The perturbation solution of the Boltzmann equation is used to analyze the relative decrease eta(T) of the rate constant k(T) of a chemical reaction in a dilute gas in the temperature T. The Prigogine-Xhrouet model of the reactive cross-section is introduced for the reaction A + A reversible arrow B + B. A large effect for eta(T) equal even nearly 75% ( for a small reduced threshold energy epsilon(0) and a large molar fraction x(B)) follows from the analytical solution for k(T). A replacement of T by the Shizgal-Karplus nonequilibrium temperatures T-A and T-B in the equilibrium rate constants (for the forward and reverse reactions) gives eta(T-A, T-B) confirming this effect. (C) 2003 Elsevier B.V. All rights reserved.