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We present an exact solution describing equilibrium properties of thecatalytically-activated A + A \to 0 reaction taking place on a one-dimensionallattice, where some of the sites possess special "catalytic" properties. The Aparticles undergo continuous exchanges with the vapor phase; two neighboringadsorbed As react when at least one of them resides on a catalytic site (CS).We consider three situations for the CS distribution: regular, annealed randomand quenched random. For all three CS distribution types, we derive exactresults for the disorder-averaged pressure and present exact asymptoticexpressions for the particles' mean density. The model studied here furnishesanother example of a 1D Ising-type system with random multi-site interactionswhich admits an exact solution.Comment: 7 pages, 3 Figures, appearing in Europhysics Letter

Exactly solvable model of A + A → 0 reactions on a heterogeneous catalytic chain