Various NO-reduction reactions on Pt(100) exhibit similar dynamical behavior, presumably due to an empty site requirement for NO dissociation. This motivates analysis of a lattice-gas model which incorporates this feature, and which here is chosen to mimic the NO+CO reaction on Pt(100) : both reactants adsorb at single empty sites, NO instantaneously dissociates given an adjacent empty site and nitrogen adatoms thus formed are immediately removed), and adjacent CO and O instantaneously react. We also include desorption of adsorbed NO and CO, but no adspecies diffusion. At lower temperatures where desorption is absent, we show that poisoning occurs with the reaction rate decreasing as R(CO2) similar to e(-kt), where k>0 except for equal reactant adsorption rates. The introduction of desorption produces reactive steady states, and (in different regimes) nonequilibrium poisoning transitions, critical points, and transitions to bistability.