The rate equation approach to the chemistry occurring on grain surfaces in
interstellar clouds has been criticized for not taking the discrete nature
of grains into account. Indeed, investigations of simple models show that r
esults obtained from rate equations can be significantly different from res
ults obtained by a Monte Carlo procedure. Some modifications of the rate eq
uations have been proposed that have the effect of eliminating most of the
differences with the Monte Carlo procedure for simplified models of interst
ellar clouds at temperatures of 10 K and slightly above. In this study we i
nvestigate the use of the modified rate equations in more realistic chemica
l models of dark interstellar clouds with complex gas-grain interactions. O
ur results show some discrepancies between the results of models with unmod
ified and modified rate equations; these discrepancies are highly dependent
, however, on the initial form of hydrogen chosen. If the initial form is m
ainly molecular, at early stages of cloud evolution there are some signific
ant differences in calculated molecular abundances on grains, but at late t
imes the two sets of results tend to converge for the main components of th
e grain mantles. If the initial form is atomic hydrogen, there are essentia
lly no differences in results between models based on the unmodified rate e
quations and those based on the modified rate equations, except for the abu
ndances on grains of some minor complex molecules. Thus, the major results
of previous gas-grain models of cold, dark interstellar clouds remain at le
ast partially intact.