  We focus here on the thermodynamic properties of adsorbates formed by
two-species $A+B \to \oslash$ reactions on a one-dimensional infinite lattice
with heterogeneous "catalytic" properties. In our model hard-core $A$ and $B$
particles undergo continuous exchanges with their reservoirs and react when
dissimilar species appear at neighboring lattice sites in presence of a
"catalyst." The latter is modeled by supposing either that randomly chosen
bonds in the lattice promote reactions (Model I) or that reactions are
activated by randomly chosen lattice sites (Model II). In the case of annealed
disorder in spatial distribution of a catalyst we calculate the pressure of the
adsorbate by solving three-site (Model I) or four-site (Model II) recursions
obeyed by the corresponding averaged grand-canonical partition functions. In
the case of quenched disorder, we use two complementary approaches to find
$\textit{exact}$ expressions for the pressure. The first approach is based on
direct combinatorial arguments. In the second approach, we frame the model in
terms of random matrices; the pressure is then represented as an averaged
logarithm of the trace of a product of random $3 \times 3$ matrices -- either
uncorrelated (Model I) or sequentially correlated (Model II).
