  A model of the grain surface chemistry involving the accretion of atoms of
two different elements, X and Y, and their reactions to form species X_2, XY,
and Y_2 was examined for a wide range of choices for the values of its three
free parameters - the accretion rate of X and Y, the desorption rate of X and
the grain surface sweeping time of Y, all considered relative to the grain
surface sweeping rate of X. Relative production rates of the diatomics were
calculated with five methods involving, respectively, a high-order truncation
of the master equation, a low-order truncation of the master equation, the
standard deterministic rate equation approach, a modified rate equation
approach and a set of approximations which are in some cases appropriate for
accretion dominated chemistry. The accuracies of the relative production rates
calculated with the different methods were assessed for the wide range of model
parameters. The more accurate of the low-truncation master equation
calculations and the standard deterministic rate equation approach gives
results which are in most cases within ten or twenty per cent of the results
given by the high-truncation master equation calculations. For many cases, the
more accurate of the low order truncation and the standard deterministic rate
equation approaches is indicated by a consideration of the average number of
atoms of the two species on the grain's surface.
