We consider a Langmuir-Hinshelwood reaction on a catalytic surface with two monomer reactants, A and B whose reaction product leaves the surface: A+B\ensuremath{\rightarrow}0. We allow different adsorption and desorption rates for the two reactants. When adsorption and reaction are fast events compared to desorption (and in the absence of diffusion), we can use an approximate mapping onto a two-state spin model that we solve using a decoupling scheme. We compute the steady-state reaction rate and compare it to Monte Carlo simulations. We show explicitly how spatial fluctuations affect the behavior and that the predictions of the spin model give a reasonable theory for the system. (c) 1995 The American Physical Society