We consider a two-dimensional catalytic surface reaction between
X and $Y_n$ with $Y_n + nX \to nXY$, where $Y_n$ is a polymer consisting
of n identical atoms, each denoted by Y, and X is a
monomer. The reactants X and $Y_n$ are present above the surface in a
gaseous phase, and bond to the surface at certain rates. The resulting atoms
X and Y on the surface react if they are sufficiently close to
each other; the product XY then leaves the surface. A classical example
is the oxidation of carbon monoxide on a platinum surface. In this case, $n =
2, X = CO$ and $Y_2 = O_2$. We consider the case in which the polymer consists
of $n = N^2$ atoms, arranged in a square of length N, with N
large. We show that when the range of interaction is large compared to the
polymer size, X and Y will typically coexist on the catalytic
surface for appropriate bonding rates. If, however, the range of interaction is
small compared to the polymer size, then, irrespective of the bonding rates,
the surface will eventually be fully occupied by the monomer X.