In the present paper we exactly solve the distributed parameter stochastic model of the heterogeneous catalytic reaction 2A+B₂→2AB and calculate the average number of reactive steps necessary to deactivate the lattice first,< t >. Results are compared with Monte Carlo simulations.< t >shows a nonmonotonic behavior with the sticking coefficient probabilitys and the desorption probability p_d, reaching a maximum value that depends on s,p_d and the lattice size N.Facultad de Ciencias ExactasInstituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas