Non-equilibrium kinetics of bimolecular exchange reactions. Part 1.—Formalism and application to Br + HCl → HBr + Cl

Abstract

A recently developed theory of non-equilibrium chemical kinetics is applied to the elementary bimolecular reaction A + BC → AB + C under conditions of translational–rotational equilibrium but vibrational disequilibrium. The diatomic molecule, BC, is treated as a harmonic oscillator truncated at the level from which reaction is primarily occurring. When the reaction can be considered as steady and truly elementary (isolated from secondary or back-reactions) expressions are given for calculating the non-equilibrium correction factor to the rate coefficient over a wide range of temperatures and reagent concentrations. the manifestation of the effect is a reduction of the magnitude of the rate coefficient and of the Arrhenius activation energy. The effect is most pronounced when the reactivity-to-relaxation ratio of rates is high. A proper rate equation is shown to be of the form rate =k[A][BC]/[1+ƒ(T)[A]/[R]) where k is a time- and concentration-independent constant, ƒ is a temperature-dependent constant and [R] is the concentration of the molecules responsible for relaxing BC via T ↔ V processes alone. The consequences for chemical kinetics and dynamics are discussed. As an example, the reaction Br + HCl → HBr + Cl is examined. Depending on the initial reagent concentrations it is shown that the rate is reduced (by factors ranging up to 11) from the equilibrium rate and that the Arrhenius activation energy is dramatically reduced by as much as 33 KJ mol–1 in the temperature range range 300–500 K, but at higher temperatures it is not affected as much. A comparison with existing thermal data for the reverse reaction is not conclusive.