General Collision Theory Treatment for the Rate of Bimolecular, Gas Phase Reactions

A collisional approach, somewhat similar to the Wang-Chang and Uhlenbeck treatment for the transport properties of polyatomic molecules, is used to obtain a general expression for the rate of a bimolecular chemical reaction in terms of reaction cross sections. Specialization is then made to the case where a Maxwell-Boltzmann velocity distribution may be assumed for the reactants. This leads to a Laplace transform relation between the rate constants for reaction of molecules in definite internal quantum states and the reaction cross sections. The further assumption of a Boltzmann distribution among the internal energy states of the reactant molecules then leads to a rate equation of the usual form and to an explicit expression for the single over-all rate constant. This expression is used to rederive the results of the old ``simple'' collision theories. Finally, a collisional approach is used to rederive the usual rate expression of the Eyring theory of absolute reaction rates. The rather drastic approximations which seem to be necessary for such a derivation are pointed out and discussed.