half those found by Roth and Just, as shown in Table 11. Since this reaction affects our results over a quite limited temperature range, we have not attempted to calculate an Arrhenius activation energy, but simply adjusted the preexponential factor to match our data. At 1700 K, the rate constant for the reaction is 1.5 X 10'' mol-' cm3 s-', Acknowledgment. This research was supported by the United States Department of Energy under Contract DE-AC02-76ER02944. The authors also acknowledge the assistance of Mr. John Dryden with the figures. (19)P.Camilleri, R.M. Marshall, and J. H. Purnell, J. Chem. Soc., Faraday Trans. 1 , 70, 1434 (1974). (20)A.Burcat, G. B. Skinner, R. W. Crossley, and K. Scheller, Znt. J. Chem. Kinet., 5, 345 (1973). (21)W.C. Gardiner, Jr., J. H. Owen, T. C. Clark, J. E. Dove, 5. H. Bauer, J. A. Miller, and W. J. McLean, Symp. (Znt.) Combust., [ h o c . ] , 15, 857 (1975). (22) T. Tsuboi, Jpn. J.Appl. Phys., 17, 709 (1978).
