General equations for the reaction kinetics of solids

Abstract

The index-of-reaction equation (i.r.e.): dF/dt^Z = k^Z(l - βF)^m is compared with a generalized Prout-Tompkins equation (g.P.T.e.): dF/dt = k_n(l - βF)^y With the boundary condition F = 0, t = 0 the equations are equivalent for z = 2 or m = 0 or β ≤ 1 and the i.r.e, is closely approximated by the g.P.T.e. for other values of the parameters by use of the following approximation ∫(1- F)^-m dF ≈ AF(1-BF)⁵ The parameter s is a function of m. Both A and B are close to unity for 1/3 < m < 3. The i.r.e. is recommended as being more useful than the g.P.T.e. because the i.r.e. has a better theoretical basis and because it is more readily integrated and fitted to experimental data.