Nearly encounter-controlled reactions: The equivalence of the steady-state and diffusional viewpoints

A very basic problem in formulating reaction rate expressions for reactions in the solution phase is how to treat the competition between spatial diffusion of reactants to form an encounter complex and the subsequent step of reaction within the encounter complex. The two textbook-level methods for treating this problem are the steady-state approximation and the approximate solution of the appropriate diffusion equation. Usually the problem is treated by one or the other of these methods, and no connection is given. In the present article the equivalence of these methods is demonstrated. It is hoped that this discussion will enable students better to appreciate the physical implications of the mathematics involved in the so-called radiation boundary condition for the diffusion equation.