Deviations from Thermal Equilibrium among Reactant Molecules

A model of a chemically reacting system is considered in which the reactant molecules are dilutely dispersed in an inert gas and reaction is the result of binary collisions between inert and reactant species. It is noted that during reaction the distribution of reactants over their internal states is not that characteristic of equilibrium. It is shown that if κ is the rate constant of the reaction and κ_eq the rate constant that would have characterized the reaction had the reactants been in equilibrium, then κ=κ_eq—$\mathrm{\tau ̄}$ ( 〈q²〉—〈q〉²), where $\mathrm{\tau ̄}$ is a mean relaxation time, q is the reaction probability per unit time from a particular reactant state, and 〈 〉 is an average over reactant states with an equilibrium distribution. The rate constant κ_eq is itself 〈q〉. A number of illustrations are given, and it is concluded that in real chemical systems 〈q²〉 is probably of the order of magnitude of 〈q〉^1+γ with 0<γ<1. This has as a consequence that κ is of the form (1 — Bκ_eq^γ)κ_eq. The quantity in parentheses describes the effect on κ of deviations from equilibrium, and it is a decreasing function of temperature. It is suggested that this might possibly be the explanation of the observed temperature‐decreasing pre‐exponential factor in the rate constant for dissociation of diatomic molecules.