Analytical solutions for the rate equations of some two-step kinetic schemes including a reversible first order later step

Abstract Analytical solutions for the ordinary differential equations are reported for the kinetics of two-step processes for which the later step is a first order reversible process. The earlier step is always irreversible: zeroth order, first order, second order and third order reactions are considered. For the first and second order cases, a qualitative analysis of the kinetic curves was also carried out and the parametric conditions of finding extrema on all the kinetic curves are explored. It is found that the scheme consisting of a second order or mixed second order earlier reaction and a reversible first order later one may feature a reactant with two extrema on its concentration–time trace. In such cases, the first extremum is always a maximum, and the second one is a minimum.