II. HYDROCARBON REACTIONS A. THERMAL REACTIONS THE THERMAL DECOMPOSITION OF HYDROCARBONS BY F. J. STUBBS AND C. N. HINSHELWOOD Received I 5th February, 195 I The following topics are discussed in the course of a general survey of the decomposition reactions of the normal paraffins : the nature of the radical- chain reactions, the probability that the residual reaction after nitric oxide inhibition of chains is a molecular reaction, the rate-pressure law which indicates that the mechanism is kinetically composite, the variation of activation energy with pressure, the relative probability of rupture of the carbon chain a t various points, and the interpretation of experiments on the composition of products. Further questions about energy-entropy relations in unimolecular reactions arise in connection with these various matters.The thermal decomposition of a paraffin follows the overall course : Higher paraffin = lower paraffin + olefine. The detailed occurrences can be formulated equally well as molecular reactions involving a relatively simple transfer of hydrogen accompanied by the splitting of a carbon-carbon bond, and, alternatively, as chain reactions initiated by the splitting of the paraffin into two radicals which then suffer further changes. The olefine is sometimes relatively stable, and sometimes suffers a rapid subsequent decomposition into a pair of molecules of lower olefines, or other more complex reactions. The general conclusion reached from a considerable amount of ex- perimental work is that the chain processes and the purely molecular processes occur simultaneously, and in the following section the evidence for this will be reviewed.The kinetic relations observed in both these types of process possess considerable interest in connection with the theory of reaction velocity, and in fact open up some new aspects of the theory of unimolecular re- actions generally. This bei-ng so, the first important matter is to examine with some care the status of the supposed molecular reaction, The Suppression of Radical Chains and the Question of the Nature of the Residual Reaction.-Nitric oxide, which suppresses radical chain reactions, reduces the decomposition rate of the paraffins to a constant limiting value. The residual reaction might be (a) the primary process of what in the absence of inhibitors would be a chain reaction, (b) the usual chain reaction imperfectly suppressed by nitric oxide, (c) a surface re- action, (d) a second type of chain reaction not influenced by nitric oxide, (e) a molecular reaction.(a) is supported by Steacie and Folkins,l who found that the products formed from butane have the same composition whether the rate is con- trolled by nitric oxide or not. They consider that a chain reaction and a competing molecular reaction would not yield the same products in the same proportions. The inhibited reactions usually account for a fifth to a third of the total normal change and if they are all primary processes this implies very short chains. Now while initially formed radicals can in fact easily go through cycles of reaction to give the same Steacie and Folkins, Can.J . Res. B , 1940, 18, I. E 129DECOhlPOSITION O F HYDROCARBONS products as the molecular processes would give, they could hardly do this if they all reacted with nitric oxide. On the whole, therefore, the evidence from the work of Steacie and Folkins might be taken to support the opposite view at least equally well. (b) has been put forward by Echols and Pease a on the basis of ob- servations with n-butane with and without nitric oxide. The Ap-time curves tend to become parallel as the reaction proceeds, giving the im- pression that the inhibition ceases (although hardly any nitric oxide is consumed). Echols and Pease assume an equilibrium in which as many radicals are regenerated from a combination with nitric oxide as are removed. This explanation is unsatisfactory because, firstly, propylene reduces the rate to the same limiting value as nitric oxide, and the forms of the A$-time curve of the inhibited reactions are the same ; and secondly, direct addition of extra nitric oxide during the reaction has no further effect.3 The apparent acceleration in the Ap-time curve is in fact an in- herent property of the reaction, and due to stoichiometric causes.The sigmoid nature of the curve for the fully inhibited reaction becomes more evident as the paraffin series is ascended. The higher paraffins on decom- position yield higher olefines which themselves subsequently decompose with further increase of pressure, whence the apparent acceleration. The Ap-time curves for the reactions with and without nitric oxide tend to become parallel not through the ceasing of nitric oxide inhibition but rather (as shown by direct experiment) because in the normal decom- position the olefine formed assumes the role of inhibitor.(c) has to be considered carefully as the evidence may easily be mis- leading. Surface has little or no effect on the uninhibited decomposi- tion, so that the chains are broken in the gas phase. The nitric oxide- inhibited reaction, however, in certain cases shows a slight apparent retardation by increased surface, and this becomes quite marked in a vessel whose internal surface is coated with potassium chloride. These effects prove, however, to be secondary.* In the early stages nitric oxide may catalyze a quite independent condensation reaction, and the re- sultant pressure decrease vitiates the measurement of the true decom- position rate.In uncoated vessels this effect is transitory, but in potassium chloride-coated vessels it is more serious. If, however, propyl- ene is used as inhibitor, the limiting rate is measurable without this dis- turbance, and is exactly the same as that observed in a vessel with a clean silica surface. The conclusion is that the residual reaction is essentially homogeneous. (d) A possibility for a second kind of chain reaction is one involving hydrogen atoms which might conceivably be immune to the action of nitric oxide. In presence of added hydrogen there would be replacement of alkyl radicals by hydrogen atoms generated in the reaction and since this would occur in competition with their removal by nitric oxide, more of the latter would be required to produce a given degree of inhibition.Now addition of hydrogen does in fact cause a marked increase in the rate of the uninhibited decomposition, so that the chains are evidently lengthened when hydrogen atoms replace methyl radicals according to the reaction shown above. But the limiting value to which the rate is lowered by sufficient nitric oxide is very little changed and moreover no greater amount of nitric oxide is now required for a pro- portional reduction of rate.4 It is highly unlikely, therefore, that the residual reaction depends simply upon hydrogen chains unsuppressible by nitric oxide. CH,. + HZ -+CHI + He, a Echols and Pease, J .Amer. Chem. SOL, 1939, 61, 1024. Stubbs and Hinshelwood, Proc. Roy. Soc. A , 1950,200, 458. Stubbs and Hinshelwood, Proc. Roy. Soc. A , 1950,201, 18 ; Ingold, Stubbs and Hinshelwood, Proc. Roy. SOC. A , 1950, 203, 486.F. J. STUBBS AND C. N. HINSHELWOOD ( e ) In the light of the foregoing facts and until evidence for somc alternative mechanism appaers, there is a prima facie case for the con- clusion that the reaction observable when the rate has been reduced to its limiting value by propylene or nitric oxide is that of a molecular de- composition of the hydrocarbon. It is of interest, therefore, to consider what properties this molecular reaction, if indeed it is such, possesses. This question will be discussed in a later section. General Characteristics of the Chain Reactions.-Firstly, however, we should deal with the chain reaction itself.For the thermal decomposition of a straight chain paraffin the types of process involved must be as follows : (I) Initiation steps : e.g. RH = R, + R,. ( 2 ) Reaction of radicals with hydrocarbons : e.g. ( 3 ) Further breakdown of radicals (4) Recombination of radicals, e.g. : 2R, = R,Rl. ( 5 ) Reaction of radicals with inhibitors, e.g. : (I) must clearly result in the production of alkyl radicals or hydrogen atoms. ( 3 ) gives lower alkyl radicals or hydrogen atoms. From the results referred to in the preceding section we may infer that no important kinetic differences in the overall character of the reaction arise if alkyl radicals are replaced by hydrogen atoms in ( 2 ) . ( 3 ) is necessary to account €or olefine production in the chain process. An important kinetic difference arises according as to whether an in- hibitor such as NO reacts predominantly with a radical which would otherwise have suffered a decomposition of type (3), or with one which would normally have reacted with more paraffin as in ( 2 ) .A decision as to which case prevails can be reached by studying the rate as a function of nitric oxide pres~ure.~ If Y , is the rate of the uninhibited reaction, Y that at a given nitric oxide concentration and vrn that at high nitric oxide concentrations, then where y is a function independent of [RH] when all the radicals affected by nitric oxide suffer alternative processes of type (3). This case is in fact found in the thermal decomposition of ether.6 Actually with the hydrocarbons y varies inversely as a power of [RH] which in various examples has been found to lie between 0.71 and 1.0.From this may be concluded that direct attack on the hydrocarbon occurs in competition with removal by the inhibitor. This suggests that any processes of type (3), that is, decompositions of longer alkyl radicals into olefine and shorter alkyls are usually rapid. The overall reaction (for the chain part of the decomposition) is usually of an order in the hydrocarbon which is between I and 2 . The rate of process (I) can vary as a power of [RH] between I and 2, that of z will be of the first order in [RH] itself, while (4) could either be inde- pendent of [RH] or involve it as a first power if ternary collisions played a part in the radical recombination.No particular problem arises, therefore, in accounting for the fractional order of the total reaction with respect to [RH]. The apparent chain length (which really indicates the relative pro- portion of chain reaction to molecular reaction) decreases as the initial pressure becomes greater, as the temperature rises, and as the number of carbon atoms in a normal paraffin increases. 5 Hobbs and Hinshelwood, Proc. Roy. Soc. A , 1938, 167, 439 ; Staveley, Proc. Roy. SOC. A , 1937. 162, 557. BHobbs, Proc. Roy. Soc. A , 1938, 167, 456. Rl + RH = R,H + R. R,CH,CH,- = R, + CH, : CH,. e.g. R, + NO = KINO. (Y - Yrn)/(Yo - Yrn) = {(r"O1)Z + I)+ - r"O1,1 32 DECOMPOSITION OF HYDROCARBONS The Rate-Pressure Law for the Molecular Reaction.-The rate of reaction has sometimes been represented as proportional to the 3 / 2 power of the pressure, but this is an oversimplification of the facts.In general, it varies as a power of the pressure between the first and the second, and with the higher paraffins (for the residual molecular reaction) is expressible over a considerable range by the formula : With ethane it conforms to the simple expression for a unimolecular reaction with collisional activation, showing a transition from second order to first as the pressure rises. With propane there is conformity with the expression rate = A p , + Bpo2. and there is, therefore, good reason to suppose that the general form should be the reaction mechanism being composite.4 On any other view it would be difficult to explain how in general over a considerable range of pressure a second order process gains predominance over a first order process, and then may subsequently return towards the first order.Two matters are relevant to the assessment of this result. In the first place, there is the question how far the pressure-time measurements constitute a valid criterion of reaction rate. They appear in fact to be quite satisfactory for comparative measurements on a given paraffin over a range of temperatures and pressures, since the curves of Ap against time for widely different conditions can be brought into complete super- position by simple changes of scale. The second question is how far the different kinetic mechanisms are associated with the formation of different sets of chemical products.This, remarkably enough, appears not to be so, as will be shown in another section. Variation of Activation Energy with Pressure.-One of the most interesting characteristics of the normal paraffin decompositions is that from n-butane upward the activation energy of the molecular reaction becomes a well-defined function of the pressure. The pressure variation, moreover, is closely correlated with the kinetic behaviour. With ethane, where E is constant, the reaction is of the first order except at lower pressures (where the normal transition to the second order occurs). In other words, there is no evidence of a kinetically composite character, and the results can be interpreted in terms of a single unimolecular reaction.A similar result has more recently been found by Mr. M. G. Peard with isobutane which satisfies the conditions of a single unimolec- ular reaction, and likewise shows no variation of E with pressure. On the other hand, with the higher normal paraffins there is a steep fall in the value of E as the pressure is increased, and this corresponds to an increasing predominance of the p 2 term in the expression for the reaction rate (see previous section). By extrapolation to low and high pressures respectively, the following values are found : %-Butane . n-Pentane . n-Heptane . E (kcal.) Lowest Pressures 69 93 88 High Pressures 9 63 59F. J. STUBBS AND C. N. HINSHELWOOD I33 A given paraffin chain can of course break in various ways yielding, for example, methane or ethane as the saturated product.These alter- natives do not, however, correspond to reactions with a different pressure or temperature dependence as shown by the analytical results to be referred to later. What we must probably conclude is that there are kinetically different modes of activation, corresponding to different relations between total energy in the molecule, energy required in a critical location, and the decomposition probability of the energized molecule. Relation to the Theory of Unimolecular Reactions.-The prima facie case statable on the basis of the experimental results and open to theoretical analysis is as follows. At low pressures large total energy accumulations in the molecule have time for redistribution, and provoke decomposition when an appropriate part is concentrated in the right bond, as in the classical theory of unimolecular reactions.' There is no difficulty with molecules of the size of butane and the higher paraffins in accounting for an energy accumulation rapid enough to provide the necessary activation rate.At higher pressures, however, an increasing part is played by a process in which a smaller amount of energy enters the molecule in a more specificially distributed manner, possibly even causing an immediate activation of one of the critical bonds. Unless decomposition super- venes rapidly this energy will flow into the rest of the molecule. This mode of activation is attended, therefore, with the necessity for rapid transformation of the molecule, and it remains of the second order up to considerably higher pressures.It involves a lower activation entropy as well as a lower activation energy, but, on balance, can compete with the other mode of reaction. Being of the second order over a large part of the experimental range, it gains on its competitor as the pressure rises. The picture thus disclosed widens in one rather interesting respect our usual conception of the energy-entropy relations in decomposition reactions. In so far as the total energy in a molecule may be thought of as the sum of amounts associated with individual bonds, the probability of a given distribution, with El in the first bond, E, in the second and so on, is proportional to e - WRT . e - EatRT . . . i.e,, to e - ~ Q I R T . A given total E can be made up in very many different ways, so that the probability of its occurrence is the sum of a great many terms of the above type which will come to Fe - E I R T , where F is large.The chance that this energy shall be localized (in the simplest model in a single bond) so as to give the transition state of the reaction, is a small fraction only of this, which, for the case of a localization of E , out of the E may be written f ( E , E,) Fe - EIRT = Ae - E P T . The temperature coefficient of the reaction is determined by E rather than E,, so that the activation energy is high. f ( E , E,) will, in general, be small but F is very large, so that A , which determines the entropy of activation, can be high. Roughly speaking, the reason why the entropy factor can be large while the activation energy is high is that although E is a large quantity, the amount of energy per degree of freedom to which it corresponds is not very many times the average when the molecule is fairly complex.Now although the probability of correct localization of this energy is small in any interval of time, dt, the whole long period between molecular collisions is available, and the reaction occurs 7 Rice and Ramsperger, J . Amer. Chem. SOC., 1927, 49, 1617; Kassel, J . Physic. Chem., 1928, 32, 225 ; Eley, Trans. Faraday Soc., 1943, 39, 168 : Evans and Rushbrooke, Trans. Faraday Soc., 1945, 41, 621 ; Barrer, Travs. Faradny sot., 1948, 44, 399.I 3 4 DECOMPOSITION OF HYDROCARBONS irrevocably should the correct distribution be reached for an infinitesimal fraction of this period.Let us now envisage the actual entry of energy into a molecule in a collision. This will in the very first instant be a quite localized affair, and the energy communicated may be thought of as entering one bond first and then being dissipated throughout the molecule in the course of a very brief relaxation time. If E,1 is communicated, E , may remain in the bond long enough for decomposition to occur. It is quite reason- able to suppose that EO1 - E , is very much smaller than E - E,. The activation energy will now be much lower than before, but the entropy of activation will be small also, since it contains no large factor F but corresponds to the requirement of a more or less precisely defined collision. Of course even with Eol in the whole molecule, E , would eventually collect into the required bond without a collision, but the time required for this would be longer than the interval during which the molecule is normally left undisturbed, and so the contribution to observable reaction would be negligible.Position of Rupture of the Carbon Chain.-When a straight chain paraffin decomposes it gives a lower paraffin and an olefine, the saturated fragment being always the shorter of the two. The probability of rupture is nearly always greatest at the link between the first and second carbon atoms, methane being the paraffin formed in highest proportion. The probability of rupture at the second link, that is, between the second and third carbon atoms, is in general rather lower, though the proportion of ethane is considerable.The formation of propane and higher paraffins is very much smaller. The rapid fall in the probability of rupture with distance from the end of the chain is shown in Table I. TABLE I.-RELATIVE PROBABILITIES OF BOND RUPTURES n-Butane . n-Pentane . n-Hexane . $2-Heptane . n-Octane . 1'0 1'0 1'0 1'0 1'0 1'0 0.78 0.5 0.64 1'0 L 0.25 0.35 0'10 In view of the fact that the activation energy for the higher paraffins varies with pressure, and that the kinetic relations indicate a composite mechanism, it is tempting at first sight to associate the various modes of rupture with processes of different activation energy. This supposition, however, would be incorrect. -4 detailed analytical investigation which Mr. K. U. Ingold 8 has recently made in this laboratory has shown that the relative proportions of the saturated hydrocarbons formed in the decomposition of n-hexane, n-pentane and n-heptane are independent of temperature and pressure over a range where marked shifts would certainly occur were their production conditioned by activation energy differences comparable with those actually observed.It appears, therefore, that the methanelethane ratio which measures the relative probability of rupture at the two different places, is deter- mined by processes of nearly equal activation energy. Inspection of the normal modes of vibration of a long carbon chain reveals no consistently applicable reason why the CIp2 and CZp3 ruptures should be so greatly favoured. On the other hand, thc relatively small differences between the methane and ethane fractions compared with the large drop in the frac- tions of any higher paraffins is suggestive of an electronic effect where 8 Ingold, Stubbs and Hinshelwood (in course of publication),F.J, STUBBS AND C. N. HINSHELWOOD I35 methyl and ethyl have a much greater facility than any higher alkyl groups for capturing an extra hydrogen atom. The delocalization of electrons in the bonds of methane is believed to confer extra stability upon it.O With ethane there is also a considerable measure of sym- metry which will favour delocalization, but with propane and any higher paraffin the carbon-carbon valency angles are such as to lower markedly the symmetry of the system of hydrogen atoms regarded as a whole. That the symmetry of the complete set of six hydrogens in ethane confers stability in a way analogous to the delocalization in methane is a possi- bility which might be susceptible of an interesting theorctical treatment.Comparison of Paraffins and 0lefins.-In comparable ranges of tem- perature a major difference between paraffins and olefins is that the reactions of the latter show no evidence of chain processes according to the usual tests. In view of the fact that olefines are themselves effective inhibitors of radical chain reactions this is not surprising. FIG. I. The general course of the decomposition is a little complex, and for the example of propylene in the range 570-650° has been examined in this laboratory.1° Primary fissioii of the propylene is followed by co- polymerization of activated intermediates with more propylene, and this reaction in turn by further breakdown and further polymerization. A generally similar course probably applies to the reactions of higher olefins, recently studied by Miss M.J. Mo1era.l' The rate under these circum- stances is mainly determined by the primary fission (activation energy 57 kcal. for propylene, 53 kcal. for hexene-I, considerably less than that found by Szwarc l2 for a more profound fission into radicals which inter- venes about 150' higher). Remarkably enough the reactions show none of the signs of composite kinetics, and are uniformly of the first order (with the usual tendency towards the second order at low pressures). The activation energies are generally lower than those for the corresponding paraffins. In Fig. I rates for paraffins and olefines are compared directly (the two branches of the curve for the latter corresponding to extreme 9 Coulson, Quart. Eev., 1947, t, 144. lo Ingold and Stubbs, J. Chem. SOC. (in press). l1 Molera (unpublished observations). l2 Szwarc, J . Chem. I'hyszcs, 1949, 17, 284.'I 36 REACTION OF METHYL RADICALS assumptions about the relation of pressure change and actual amount of primary decomposition). The higher olefines decompose more rapidly than the paraffins with an equal number of carbon atoms. This fact, taken in conjunction with the simpler order of the primary fission, suggests that the initial seat of reaction with the higher olefines is adjacent to the double bond in each case. It is perhaps tempting to attribute this to the circumstance that there is a greater relative gain in symmetry of structure accompanying the primary fission in changes such as 9 CHECH + CH3CHzCH3 CH, = CH . CH,CH,CH,< CH,=CH, + CH,=CHCH, than there is in CH,CH,CH2CHzCH3 -+ CH, -t CHz=CH - CHZCH,. With propane, however, there is a great gain in the process and this is in fact slightly faster than the .decomposition of propylene of which the first step is probably CH,CH,CH3 -+ CH, + CH,=CH, CH,CH=CH, -+ CH=CH + CH,. In the absence, however, of a quantitative measure of symmetry such considerations unfortunately lack precision, and will therefore not be enlarged upon. Physical Chemistry Laboratory, South Parks Road, Oxford