Edward L. King University of Colorado Boulder. CO 80309
A General Rate Equation for Reactions Governed by a Single Relaxation Time
Most textbook treatments of chemical kinetics include a derivation of the relaxation time r (which is the half-time divided by In 2,r = t 1pJ0.693) for the approach to equilibrium in a reaction
&I
after a small perturbation abrupt change of temperature, pressure, or concentrations). This derivation involves expression of the perturbed concentrations in terms of the equilibrium concentrations, [A]., [Dl., and [El., and the displacement from equilibrium, Ax, [A] = [A]. Ax, [Dl = [Dl. - Ax, and [El = [El, - Ax. Substitution of these expressions for [A], [Dl, and [El into the complete rate law gives the differential equation in the displacement Ax T - ~= -dln(Ax)/dt = kr + k,([DI. + [Ele)
+
In this derivation, the term in (Ax)? was dropped, a justifiable operation for Ax
