A Treatment of Chemical Kinetics with Special Applicability to Diffusion Controlled Reactions

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Abstract
If a molecule is produced in a medium containing molecules able to react with it, its instantaneous reactivity is a function of the time since its formation. At very short times the reactivity is determined by the conventional ``true'' rate constant k, which is the product of the rate constant for encounters and the probability of reaction during an encounter. At long times (10—9 sec or greater in many liquids), the reactivity falls to a value determined by the ``long‐time'' rate constant k′. The constants k and k′ differ by the factor 1 — β′, where β′ is the probability that a specific pair of molecules separating from a nonreactive encounter will ultimately react with each other. If β′ is small either because there is little chance of reaction per encounter (activation control), or because there is little chance the specific pair will undergo a subsequent encounter (as in gas phase), the two rate constants are virtually identical and conventional kinetics apply. Equations are developed for the time dependence of the reactivity of a molecule in such a system, and a model is suggested for evaluating the necessary parameters in terms of the relative diffusion coefficient, the encounter diameter, and the root‐mean‐square displacement distance during diffusion. Application of available kinetic data indicates that diffusive displacements in liquids are of the order of a molecular diameter and take place with a frequency of the order of 1011 sec—1. In the quenching of fluorescence and other processes where reactive molecules are produced singly, experimental measurements have given the ``long‐time'' rate constant, k′. When reactive molecules are produced in pairs, the recombination process in a thermal equilibrium is described by the ``true'' rate constant, k; but k′ has been obtained from all rate measurements on the recombination of pairs produced photochemically. Experiments are suggested for obtaining information on systems during the short time in which the apparent rate constant in changing.