Effect of brownian diffusion on chemical kinetics

Abstract

A new method of theoretical prediction of the kinetic rate constants of fast chemical reactions in solutions is presented. It takes into account the effect of finite diffusive displacements of the reacting molecules. The approach is based on the solution of the steady-state Fokker-Planck equation by the moments method of Grad developed in the theory of coagulation of aerosol particles. A comparison of the predicted rate constants with the experimental data provided by Schuh and Fischer for the self-reaction of tert -butyl radicals in n-alkanes shows a good correspondence.

Absolute rate constants for the self-termination of the isopropyl radical and for the decarbonylation of the 2-methylpropanoyl radical

“…underestimates D, whereas the other treatments yield satisfactory estimates. To test the self-termination constants for diffusion control we calculated 2kt from the Smoluchowski equation10 [0.06ir(2 -<x)aRI2 + (0.68a2 + 0.lir(2 -<x)2)K + a(2 -a)]'1 (11) Here D is the diffusion coefficient of the radical, p the reaction distance, the spin statistical factor, k0 the radiation boundary constant, 0 < < 1 a reactivity parameter, and K = lOZfyf1• (M/2wRT)ll2 the effective Knudsen number. As in previous work1"6 D is approximated by the diffusion coefficient of a parent molecule, and the average of :3 , and Z)CiH6 (Table II) was used.…”

Modelling of mass transfer in combination with radical reactions

“…Reactions involving radical intermediates are in general fast to very fast reactions. For radicals, the reaction rate constants are typically in the range of 10 5 -10 9 m 3 /kmol/s for second order reactions (Carey and Sundberg, 1990;Sitarski, 1981). For very fast or instantaneous reactions the equations of Higbie's penetration theory can be solved analytically.…”