Particular solution for any consecutive second-order reaction

Abstract

Arguments are presented against the accepted notion that multiple rate constants may be obtained from observed singular or pooled kinetic runs. For any competitive consecutive second-order reaction, the particular solution satisfying the total differential equation, derived from (n + 1) simultaneous differential equations, is S = (aA0 - S0){(aA0/S0)[exp (aA0 - S0)kt] - 1}-1, where S is the concentration of reactant common for all the steps, A is the concentration of the substrate with a reactive sites, A. and So are the concentration of reactants at zero time, k is the observed rate constant, and t is the time. This equation is shown to reproduce the experimental reported data and yields k = min(k(l),⋯, k(n)), where k(i) is the rate constant assigned to step i. It is also shown that the initial conditions need not be known. For experiments with the initial condition (aA0 = S0), with only species A and S are present at zero time, the expression (S0{∫x0(S - α)2dt}-1) may be useful for an approximate evaluation of k when values of S do not approach zero after an infinite time (i.e., Sx = α ≠ 0, where α is the asymptote for the data).