A spatially homogeneous gas mixture consisting of structureless molecules of kind A, B, C, D is considered in which the reversible bimolecular reaction A + B $\rightleftharpoons $ C + D occurs. The Boltzmann equation describing this model gas is solved numerically by using the multigroup method. The collision cross sections correspond to the reactive hard sphere model. Parameters are the heat of reaction, the activation energy and the steric factor. Emphasis in the presentation of the results is laid on highly exothermic reactions with large activation energy, in which case the gas undergoes a thermal explosion. It is found that the corrections of the chemical rate constants due to translational non-equilibrium effects are noticeable. The result is a shortening of the reaction period by up to 25%.