The model recently proposed by Ziff et al. [1] for reactions of the type A+(1/2)B2 → AB is extended in order to study the effect of A-desorption on irreversible (kinetic) phase transitions (IPT). The IPT from a stationary state with AB-production to a B-poisoned state is not influenced by A-desorption. On the other hand, desorption of A-species prevents the existence of a truly A-poinsoned state. Therefore the IPT from the stationary regime to an A-poisoned state does not occur but an apparent phase transition is observed for small values of the desorption probability (PD). The rate of AB-production (R AB) crosses over from a regime where it becomes dominated by the rate of A-adsorption, when the coverage with A-species is negligible to another regime where R AB is dominated by the rate of B2-adsorption, when the coverage with B-species is negligible. Within the former regime, R AB decays exponentially with the mole fraction of A-molecules in the gas phase and exhibits a power law dependence with P D (exponent γ=2).