  We study equilibrium properties of a catalytically-activated annihilation $A
+ A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N
\to \infty$) in which some segments (placed at random, with mean concentration
$p$) possess special, catalytic properties. Annihilation reaction takes place,
as soon as any two $A$ particles land onto two vacant sites at the extremities
of the catalytic segment, or when any $A$ particle lands onto a vacant site on
a catalytic segment while the site at the other extremity of this segment is
already occupied by another $A$ particle. Non-catalytic segments are inert with
respect to reaction and here two adsorbed $A$ particles harmlessly coexist. For
both "annealed" and "quenched" disorder in placement of the catalytic segments,
we calculate exactly the disorder-average pressure per site. Explicit
asymptotic formulae for the particle mean density and the compressibility are
also presented.
