'I 36 REACTION OF METHYL RADICALS THE REACTION OF METHYL RADICALS WITH HYDROGEN BY R. D. ANDERSON, S. DAVISON, AND &I. BURTON Received 29th January, 1951 The reaction between methyl and molecular hydrogen follows the simple mechanism CH, +H,+CH, +H. Interpretations of the older literature are confused by use of low activation energy and low steric factor for this reaction. The effects of reaction order, hot radicals, surface and uncertainties regarding elementary reactions have been largely eliminated. The results lead t o a value of El? 13 kcal. and S1= I O - ~ . The former figure is in agreement with recent best values on activation energy of the reverse reaction and pertinent bond dis- sociation energies. The reaction CH, + H, +CHI + H, . * (1) CH, + RH +CHI + R, , * (2) has received much attention because it is the simplest of the important series where RH represents hydrogen, a simple aliphatic compound, or an oxygen derivative of the latter.However, the activation energy E, and the steric factor for reaction (I) have been disputed. 1 Contribution jointly from the Radiation Chemistry Project operated by the University of Notre Dame under U.S. Atomic Energy Commission Contract AT( I I-1)-38 and the Sinclair Research Project. Sinclair Fellow.R. D. ANDERSON, S. DAVISON AND hl. BURTON 137 Table I includes a list (in chronological order) of the various activation energy values proposed for reaction ( I ) with a brief description of the basis for each value. It will be shown that the new and higher value recom- mended herein of about 13 kcal.for El and a steric factor of about IO-, remove apparent anomalies which exist when the lower values for these quantities are assumed. TABLE ACTIVATION ENERGY VALUES Authors Hartel and Polan yi F. 0. Rice Paneth, Hofeditz and Wunsch Patat and Sachsse Taylor and Rosenblum Cunningham and Taylor Phibbs and Darwent Anderson and H. A. Taylor Davison and Burton Davison and Burton Basis Decomposition of methyl halides by sodium atoms in hydrogen as carrier gas Detection of methyl radicals from pyrolysis of Pb(CH,)* in the presence of hydrogen Recombination of methyl radicals from the pyrolysis of Pb(Cg,), in hydrogen as carrier gas Para-ortho hydrogen conversion in the presence of methyl radicals Photolysis of acetone plus hydrogen Photolysis of mercury dimethyl in the presence of hydrogen Photolysis of mercury dimethyl in the presence of hydrogen Photolysis of cadmium dimethyl in the presence of hydrogen High temperature photolysis of acetaldehyde with deuterium High temperature photolysis of acetone, with deuterium, and with a mixture of hydrogen and deuterium The value of E , may also be calculated from presently accepted bond dissociation energies and the activation energy of the reverse reaction H + CH, --f CH, + H, .where E , = 11 f 2 k ~ a l . , ~ , 4 CHI --f CH, + H - IOI 5 I kcal.5 . * (4) H, 3 2H - 103 kcaLg . - ( 5 ) Hence El should be equal to about 13 kcal. This value agrees excellently' with the new higher value for E, found by Anderson and Taylor and by Davison and Burton.8 In both cases E, has been evaluated by direct experimental methods free from several objectionable features of earlier work.Early Work.-Hartel and Polanyi investigated decomposition of the methyl halides (chloride, bromide and iodide) by sodium atoms in hydrogen as carrier gas. They assumed, for methane production, the mechanism Na + CH,X +NaX + CH, - (6) CH, + Ha +CH, + H. . * (1) Steacie, Darwent and Trost, Faraday SOC. Discussions, 1947, 2, 80. Evans and Szwarc, Trans. Faraday SOC., 1949, 45, 940. 5 Szwarc, Chem. Rev., 1950, 47, 75. 6 Gaydon, Dissociation Energies and Spectra of Diatomic Molecules (Chapman 7 Anderson and H. A. Taylor, forthcoming paper in J . Physic. Chem. 8 Davison and Burton, forthcoming publication. and Hall, London, 1947). Hartel and Polanyi, 2. 9hysik.Ckem. B, 1930, 11, 97.13s REACTION OF METHYL, RADICALS No mention was made of the fate of the hydrogen atoms produced by re- action (I). Furthermore, it was assumed that the methyl radical con- centration was temperature independent. The rates of methane pro- duction were inferred from the rates of hydrogen consumption, and the temperature dependence of the latter provided an estimated El value of 6-8 kcal. The experimental approach did not permit a very accurate estimate of the actual reaction temperature. The low El values pro- posed by Hartel and Polanyi should not, consequently, have received much credence. However, they actually had much in'fluence on later considerat ions. objected to the low value of about 8 kcal. since it led to the result that at 600° C only exp (- 8000/2 x 873) or about IOO collisions of CH, and Ha would be required for reaction.If this low number of col- lisions were correct, it should not be possible to detect methyl radicals in the presence of hydrogen at 600' C. Actually, Rice did detect methyl radicals in experiments carried out under such conditions and on the basis of collision theory, proposed a high El value of about 20 kcal. This estimate would be consistent with El= 13 kcal. and steric factor Paneth, Hofeditz and Wunsch l1 investigated reactions of methyl radicals from thermal decomposition of lead tetramethyl in hydrogen as carrier gas. Although the authors did not do so, an El value of about 15 kcal. was calculated from their data by Patat. Patat and Sachsse l2* la, l 4 published a series of papers concerning occurrence of chain reactions, measurement of methyl radical concentra- tions, and selection of activation energy value and steric factor for reaction (I).Their general procedure was to photolyze or pyrolyze a compound in the presence of para-hydrogen. A steady state hydrogen atom con- centration was assumed due to the reactions Rice SIC= 10-2. and CH, + H, +CH, + H . - (1) H + A + H , + R , . - ( 7 ) where A represents the parent organic compound, e.g., acetone, acetal- dehyde, ether, etc., and R represents a free radical. The usual kinetic treatment yields the expression Experimental procedure kept (A) and (H2) essentially constant. The (H) was determined from the observed rate of conversion of para-hydrogen to ortho-hydrogen by the method of Geib and Harteck.If a very accurate value for K,/K, could have been found, a method for the measurement of the (CH,) would have been available. In order to evaluate the ratio kl/k,, Patat and Sachsse assumed a particular value (- 8 kcal.) for El and used the appropriate E7 value available at the time. The (CH,) in the acetaldehyde case was evaluated on the basis of a detailed decomposition mechanism of Leermakers and was used to complete the evaluation of k1/K7. The selection of a steric factor of about 1 0 - 4 for (I) was a result of the use of the El value of 8 kcal. The entire scheme for measuring methyl radical concentration depends so completely upon assumptions that, in the words of Steacie,16 " it is lo Rice, J . Amer. Chem. SOC., 1934, 56, 488.11 Paneth, Hofeditz and Wunsch, J . Chem. Soc., 1935, 372. 12 Patat and Sachsse, 2. physik. Chem., 1935, 31, 105. Patat, 2. physik. Chem. B, 1936, 32, 274. 14Patat, 2. fihysik. Chem. B, 1936, 32, 294. 15 Steacie, Atomic and Free Radical Reactions (Reinhold, New Yorlr, 1946), P- 64-R. D. ANDERSON, S. DAVISON AND M. BURTON 139 difficult to obtain unequivocal results by this method ”. Nevertheless, Patat and Sachsse calculated methyl radical concentrations by the application of (I) to the decomposition of each substance studied. They then compared the results with the theoretical values obtained by application of a detailed Rice-Herzfeld chain mechanism to each decom- position. Where the latter was not available for a particular reaction, the general expression (CHd EI-E7 Expermental (cal.) (E1==g kcal.in Formula (I)) Substance CH30CH, 797 -2000 Io-11.8 CH3COCH3 820 0 10 -10.23 C2H5CH0 8 20 2000 10-10.04 C3H8 834 0 10-10.2 CH,CHO 820 I 800 10-9.91 was used. hexpt., and kchsin represented the rate constant for the reaction The observed experimental rate constant was represented by CH, + A -+CHI + R. . * (8) Table I1 contains some of the data reported by Patat. The fact that the Rice-Herzfeld theory leads to methyl radical concentrations which are larger in every case than those found by Patat has been used as an argument against the former theory. In column 6 we have recalculated the experimental (CH,) using El = 13 kcal. The methyl radical con- centrations so obtained are in better agreement with those obtained by the Rice-Herzfeld chain mechanism.However, there should be no expectation of close agreement, since the method of Patat l4 for measuring free methyl radical concentration is probably not accurate. In any case, it does not provide sufficient reason for abandoning the concept of chain mechanisms in reaction kinetics. (CH3). (CH3) Theoretical Experimental (Chain (El=13 kcal. Mechanism) in formula (I)) I 0 -9.39 10-10.7 10-9.66 1 0 -9.18 10-8.65 10-8.89 10-9.56 10-9.2 10-8.16 10-8.86 * All concentrations are in reality calculated. See discussion. Taylor and Rosenblum 16 photolyzed acetone in presence of hydrogen. They assumed that methane was produced by reaction (I) and proposed several methods for ethane production. Several mathematical treat- ments were employed with their results to give an average estimate of - II kcal.€or El. Cunningham and Taylor investigated the photolysis of mercury dimethyl in the presence of hydrogen and proposed the following mechan- ism for methane production Hg(CH3)2 + h v +- 2CH3 + Hg . - (9) CH, + H2 +- CH, + H . - (1) H + Hg(CH3)z -+ CHI + HgCH3 - (10) By the usual steady state treatment, they were able t o show that the rate of methane production was proportional to the product of concentra- tion of methyl radicals and concentration of hydrogen. They assumed both of the latter to be constant over the temperature range studied and l6 Taylor and Rosenblum, J . Chem. Physics, 1938. 6, 119. l7 Cunningham and Taylor, J . Chem. Physics, 1938, 6, 359.130 REACTION OF METHYL, RADICALS found El = 8.1 kcal.from the temperature dependence of the rate of methane formation. However, they referred to the work of Hartel and Polanyi, and of Taylor and Rosenblum, and then reported g f 2 kcal. as the “ most trustworthy ” value for El. In a further study of mercury dimethyl Phibbs and Darwent l8 showed that a “ h o t ” methyl effect was a plausible explanation for results of photolysis in the presence of hydrogen. Should this effect persist into the higher temperature range, the calculated value for El would be lower than the true one. Since methyl radicals have been shown to react with metal deposits, a back reaction between methyl radicals and mercury undoubtedly takes place. A complication arises from the fact that at lower temperatures any mercury set free during photolysis is deposited almost entirely on the walls of the reaction vessel, while in the high temperature range, the mercury would exist entirely as a vapour.Any back reaction of methyl radicals with mercury would be of a heterogeneous nature in the former cases, but of a homogeneous nature in the latter case. Recent Experimental Results .-Anderson and Taylor investigated the photolysis of cadmium dimethyl in the presence of hydrogen. Enough runs were made to permit calculation of rates of methane production at zero time. The quartz reaction vessel was a short cylinder 5 cm. long which was fitted at each end with plane quartz windows 10 cm. in dia- meter. The surface of each window was irradiated by its own 2537 A light source. The relatively large surface irradiated prevented serious light attenuation by the cadmium deposits produced during photolysis.It should be noted that the cadmium was deposited almost entirely on the walls of the reaction vessel over the complete range of temperature em- ployed (5ooC to 250’C). Hence, any back reaction between methyl radicals and cadmium would be of a heterogeneous nature at all times. Certain precautions were taken to ensure accurate temperature control. The furnace containing the reaction cell was controlled automatically so that its temperature was within 0.1’ C of the desired temperature. The light sources were in a thermostat whose temperature was within 0.2’ C of the constant temperature at which the latter was maintained. Suf- ficient pre-heating periods were used so that the reaction mixture would be at the temperature of the furnace during a run.Loading of the reaction vessel was carried out in such a way that no mercury vapour could enter the reaction vessel, and all analyses were carried out on a Consolidated Engineering mass spectrometer. The cadmium dimethyl used was made from the Grignard reaction involving methyl magnesium iodide and anhydrous cadmium chloride in ethyl ether. The last traces of ether were removed from the crude product by very efficient fractional distillation. The resulting product had a freezing point of - 2.4’ C over the entire range of solidification. The important part of the decomposition mechanism is as follows : Cd(CH,), + hv -+ 2CH3 + Cd * (11) 2CH3 + C,H,. (12) CH, + H, --f CH, + H .* (1) H + Cd(CH,), -+CH, + Cd + CH, . * (13) The reaction of methyl radicals with cadmium dimethyl to yield ethane was ruled out as insignificant since ethane production was independent of the concentration of cadmium dimethyl. A plot of log B,, against I / T gave a line whose slope increased constantly with increasing temperature. The best explanation of this was an increasing concentration of methyl radicals. From reaction (12), RlZ = h12 - (CH,I2 - . (111) :. (CH,) = (R12/K12)*. . . (IV) Phibbs and Danvent, Trans. Faraday Soc., 1949. 45, 541.R. TI. ANDERSON, S. DAVISON AND M. BURTON 141 However, the total rate of methane production, and by the usual steady state treatment Rm = 2K1. (CH,)(H,) . - (VI) But (H,) is essentially constant and may be set equal to B .When the proper substitutions are made for (CH,) and (H,) in (VI), there is obtained the expression The different (R,/Rl,*) values were substituted in pairs in the integrated form of the Arrhenius equation in such a way as to make equal use of all values. Temperature interval weighting was employed, and the final ( E l - +El,) value obtained was 13 f z kcal. I f the value of El, is taken as zero, then El = 13 f z kcal. A consideration of the energies involved in the reactions Cd(CH,), -+ 2CH, + Cd * (14) and Hg(CH3)2 --t 2CH3 f Hg * (15) indicates that the " hot '' methyl effect in the case of cadmium dimethyl should be much less than that attributed to mercury dimethyl. Actually no such effect was found with cadmium dimethyl over the range where methane analysis was accurate.The low El value (9 kcal.) and the low steric factor (10-4) sponsored by Steacie et aZ.,, 2 o for reaction (I) seem to be based upon the work with mercury dimethyl, whose defects have been noted above, and upon the conclusions of Patat and Sachsse in their attempt t o reconcile their experi- mental data with the low El value proposed by Hartel and Polanyi. The new high value for El removes the need for assuming a low steric factor to account for the slowness of reaction (I) at ordinary temperature. Furthermore, the work of Evans and Szwarc 4 shows that relatively high steric factors are to be expected for reactions between methyl radicals and the simple hydrocarbons. Reaction ( I ) is practically in this class, and Davison and Burton actually found a steric factor of -10-2 for ( I ) .Davison and Burton * studied photolpses of acetone and of acetal- dehyde in presence of deuterium, and in presence of equimolar mixtures of hydrogen and deuterium. One result of this work was elucidation of the mechanism of the reaction between methyl and molecular hydrogen. Eyring and his associates 21 calculated a potential energy surface for re- action (I). They proposed formation of a stable CH,-H, complex based upon a rather deep hole intercepting the path of reaction on the potential energy surface. Methane formation could then be ex- plained as reaction of this complex with another methyl radical. As a matter of fact, Taylor and Burton 2 2 had indicated that some of the diffi- culties presented by the Patat and Sachsse results were explicable on the basis of such a termolecular mechanism.However, the experimental results of Davison and Burton indicated that such a reaction was extremely unlikely since a value of - I was obtained by them for the ratio HD/CH,D during the photolysis of acetone plus deuterium. Such a ratio would be expected from the successive reactions CH, + D2 -+CH,D + D - (16) and D + C,H,CO -?. HD + CH,COCH,. * (17) 19 Long and Norrish, Phil. Trans. Roy. Soc. A , 1949, 241, 587. 2o Trotman-Dickenson and Steacie, J . Chem. Physics, 1950, IS, 1097. 22 Taylor and Burton, J . Chem. Physics, 1939, 7, 676. Gorin, Kauzmann, Walter and Eyring, J . Chem. Physics, 1939~ 7, 633.142 REACTION OF METHYL RADICALS The formation of HD and the value of the ratio HD/CH,De I provide strong evidence for the reality of reaction (I).When acetone is photolyzed in the presence of deuterium by the self- reversed radiation of a high pressure mercury arc, reaction (16) is ac- companied by The pressures of acetone vapour and deuterium are essentially constant so that it is possible to write CH, + (CH,),CO -+ CH, + CH,COCH,. . - (18) (VIII) In order to ensure the strict applicability of (VIII), and also to minimize the effect of side reactions of the products such as the experimental rates of methane production were corrected to zero time at each temperature. A plot of log (h16/i&) against I/T for different temperatures in the range from 1 5 0 O C to 4z5O C was then used to deter- mine the quantities (& - E18) and &6/&8, where S is used to represent steric factor.A similar procedure was used for the photolysis of acetal- dehyde in the presence of deuterium. Reactions (I) and (16) should have different rate constants because of the difference in zero point energies of H, and D,. To correct for this difference, a series of runs was made where acetone was photolyzed in the presence of an equimolar mixture of hydrogen and deuterium. Since some methane arises by reaction (18) it is necessary t o calculate this amount .by substituting the known (CH,D) in (VIII). This correction is subtracted from the total (CH,) resulting from the photolysis of acetone in the presence of deuterium and hydrogen. The (CHJcorr. and the measured (CH,D) are then used in the following expression D + CH, -+CH,D + H - (19) to evaluate the ratio &/k16 at different temperatures. A plot of log (kl/&) against I/T will permit the evaluation of (El6 - El) which was found to be 1-1 kcal.The difference in zero point energies between the H, and D2 molecules is 1.8 kcal. Since this method yields differences in activation energies and ratios of steric factors, it is necessary to select suitable reference points. Trotman-Dickenson and Steacie 2 o have studied the rates of production of methane and ethane in the photolysis of acetone and have arrived at the values El, - +El, = 9.7 kcal. Similar work by Saunders and Taylor 23 gave a value of 9.6 kcal. for The work of Grahame and Rollefson a4 on the high temperature and S,*/S,,B = 10-3. (El8 - *-w- photolysis of acetaldehyde where CH3 + CHSCHO + CH4 + CHaCO * (20) gave a value of 8.6 kcal.for (E20 - *El$). Since other experimental work indicates a small or zero value for El, we can set E12 = o in the above expressions. Recent work by Gomer 25 and by Szwarc and Roberts 26 shows that S,, is close to unity. From the assumption S,, = I 2s Saunders and Taylor, J . Citem. Physics, 1941, 9, 616. 24 Grahame and Rollefson, J . Chem. Physics, 1940, 8, 98. 25 Gomer, J . Chem. Physics, 1950, 18, 998. 26 Szwarc and Roberts, Trans. Faraday Soc., 1g50,46, 625.R. D. ANDERSON, S. DAVISON AND M. BURTON 143 and the quantities evaluated by Davison and Burton El6 - El = 1-1 kcal. El6 - El, = 4.6 kcal. El, - E,, = 6 2 kcal. and sl*/sl = 10-1, the data of Table I11 have been calculated. El kcal. from Reaction (CHdaCO CHsCHO TABLE III.-DAVISON-BURTON RESULTS Steric Factor CH, + H2 -+ CH, + H CH, + D, -+ CH,D + H In the case of acetaldehyde the hot radical effects are insignificant because the experiments were conducted in a temperature range where the chains were long. Thus, if the difference between the results from acetone and acetaldehyde is real, the upper values are to be preferred. The Davison-Burton method is completely independent of assumptions regarding the methyl radical concentration since methane production was always first order with regard to the (CH,) terin which cancelled out of the kinetic expressions used. Hence, it is not necessary to main- tain a constant value of (CH,) throughout the reaction vessel during the runs. Department of Chemistry, For the same reason, constant light intensity is not required. University of Notre Dame, U.S.A. I 3-2 10-2 14-3