Two Monte Carlo methods are used to simulate a dynamics of molecules of a foreign gas A, highly diluted in a carrier gas C. Diffusion in the presence of bimolecular reaction A + C --> products is studied. Nonequilibrium corrections to the reaction rate constant and diffusion coefficient are calculated for a wide range of molecular mass ratio m(A)/m(C) and activation energies of the reaction. Some differences between simulation results of the two methods are observed. The deviation of the velocity distribution from the Maxwellian form is quantified by means of the fourth order cumulants. The nonequilibrium effects are most significant in the Lorentz range, that is for m(A)/m(C). The simulation results prove that the theoretical predictions based on a perturbative solution of the Boltzmann equation are valid for not too small values of m(A)/m(C), but are not correct in the Lorentz range.