BATEMAN, GEE, MORRIS AND WATSON 259 THE KINETICS OF OXIDATION OF HYDRO- CARBONS IN THE GAS PHASE A THEORY OF THE LOW-TEMPERATURE MECHANISM BY M. F. R. MULCAHY Received 2nd January, I 95 I It is suggested that the mechanism of oxidation of hydrocarbons in the gas phase in the region of 200-300° C is basically similar t o that shown by Bolland and others to occur in the oxidation of more reactive hydrocarbons in the liquid phase at lower temperatures. The kinetic consequences of such a mechanism are worked out for the conditions which occur in gas phase experiments and shown to be in agreement with the experimental results. Introduction.-Evidence has accumulated that in the oxidation of many organic compounds at not too elevated temperature, the first product to be formed is a hydroperoxide,* viz.RH + O8 + ROOH. . * (1) The evidence is most clear in the cases in which the molecule contains a weak C-H bond (e.g. aldehydic, s, 6m * or a to a double bond or conjug- ated system 1, 8s 6 ) , presumably since the reaction proceeds at measureable speed at a sufficiently low temperature for the resultant hydroperoxide to remain undecomposed. On the other hand, such low-temperature * For examples, see ref. (I)-(8). 1 Farmer and Sutton, J . Chem Soc., 1942, 139. George, Rideal and Robertson, Proc. Roy. SOC. A , 1946, 185, 288. Almquist and Branch, J . Amer. Chem. Soc., 1932, 54, 2293. McDowell and Thomas, J . Chem. SOL, 1949, 2208. 6 Wittig and Pieper, Liebig’s Ann., 1941, 546, 142. 6 Bolland, Proc. Roy. SOC. A , 1946, 186, 218. 7 Badin, J .Amer. Chew. Soc., 1950, 72, 1550. Bowen and Tietz, J . Chem. SOL, 1930, 234.260 LOW TEMPERATURE MECHANISM oxidatjons are catalyzed by decomposing peroxides 6* sp l o p loa and, in suitable circumstances, may become autocatalytic, hydroperoxide being regenerated faster than it is decomposed. There is ample evidence that these reactions proceed by free radical chain mechanisms. The experiments of Cullis and Hinshelwood,ll of Egerton and Young,12 and others have shown that during the gas-phase oxidation of hydro- carbons at 200-300° C the peroxide content of the mixture rises to a maximum and falls away again, the maximum peroxide concentration being reached close to the time at which the maximum rate of pressure change occurs.11 Cullis has obtained evidence that during my one reaction (with hexane) the rate of pressure change is proportional to the instantaneous con- centration of peroxide.It is the purpose of this communication to examine to what extent the type of kinetic mechanism shown by Bolland %I4 and others to be operative in reactions proceeding in the liquid phase near room temper- ature may also apply to the oxidation of hydrocarbons in the gas phase in the region of 200-300° C. Probably the three most outstanding phenomena associated with the low temperature oxidation of hydrocarbons in the gas phase are (a) the autocatalytic nature of the reaction, (b) the steep dependence of the maximum rate of pressure change on the initial partial pressure of hydro- carbon combined with independence of the oxygen pressure (both under conditions of excess oxygen) l1 and (c) a large effect of the structure of the hydrocarbon on the maximum rate which, for example, increases about fivefold with each successive member of the paraffin series.1l If then a mechanism is to be considered valid for these conditions it is necessary at least to show that it provides an explanation of these basic facts.The Reaction Mechanism.-If, by some means, the radical R (or RO,) is produced (at the rate given by 4), then hydroperoxide is formed by the following reactions : R- + 0 2 -+ ROZ- . (2) ROZ- + RH -t RO2H + R- . * (3) RO2- + ROZ- -+ X . * (4) R-++- - t X . - ( 5 ) Chain termination may occur either by bhnolecular recombination of radicals, viz. { RO2 + R -tx . * (6) A or by some reaction first order with respect to the radicals, e.g.by collision with the wall or with some other (inhibiting) molecule ROS--+X . * (4’) B {Ib 4 x . * (5’) Chain termination of type A leads (for long chains) to the following expression : l4 * (1) --= dP21 d[ROOHI - --- d[PI %d* [RHI [Ozl dt dt - dt - KZK4) [O,] + K3k5) [RH]’ Chain termination of type B yields 9 George, Proc. Roy. Soc. A , 1946, 185, 337. 10 Bolland, Trans. Furaduy Soc., 1950, 46, 358. 10a Robertson and Waters, Trans. Faruday SOC., 1946, 42, 201. 11 Cullis, Hinshelwood, Mulcahy and Partington, Dzscusszon Fuvaduy Soc., 12 Egerton and Young, Trans. Faraduy SOC., 1948, 44, 755. 13 Cullis, Thesis (Oxford, 1947). 1947, 2, 111. 14 Bolland, Quart. Rev., 1949, 3, I.M. F. R. MULCAHY 26 I Except for the exponent of r j l both expressions are of the same form with regard to the concentrations of oxygen and hydrocarbon, and for our present purposes need not be distinguished.However, it may be remarked that, for a gas phase reaction, first-order chain termination (B) seems the more probable. In uncatalyzed reactions 4 is a function of [RH] and [O,]. Where peroxide decomposition is the only initiating reaction 4 is a function of [PI. Derivation of an Expression for the Maximum Rate in Terms of Initial Concentrations.-We shall take as our fundamental assumption that the rate of pressure rise is given by p = 22 = K[P], . (111) dt where K is a numerical constant. In the system under discussion in which peroxide is both decomposing and being regenerated at comparable rates, we have for the rate of change of peroxide concentration : dB = A + B[P] - C[P].. dt A is the rate of production of peroxide in the absence of peroxide, and is of the form (see eqn. (11)). This gives the rate at the very beginning of the reaction and in a favourable case may approximate to the rate during the in- duction period.l% lo B[P] gives the rate of peroxide production produced by autocatalysis. B is of the form This term is taken proportional to the first power of the peroxide con- centration, without deciding whether this results from unimolecular radical-producing decomposition of the peroxide followed by first-order termination reactions (eqn. (11)) or bimolecular decomposition (which occurs in solution in some cases14) followed by second-order radical recombination (eqn.(I)). * C is a constant which allows for the possibility that the peroxide may also decompose (unimolecularly) in a manner which does not give rise to active radicals. We may now write where K is a constant including the speci,fic rate of chain initiation by per- oxide breakdown. We shall not deal further with the very early part of the reaction, but shall consider the (usual) case in which the rate during the induction period is very small compared with the rate subsequently attained. This means that from the end of the induction period, the contribution of A to the rise of peroxide concentration may be neglected. We have therefore from (IV) ( V I ) l5 Mulcahy, Trans. Faraday SOC., 1949, 45, 575. 16 Ridge and Mulcahy (to be published).* The molecularity of the initial act of decomposition of hydroperoxides in the homogeneous gas phase is not known. has found that when hydroperoxides are caused to decompose per se, the reaction occurs largely a t the walls of the vessel. Harris Harris, PYOC. Roy, SOC. A , 1939, 173, 126.262 LOW TEMPERATURE MECHANISM The solution of eqn. (VI) does not follow immediately, since B is time-dependent because of the diminution of [RHI and [O,] as the reaction proceeds. A simplification may be introduced, however, by considering the case in which one of the reactants is in excess so that its change in concentration during the reaction may’ be neglected. Taking [O,] to be in sufficient excess that [O,] > Y’[RH] in eqn. (V),* and that this condition remains until the end of the reaction, we have In this case, therefore, the eventual falling-off in the rate is due to de- pletion of RH.Now in the ideal case, RH disappears from the system exclusively by reaction leading to peroxide : RH + 0, -+ ROOH. (The rise in pressure may be attributed to breakdown products from ROOH.) B = K[RH]. . . . (VII) Hence, at any time t [RH] = [RH], - Dr[P]dt, . (VIII) where [RH], is the initial concentration of RH and D a numerical con- stant which will not be far from unity. We now have from (VI), (VII) and (VIII) Setting (K[RH], - C) = ,!? we have from (111), This gives, on transformation and integration, - (XI) dAP KD p = dt = PAP - -(Ap), + const . 2k Since p is small where Ap is small it is clear that the integration constant is small compared with PAP.Moreover, in order to make the solution continuous with that which obtains for conditions towards the end of the induction period, it is also necessary that the integration constant should be small. We shall take it to be zero. However, though this step is not unreasonable, it can only be strictly justified a posteriori. Integration of eqn. (XI) then gives Ap = (I + tanh . (XII) KD where t, is a constant of integration. At t = t , we have (XIII) and from (X), ( $ ) , = o . . (XIV) Thus from (XIV) it follows that t , is to be identified with the time at which the maximum rate Pmax is reached. Hence, substituting (XIII) in (XI) gives where k’ is a numerical constant. * It is to be remarked from (I) and (11) that Y’ is very probably < I since k , is almost certainly > k,, and k , and k, probably of the same order of magnitude.M.F. R. MULCAHY 263 A very simple result may be had from (XIII) and (XV), viz. . (XVI) . (XVIU) Pmax fl Apmax 2' Pmsx I Apmax 2 -=- i.e. -- --(K[RH]o - C), . Apmax being the pressure increment from the beginning of the reaction to the point at which Pmax occurs. Comparison with Experiment.-The slow beginning and eventua.1 acceleration of the reaction are accounted for in terms of a slow produc- tion of hydroperoxide from the pure reagents followed by auto-catalysis due to free-radical-producing breakdown of the hydroperoxide, as set out above. This general explanation coincides with that previously proposed by Hinshelwood.17. 11 THE RATIO Pmax/Apmax.-Eqn. (XVIa) predicts a linear relationship between Pmax/A$max and the initial concentration of hydrocarbon, pro- vided an excess of oxygen is present.In Fig. I Pmax/Apmax derived from experiments with different initial pressures of butane with 250 mm. FIG. I .-Variation of hx/APmax with initial pressure of hydrocarbon. (Initial oxygen pressure constant.) oxygen at 263OC and with different initial pressures of propylene with 400 mm. oxygen at 298OC l6 respectively, is plotted against the initial partial pressure of hydrocarbon. In both cases a linear relationship is found. It is interesting to observe that with butane the straight line passes through the origin, i.e. C = o in eqn. (XVIa). In terms of the present theory (eqn. (IV)) this means that the decomposition of butane hydroperoxide under these conditions occurs only by a mechanism (one or more) which produces radicals capabIe of initiating more peroxidc formation.On the other hand, with propylene C 9 0, which indicates that the peroxide formed from propylene decomposes in two ways, one of which does not produce active radicals. It is to be observed that K in eqn. (XVIzz) is independent of oxygen concentration when the latter is in excess. Hence Pmax/Apmax should also be independent of oxygen pressure under these conditions. Fig. z shows that this is so for butane (50 mm.) + oxygen mixtures at 258.5" C when the partial pressure of oxygen is greater than - zoo mm. Measure- ments of the final pressure reached at the end of the reaction indicate that three molecules of oxygen are required for complete reaction with one of butane ; hence in these experiments the condition of excess oxygen Mulcahy, Faraday SOC.Discussion, 1947, 2, 128. 17 Hinshelwood, J . Chem. Soc., 1948, 531. lS Mulcahy, Thesis (Oxford, 1948).264 LOW TEMPERATURE MECHANISM is not fulfilled until at least 150mm. are present. Below this pressure PmaxlApmax rises steeply. A similar result was found with 80 mm. butane and various oxygen'pressures at 263O C (cp. ref. (IS)).* THE MAXIMUM RATE.-h cases where C = 0, the theory indicates that, in the presence of excess oxygen, Pmax should increase with the square of the initial hydrocarbon pressure and where C .c: o with a power be- tween the second and first. In both cases Pmax should be independent of oxygen pressure. The latter result has been observed in many cases.lln 20* 2 l s 2 2 ~ 25 A steep rise in pmax with [RH], is invariably observed.In several cases 1% 20, 21, 2 2 the exponent of [RH], has been found to be approximately 2 (1.7 in the butane experiments and ca. 2 in the propylene experiments in Fig. I). FIG. 2 .-Variation of pmax/APmaxwith initial pressure of oxygen. (Initial butane pressure constant.) THE STRUCTURAL EFFECT.-For equal pressures of different hydro- carbons with excess oxygen under the same conditions and C = o in from eqn. (XV). Taking the case of unimolecular chain termination, reference to eqn. (11) shows that K = k,"k,/k,' where k" is the specific rate of radical production from peroxide decom- position. Assuming that all peroxides produce the same number of active radicals for each molecule decomposed, this may be taken to be directly proportional to the unimolecular rate constant K, of peroxide decomposition : k,' is unlikely to be very specific, consequently the effect of the structure of the hydrocarbon on Pmax is to be attributed mainly to variations in KIA,.The increase in K with increasing chain length of the straight chain paraffins and its decrease with branching in the chain must then be ascribed to corresponding variations in A,, since k , would be expected to alter little with increasing chain length and to increase in those cases where branching involves introduction of tertiary C-H groups into the molecule. A similar conclusion has been arrived at by Hinshelwood on somewhat different grounds.ll9 l7 Ceteris paribus, a variation of 2 kcal./ * There is some indication that Pmax/Afimsf reaches a maximum when the 2o Cullis, Trans.Faraday Soc., 1949, 45, 709. 21 Cullis, Hinshelwood and Mulcahy, Proc. Boy. SOC. A , 1949, 196, 160. 22 Pease, J . Amer. Chem. SOG., 1938, 60, 2244. 23 Day and Pease, J. Amer. Chem. SOC., 1941, 63, 914. each case pmax = const. K ROOH -+ RO- + -OH. initial oxygen and butane pressures are approximately equal.M. F. R. MULCAHY 265 per mole in the dissociation energy of the 0-0 bond would produce (at 250' C) a seven-fold change in Pmax ; 5 kcal./mole difference would change the rate by a factor of 120. Conclusions.-In brief, the theory postulates that the mechanism of oxidation of hydrocarbons in the gas phase at 200-300' C is basically similar to that by which more reactive hydrocarbons are oxidized in the liquid phase at lower 14, 32 Hydroperoxide is formed during the induction period and thereafter catalyzes its own formation.This occurs by the production of radicals incidental to the decomposition of the peroxide. The rate is prevented from accelerating indefinitely by the consumption of one or both of the reagents; in the case con- sidered this is due to depletion of the hydrocarbon concentration. The rise in pressure during the reaction is attributed to the formation of products of peroxide decomposition and their subsequent (non-rate- controlling) oxidation. It is clear that the rate equation developed from this mechanism (eqn. (IX)) and its solution ((XV) and (XVI)) can only be approximate, since no account is taken of the possibility of sensitization of the reaction by radicals produced during the oxidation of degradation products or of inhibition by substances formed during the reaction. In view of the complexity of the reaction products, which usually include both formalde- hyde and higher aldehydes, it is most probable that both effects occur to some extent.However, the theory accounts well for the very different effects of initial hydrocarbon and oxygen pressures on the maximum rate. Furthermore the prediction of the correct relation between the initial concentrations and Pmax/Apmax is particularly striking. Again, the strong dependence of Pmax on the structure of the hydrocarbon is quali- tatively in accordance with the considerable range of stability shown among different peroxides (for example, cf. ref. (16a), (24)-(31)). It is evident, therefore, that the proposed reaction mechanism, which is itself a natural extension of a mechanism well substantiated for liquid phase reactions, provides a. reasonable correlation of several of the main facts of the kinetics of the low-temperature gas-phase oxidation. There are various other points at which the ideas and conclusions given above may be tested experimentally. Such experiments are at present in progress. The author is very much indebted to Dr. J. K. Mackenzie for providing him with the solution of the differential eqn. (IX). This work forms part of the general programme of research of the Division of Tribo- physics, Commonwealth Scientific and Industrial Research Organization. C.S.I. R.O., Division of Tribophysics, The University, Melbourne, A ustrali a. 24Harris and Egerton, Proc. Roy. SOC. A , 1938, 168, I. 25 Raley, Rust and Vaughan, J . Amer. Chem. SOC., 1948, 70, 88. 26 Milas and Surgenor, J . Amer. Che.m. SOC., 1946, 68, 205. 27 Medwedew and Alexejewa, Ber., 1932, 65, 131. 28 Robertson and Waters, J. Chem. Soc., 1948, 1578. 29 Farkas and Passaglia, J . Amer. Chem. SOC., 1950, 72, 3333. 30 Nozaki and Bartlett, J . Amer. Chem. SOC., 1948, 68, 1686. 31 Redington, J. Polymer Sci., 1948, 3, 503. 32 Ramford and Dewar, Proc. Boy. SOC. A , 1949, 198, 252.