  We study the equilibrium properties of a lattice-gas model of an $A + B \to
0$ catalytic reaction on a one-dimensional chain in contact with a reservoir
for the particles. The particles of species $A$ and $B$ are in thermal contact
with their vapor phases acting as reservoirs, i.e., they may adsorb onto empty
lattice sites and may desorb from the lattice. If adsorbed $A$ and $B$
particles appear at neighboring lattice sites they instantaneously react and
both desorb. For this model of a catalytic reaction in the
adsorption-controlled limit, we derive analytically the expression of the
pressure and present exact results for the mean densities of particles and for
the compressibilities of the adsorbate as function of the chemical potentials
of the two species.
