New approximate limiting laws for activity and rate coefficients of ions in solution

A new approach is present for concentration effects on ionic reactions in solutions of small electrolyte concentrations. It is assumed that the mutual Coulomb interaction is felt by an ion pair only when their separation is smalller than the "Coulombic horizon", R_av, namely when there is no intervening ion. This leads to an approximate but simple and parameterless, formula for activity coefficients, with a cube root dependence on concentration in this regime. Steady-state diffusional rate coefficients are calculated to and from the sphere at R_av. Comparison made with experimental activity coefficients of strong and weak electrolytes shows that the upper validity limit of the new formula exceeds that of the Debye-Hückel limiting law. The diffusional rate constant from R_av gives a reasonable description of the concentration dependence of the ionic association rate coefficients, for concentrations where the Brönsted-Bjerrum limiting expression ceases to apply.