Theory of Diffusion-Controlled Processes. II. Consideration of Conceptual Framework

Abstract

The fundamental concepts and equations used in describing diffusion-controlled processes in liquids are defined and analyzed in terms of the behavior of an ensemble of reacting molecules. Rate equations are derived and written in forms familiar in reaction kinetics. The physical meaning of the various forms of these equations is discussed in terms of a priori and a posteriori probabilities. The probabilistic equations are also expressed in terms of particle concentrations; the measurables of experiments, in reaction kinetics. The final equations constitute the correct formal description of the reaction of molecules in liquids under conditions explicitly specified. The results derived here are compared with those of a previous paper in which the macroscopic behavior of a system of reacting molecules is expressed in the form of a power series derived from consideration of molecular diffusion and microscopic molecular distribution. It is shown that the fundamental rate equation previously used is only approximately correct and that higher-order terms of the power series arise from the approximate nature of the rate equation.