THE REACTIONS OF METHYL RADICALS WITH THE HYDROGEN ISOTOPES BY T. G. MAJURY * AND E. W. R. STEACIE Division of Chemistry, National Research Council, Ottawa, Canada Received 3rd March, 1952 CH3 and CD3 radicals were prepared by the photolysis of the appropriate acetone and their reactions with hydrogen and deuterium studied in the range 130-300". The energies of activation and steric factors for the four reactions were evaluated ; the former lie in the range 9-12 kcal and the latter are of the order of 10-3. The main influence on reaction rate is due to the isotope of hydrogen concerned, the nature of the methyl radical exerting relatively little effect. In a recent series of papers,l we have attempted to obtain information on the reactions of methyl radicals with a variety of hydrogen-containing substances, of the type The results obtained are of some interest in connection with the effect of structure on the reaction rate. They are also of interest in that they show that the steric factors for these reactions are of the order of 10-3 to 10-4, which is considerably lower than the value of 0.1 often arbitrarily assumed in the past.From a similar point of view it is of interest to investigate the reaction of methyl radicals with hydrogen, especially in view of the importance of this re- action, and of the wide discrepancies in previous results? It is also of interest in connection with isotope effects to extend such an investigation to include the reactions of CH3 and of CD3 with H2 and with D2. Finally, as discussed later, the results are of considerable interest in connection with the reverse reaction CH3 + RH + CH4 + R.H + CHq --+ CH3 + H2. EXPERIMENTAL METHoD.-It has been shown3 that in the photolysis of acetone between 130" and 300" the production of methyl radicals and the formation of methane and ethane are accounted for by the following reactions : (1) (2) (3) CH3. CO . CH3 -+ 2CH3 + CO CH3 + CH3 -> C2H6 CH3 + CH3. CO . CH3 -> CH4 -1- CH2. CO . CH3 Assuming a steady concentration of methyl radicals, it follows that In the presence of hydrogen the methyl radicals also react as follows whence CH3 + H2 -+ CH4 + H (4) where (RCHJ4 represents the rate of production of methane by reaction (4). The value of (RCH$4 can be obtained by subtracting (RcHo)3 from the total methane, the value of * National Research Council of Canada Postdoctorate Fellow, 1950-51.4546 REACTIONS OF METHYL RADICALS (&H4)3 being obtained from experiments with acetone alone. Alternatively, for CH3 and D2, or for CD3 and Hz, (RCH4)4 can be obtained from an isotopic analysis of the methanes produced, using a mass spectrometer. The fate of the H atom produced in reaction (4) is presumed to be H + CH3 CO . CH3 --> Hz + CHz . CO . CH3. ( 5 ) The alternative (6) appears to be ruled out as a significant process by evidence obtained in the course of the present work. The apparatus, experimental procedure, etc., were similar to those described in previous papers.1 No details will be given here, since the work will be published in full shortly. H + CH3 -+ CH4 RESULTS Six sets of experiments were performed in all, viz.the photolyses of normal and of deutero-acetone alone, and of each of these in the presence of hydrogen and of deuterium. The results for acetone and deutero-acetone done are in excellent agreement with previous work.1 e.0 1'5 1'0 0 5 0 I I I I \ I 1-9 2'1 2.3 2'5 FIG. 1. CH3 -F CH3COCH3 open circles CH3 + H2 open squares CH3 i- D2 open triangles CD3 --I- CD3COCD3 filled circles CD3 + H2 filled squares CD3 + D2 filled triangles In investigating the reaction of CH3 with D2 (the photolysis of ordinary acetone in the presence of deuterium), and of CD3 with Hz (deutero-acetone in the presence of hydrogen) it was possible to use two methods, as mentioned above, one depending only on gas analysis for methane, and the other involving an isotopic analysis of thc methanes.In both cases the results agreed to within the experimental error, but the latter method was considerably more precise. It was necessary t o make corrections for isotropic impurities in the deuterium and deutero-acetone used. In the deutero-acetone, 93.2 % of the molecules present had 6 D atoms. Roughly 96 % of the methyl radicals formed were therefore CD3, The deuterium used contained ap- proximately 95 % D2, 5 % HD. In the reaction of CD3 with D2, by basing all results on fully deuterized products no correction was necessary. In the reactions CD3 + H2 The remaining 6.8 % had 1 or 2 H atoms per molecule.T. G . MAJUKY AND E. W. K. STEACIE 47 and CH3 -1. D2 corrections were applied for isotopic impurities.These were, however, small enough so that any uncertainty in the corrections introduces no appreciable error into the results. The fate of the H atom resulting from reaction (4) introduces some,uncertainty into the results. It seeins most likely that this is removed by (5). If so, no complications will be introduced. If the H atom were always removed by (6) it would make little differ- ence, since methane formation would merely be twice too high throughout. If, however, the relative importance of (5) and (6) varied greatly with temperature an error would be introduced into the observed temperature coefficient. It seems highly probable that reaction (6) would be affected by third-body restrictions. It was found, however, that variations in hydrogen concentration and the addition of carbon dioxide had no effect on the kinetics.It therefore seems safe to assume that no appreciable error is introduced by the occurrence of reaction (6). For the present they are merely plotted in fig. 1 and a summary of activation energies and steric factors is given in table 1. The results will be reported in detail later. T A A u , s . 1 ,7-*fiF,DAF~m7WSu w* CHq- 4 N L ~ . l ~ - ~ . B ~ r ~ I s ; u I I T H , Y Y ~ ~ ~ ~ . , ~ ~ ~ ~ l ~ I M AND THE PARENT ACETONE kA/kBa X loi3 EA - WB PA,/PB* x 103 kcal reaction 130" 210" 290" CH3 + CH3. CO . CH3 5.2 37.0 151 1.9 f 0.3 9.5 f 0.1 CH3 + H2 3.3 22.0 87 0.7 f 0-2 9.2 f 0.3 CH3 3. D2 0.6 6.6 37 3.5 f 0.5 11.7 f 0.1 CD3 + CD3. CO . CD3 1.2 10.7 51 1.8 j: 0.5 10.6 -j= 0.3 CD3 -t D2 0.9 8.9 46 2.0 3; 0.6 10.9 f 0-3 CD3 + H2 3.7 31.0 140 2.5 -i- 0.5 10.2 0.2 k A is the rate constant for H or D abstraction ; kB is the rate constant for methyl recombination ; rate constants are expressed in terms of molecules, cm3 and sec.DISCUSSION The values of the ratios of the steric factors to that for methyl combination are given in the second to last column of table 1. The last column of the table gives values of EA - QEB, where A refers to H abstraction and B to methyl com- bination. Recent work on the combination of CH3 radicals4 indicates that median values for PB and En can be accepted as ca. 1 and zero respectively, and these values are no doubt valid also for the combination of CD3 radicals. The figures in the last column of table 1 can therefore each be taken as the actual energy of activation of the reaction in question, and the absolute steric factors will differ little from the values in the preceding column.The steric factors are thus of the order of 10-3 and, like those for other reactions of methyl radicals, are thus considerably lower than the value of 0.1 which has frequently been arbitrarily assumed in the past.5 The values of PA and EA for the reactions of CH3 radicals with hydrogen and deuterium differ appreciably from those recently published by Anderson, Davison and Burton.6 They investigated the reaction of methyl radicals with deuterium by a method similar to that of the present work, and concluded that the activation energy of CH3 + D2 -+ CH3D 4- D (7) was 4.6 kcal higher than that of CH3 + CH3COCH3 -+ CH4 + CH3COCH2 (3) i.e.However, the Arrhenius plot from which the difference was deduced consisted of two portions, corresponding to activation energy differences of 3-0 and 4.6 kcal. E7 = 9.7 + 4.6 = 14.3 kml.48 KEACTIONS OF METHYL RADICALS No real reason was advanced for the choice of 4.6 kcal. In view of this and of other uncertainties we think that their results can be fairly expressed by the average difference, with an uncertainty of about 1-5 kcal, i.e. Whence, allowing for the zero-point energy difference, their results for the re- action CH3 + H2 --t CH4 -j- H (4) become approximately E4 = 11.7 & 1.5 kcal. As discussed later, we believe that our results have an uncertainty of about 0.5 kcal, i.e. E4 = 9.7 f 0.6, which virtually agrees with their value.We therefore feel that their results are quite compatible with the lower value of E4 which we have obtained. ISOTOPE EFFECTS.-The standard errors quoted for the activation energies indicate their experimental precision, but having regard to small uncertainties of mechanism their true uncertainty is probably of the order of 0.3 to 0-5 kcal. It is clear that this variance, being fairly large relative to the experimental differ- ences, precludes any very precise interpretation of the results. However, it seems possible to draw two general conclusions regarding isotope effects. First, com- paring the reactions of the CH3 radical with those of the CD3 radical, there is no consistent evidence of any significant difference in their behaviour. Secondly, comparing the reactions of hydrogen with those of deuterium, it will be seen that the latter require the higher activation energies, the average value of the differ- ence being 1.6 -l 0.6 kcal.This is in agreement with theory7 which predicts that at low temperatures the difference in activation energies for reactions of isotopic molecules should approach the difference in their zero-point energies, which in this case is 1.8 kcal. The values of both P and E for the reaction of CH3 with D2 are somewhat out of line with the others. It is probable that in this case errors in E and P compensate one another, and that the real values of both may be somewhat lower. All that can be said for the moment is that for both CH3 and CD3 the results can be expressed by the average values E7 = 13.5 f 1.5 kcal.CH3 (or CD3) + H2 CH3 (or CD3) + D2 E = 9.7 f 0.6 kcal E = 11.3 i- 0.6 kcal. It is also instructive to consider the relative values of the rate constants at a given temperature, since here the results are not affected by compensating errors in E and P, and such relative values should therefore be somewhat more precise. Thus, at 210" C, for the ratios of values of kA/k3, we have CD3 + D2 3.3 1 3.5 j average 3.4 I average = cH3 + D2 = 0.74 I CD3 + D2 0.7. This gives further confirmation of the considerable effect of the substitution of D2 for H2 and the relatively small effect of the substitution of CD3 for CH3. In one case information is available on the corresponding reaction of ethyl radicals, since Wijnen and Steacie 8 have investigated the reaction C~HS + D2 -+ C2H5D + D CH3 + D2 -+ CH3D + D Comparing this withT. G .MAJURY AND E. W. R . STEACIE 49 we have E kcal PIP,* C2H5 f D2 13.3 31 0.5 10-3 CH3 + D2 11.7 f 0.5 3.5 x 10-3 There thus appears to be little difference in the steric factors of the two reactions. The fact that Es is somewhat higher than E7 is in line with the lower value of the bond dissociation energy of C2H6, which makes reaction (8) 3 or 4 kcal more endothermic than (7). of the bond dissociation energy D(CH3-H) is well established at 101 f 1 kcal9 and that D(H-H) is accurately known, we may write THE REACTION OF H ATOMS WITH METHAF4E.h View of the fact that the Value E 9.2 f 0.5 k u l Es CH3 + H2 CHq + H - 2.2 & 1 kcal. Hence, for the activation energy of the reverse reaction Eg = 9.2 - 2.2 = 7.0 f 1.5 k a l .Considerable work has been done on this reaction, almost all by producing H atoms by means of a discharge. Under these circumstances, it is impossible to obtain sufficient accuracy to determine a temperature coefficient with any precision. The results thus obtained are consistent with values of Eg -= 13 j, 2 kcal, assuming a steric factor of 0.1. In all probability the results obtained at higher temperatures should be disregarded, and the true activation energy may be much lower than this if P is also lower. In view of the many qualitative results which show that the reaction of H atoms with methane is much slower than that with other hydrocarbons, it appears, however, that if Eg is significantly lower than the above figure P must be lower also.If 8-5 kcal is the extreme upper limit of Eg from the present work, there remains a considerable discrepancy in E which must be taken care of by a lower steric factor. It may, therefore, be concluded that the present results can only be reconciled with the results on the rate of reaction (9) if P g is between 10-3 and 10-4. It is of interest to note that the results on the reaction which Professor LeRoy is presenting to this Discussion indicate a lower activation energy, together with a lower steric factor for this reaction also than had pre- viously been inferred from experiments by the discharge-tube method. 1 Trotman-Dickenson and Steacie, J. Chem. Physics, 1950, 18, 1097 ; 1951, 19, 169, 329. Trotman-Dickenson, Birchard and Steacie, J . Chem. Physics, 1951, 19, 163. Raal and Steacie, J . Chem. Physics, 1952, 20, 578. 2 for references to previous work, see Steacie, Atomic and Free Radical Reactions (Reinhold Publishing Corporation, New York, 1946). 3Davis, Chem. Rev., 1947, 40, 201. Noyes and Dorfman, J. Chem. Physics, 1948, 16, 557, 788. 4Dodd, Trans. Farahy SOC., 1951, 47, 56. Durham and Steacie, J. Chem. Physics, 1952, 20, 582. Gomer and Kistiakowsky, J. Chem. Physics, 1951, 19, 85. Lucas and Rice, J. Chem. Physics, 1950, 18, 993. Miller and Steacie, J . Chem. Physics, 1951, 19,73. 5 for a discussion of the status of such frequency factors, see Steacie and Szwarc, J . Chem. Physics, 1951, 19, 1309. 6 Anderson, Davison and Burton, Faraduy SOC. Discussion, 1951, 10, 136. Davison and Burton, J. Arner. Chem. SOC. (in press). We are very much indebted to Dr. Burton for communicating his full results to us prior to publication. 7 Bigeleisen, J . Chem. Physics, 1949, 17, 675. 8 Wijnen and Steacie, J. Chem. Physics, 1952, 20, 205. 9 Kistiakowsky and Van Artsdalen, J . Chem. Physics, 1944, 12,469.