Abstract
In the present paper we extend the exact solution previously obtained for the heterogeneous catalytic reaction 2A + B_{2} → 2AB on small \(2\times 2\) domains, to arbitrary lattice sizes (\(N \times N\)) and calculate the average number of reactive steps necessary to poison the lattice first, \(\langle t \rangle\). We determine \(\langle t \rangle\) as a function of \(N\) through Monte Carlo simulations previously contrasted with the exact solution in \(2 \times 2\) lattices. We show that \(\langle t \rangle\) follows a power law with \(N\), without appreciable transient behaviors, and a scale factor (\(\nu\)) dependent on the two parameters of the model, the sticking coefficient probability \(s\) and the desorption probability \(p_d\). The dependence of \(\nu\) on both \(s\) and \(p_d\) is determined.