  We present an \textit{exactly solvable} model of a monomer-monomer $A + B \to
\emptyset$ reaction on a 2D inhomogeneous, catalytic substrate and study the
equilibrium properties of the two-species adsorbate. The substrate contains
randomly placed catalytic bonds of mean density $q$ which connect neighboring
adsorption sites. The interacting $A$ and $B$ (monomer) species undergo
continuous exchanges with corresponding adjacent gaseous reservoirs. A reaction
$A + B \to \emptyset$ takes place instantaneously if $A$ and $B$ particles
occupy adsorption sites connected by a catalytic bond. We find that for the
case of \textit{annealed} disorder in the placement of the catalytic bonds the
reaction model under study can be mapped onto the general spin $S = 1$ (GS1)
model. Here we concentrate on a particular case in which the model reduces to
an exactly solvable Blume-Emery-Griffiths (BEG) model (T. Horiguchi, Phys.
Lett. A {\bf 113}, 425 (1986); F.Y. Wu, Phys. Lett. A, {\bf 116}, 245 (1986))
and derive an exact expression for the disorder-averaged equilibrium pressure
of the two-species adsorbate. We show that at equal partial vapor pressures of
the $A$ and $B$ species this system exhibits a second-order phase transition
which reflects a spontaneous symmetry breaking with large fluctuations and
progressive coverage of the entire substrate by either one of the species.
