  A prominent chemical reaction in interstellar clouds is the formation of
molecular hydrogen by recombination, which essentially takes place on dust
grain surfaces. Analytical approaches to model such a system have hitherto
neglected the spatial aspects of the problem by employing a simplistic version
of the sweeping rate of reactants. We show how these aspects can be accounted
for by a consistent definition of the sweeping rate, and calculate it exactly
for a spherical grain. Two regimes can be identified: Small grains, on which
two reactants almost surely meet, and large grains, where this is very
unlikely. We compare the true sweeping rate to the conventional approximation
and find a characteristic reduction in both regimes, most pronounced for large
grains. These effects can be understood heuristically using known results from
the analysis of two-dimensional random walks. We finally examine the influence
of using the true sweeping rate in the calculation of the efficiency of
hydrogen recombination: For fixed temperature, the efficiency can be reduced
considerably, and relative to that, small grains gain in importance, but the
temperature window in which recombination is efficient is not changed
substantially.
