Rate Equations for Reactions at High Temperatures Involving Radical Intermediates: Consecutive-Parallel and Rice–Herzfeld Mechanisms

Abstract

For complex reactions which produce, in the initial step, radical intermediates that attack the reactant in a subsequent step, the form of the rate equation will change as the reaction temperature increases. This is caused by a change in the relative rates of the individual steps in the mechanism due to differences in activation energies. A method has been developed for calculating the form of the rate equation at these higher temperatures for two mechanisms: a consecutive-parallel nonchain process and the Rice–Herzfeld chain reaction. The method is based on the elimination of time as the independent variable from the rate equations. It was calculated, for the consecutive-parallel mechanism, that the rate is a complex increasing function of the extent of reaction at temperatures high enough so that the steady-state assumption was not valid, i.e., the rate of the radical attack step was too slow compared to rate of radical production. Using this approach it was shown that significant deviations from steady state would be found in the case of methane pyrolysis at about 2200°K for concentrations below 10−6 mole/cm3. It was found for the Rice–Herzfeld mechanism that a shift from three-halves to first-order kinetics occurs as the temperature increases, although the concentrations of radicals in the transition temperature range would still be low enough not to invalidate the steady-state assumption. For acetaldehyde and dimethyl ether pyrolyses, these shifts would occur at about 1100° and 900°K, respectively.