Chain reactions Rice-Herzfeld mechanisms

There has been much controversy regarding the order of the reaction (see Steacie, loc, cit.) and the importance of a chain mechanism vs. a molecular decomposition of acetaldehyde. The bulk of the present evidence, however, indicates that the chain decomposition is the important path for the reaction, - and in view of the simplicity of the products a fairly simple Rice-Herzfeld mechanism may be presented. 

Here, in spite of the chain sequence of steps, the reaction is apparent first-order. However, it can be seen that the apparent first-order rate constant is a combination of the rate constants of the individual elementary steps. A comparison of this example with the contents of Table 1.3 shows that the Rice-Herzfeld mechanism corresponds in this case to Two Active Centers with Second-Order Cross-Termination Chain. The apparent first-order behavior here is a consequence of the particular kinetics of the initiation and termination steps. It is not difficult to show that various combinations of unimolecular or bimolecular initiation with bimolecular or even termolecular termination can result in apparent orders that range from 0 to 2 (M.F.R. Mulcahy, Gas Kinetics, John Wiley, New York, 1973, pp. 87-92). 

Since chain reactions are so common, it would be unreasonable to expect all mechanisms to fit neatly into the four examples of Table 1.3. Illustration 1.5 has already given some further information on thermal decomposition reactions following Rice-Herzfeld mechanisms. Before going on to additional reaction systems, we should add a few comments on the two-active-center reaction illustrated by the combination of hydrogen and bromine in the gas phase. This is probably the first reaction for which a suitable chain sequence was identified. The kinetics of the reaction were carefully studied and reported as early as 1907 [M. Bodenstein and S.C. Lind, Z. Physik. Chem., 57, 168 (1907)] and the chain reaction interpretation of the reported kinetics, as shown in the tabulation of Table 1.3, was given over a decade later [J.A. Christiansen, Kgl. Danske Videnskab. Selskab., 1, 14 (1919) K.F. Herzfeld, Ann. Physik. Chem., 59, 635 (1919) M. Polanyi, Z. Elektrochem., 26, 50 (1920)]. A through discussion of this is given in the text by Frost and Pearson. 

Because of their commercial importance, we still need to do more work on thermal cracking reactions, since their scope and complexity extend considerably beyond the world of Rice-Herzfeld mechanisms. For example, consider the pyrolysis of butane (K.J. Laidler, Chemical Kinetics, McGraw-Hill, New York, 1965). This molecule affords the formation of a number of radical chain-carrier species, and the number of elementary steps increases accordingly... 

For Rice-Herzfeld mechanisms the mathematical form of the overall rate expression is strongly influenced by the manner in which the chains are broken. It can also be shown that changing the initiation step from first- to second-order also increases the overall order of the reaction by (1/2) (31). These results are easily obtained from the eqnations derived previonsly by substituting (k [M]) for ki everywhere that the latter term appears. Since ki always appears to the (1/2) power in the final rate expressions, the exponent on M in the existing rate expression must be added to 0.5 to obtain the overall order of the reaction corresponding to the bimolecu-lar initiation step. In like manner, shifts from bimolecular to termolecnlar termination reactions will decrease the overall order of the reaction by (1/2). 

At partial pressures near one atmosphere, ethane decomposes by a simple Rice-Herzfeld mechanism, with combination or disproportionation of ethyl radicals as the predominant chain-ending step. However, at a total pressure ot 100 mm., or at a partial pressure of 0.01 atm. another chain-ending step predominates. Unlike butane formed from ethyl, the products of this step cannot be distinguished analytically from the major products of the reaction chain. It is therefore believed to involve reaction of H and C2H5, either homogeneously or at the reactor wall. Quantitative rate and yield data are given, as are methods of correction for secondary reactions and of extrapolation to zero reaction time. 

In order for the overall rate expression to be 3/2 order in reactant for a first-order initiation process, the chain terminating step must involve a second-order reaction between two of the radicals responsible for the second-order propagation reactions. In terms of our generalized Rice-Herzfeld mechanistic equations, this means that reaction (4a) is the dominant chain breaking process. One may proceed as above to show that the mechanism leads to a 3/2 order rate expression. 

The enumeration of all the possible reactions involving radicals and molecules in the ethane system would be a tedious task, but one is not really justified in accepting a mechanism for the ethane pyrolysis until such an exhaustive inquiry has been completed. On the other hand, at our present stage of knowledge, the detailed investigation is impracticable if not impossible. The Rice-Herzfeld principle presents about as practical and complete a guide as is at present warranted for the economical discussion of hydrocarbon reactions. However, even this scheme for the ethane pyrolysis [Eq. (XIII. 10.4)] has been considerably shortened in the discussion already presented [Eq. (XIII.10.5)], and we may now go back and look at some of the reactions which have been neglected in the latter, simplified chain. 

The thermal decompositions (pyrolyses) of hydrocarbons other than the cyclic ones invariably occur by complex mechanisms involving the participation of free radicals the processes are usually chain reactions. In spite of this, many of the decompositions show simple kinetics with integral reaction orders, and this led to the conclusion by the earlier workers that the mechanisms are simple. Ethane, for example, under the usual conditions of a pyrolysis experiment, decomposes by a first-order reaction mainly into ethylene and hydrogen, and the mechanism was thought to involve the direct split of the ethane molecule. Rice et however, showed that free radicals are certainly involved in this and other reactions, and this conclusion has been supported by much later work. An important advance was made in 1934 when Rice and Herzfeld showed how complex mechanisms can lead to simple overall kinetics. They proposed specific mechanisms in a number of cases most of these have required modification on the basis of more recent work, but the principles suggested by Rice and Herzfeld are still very useful. 

Later these experiments were repeated -with the conclusion that Morris findings were dubious. Zemany and Burton used equimolar mixtures of acetaldehyde and acetaldehyde- /4, at temperatures 510 and 465 °C, and found that partially deuterated methanes were formed in appreciable amounts. The ratio CHD3/ CD4 was found to be 1.2 and 1.0 at 510 and 465 °C, respectively (compared to the value of 1.6 obtained in the photolysis at 140 °C). These results clearly indicate the free radical origin of the methane. However, the fact that the CHD3/CD4 ratio is lower than the one found in the photolysis made the authors conclude that there IS some contribution from the molecular mechanism. An upper limit for the latter was estimated to be approximately 15 and 25 % of the total reaction at temperatures 510and465 °C, respectively. Zemany and Burton estimated the values for the ratios methane-rf3/ethane-d6 and methane-t /ethane-rfe, from which a chain length of 1000 can be derived, at 465 °C, for the Rice-Herzfeld type decomposition. 

F, O. Rice and K. F. Herzfeld. The thermal decomposition of organic com pounds from the standpoint of free radicals. VI. The mechanism of some chain reactions. J. Amer. Chem. Soc., 56 284-289, 1934. 

Storch (65) reviewed the probability of acetylene formation in thermal reaction, as shown in experiments such as the early ones of Bone and Coward (13). Voge and Good (69) and Laidler (40) reviewed more recent results. In general, reaction seems to follow a chain mechanism of the type originally suggested by Rice and Herzfeld ... 

Thermal cracking of organic substances is an important reaction in the petroleum industry and has been extensively studied for over seventy years. At least for simple alkanes, the decay is first order in good approximation and therefore was long believed to occur in a single, unimolecular step [21]. However, in the 1930s, Rice and coworkers [22-24] established the presence of free radicals under the conditions of the reaction by means of the Paneth mirror technique [25,26], This observation led Rice and Herzfeld to propose a chain mechanism [22,27,28], Extensive later studies proved the essential features of their mechanism to be correct not only for hydrocarbons, but also for many other types of organic substances. 

The first quantitative investigation on the thermal decomposition of acetone vapour was carried out by Hinshelwood and Hutchison by pressure measurement in the temperature range 506-632 °C. The authors concluded that the thermal decomposition of acetone is a unimolecular reaction. In contradiction to this conclusion Rice and Herzfeld suggested a chain mechanism, viz. 

With respect to theories of wall heterogeneous effects in hydrocarbon pyrolysis reactions, the literature is almost void. Rice and Herzfeld (1951) have presented some theoretical arguments but with some severely simplifying assumptions Polotrak, et al. (1959) proposed mechanisms involving both chain initiation and termination as heterogeneous processes. More elaborate theoretical work on the interaction between hydrocarbons (paraffins and olefins) and metal oxide surfaces was done by Semenov (1958) and Kasansky and Pariisky (1965) in which the authors tried to explain the heterogeneous effects (activity) of the surfaces in terms of electronic conductivity. 

Rice and Herzfeld studied many pyrolyses (heating in the absence of air) of organic substances, and have deduced an unbranched-chain mechanism for all these reactions. 

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