  We study the evolution of molecular hydrogen on the grain surfaces and in the
gas phase using both the rate equation (which tracks the average number of
molecules) and the master equation (which tracks the expectation values of
molecules). We show that above a certain critical accretion rate of $H$ on the
grains, the results from these two methods become identical. We used this
result to follow the collapse of a dense interstellar cloud and studied the
formation of molecular hydrogen for two different temperatures (T=10K and 12K)
and two different masses ($1M_\odot$ and $10M_\odot$) of the cloud when olivine
grains were used. Since at higher temperatures, the recombination is very small
for these grains, we also studied a similar hydrodynamic processes at higher
temperatures (T=20K and 25K) when amorphous carbon grains were used. We find
that generally, for olivine grains, more than 90% $H$ is converted to $H_2$
within $\sim 10^{5-7}$yr whereas for amorphous grains it takes $\sim
10^{6-7}$yr. $H_2$ formed in this manner can be adequate to produce the
observed complex molecules.
