  The formation of molecular hydrogen in the interstellar medium takes place on
the surfaces of dust grains. Hydrogen molecules play a role in gas-phase
reactions that produce other molecules, some of which serve as coolants during
gravitational collapse and star formation. Thus, the evaluation of the
roduction rate of hydrogen molecules and its dependence on the physical
conditions in the cloud are of great importance. Interstellar dust grains
exhibit a broad size distribution in which the small grains capture most of the
surface area. Recent studies have shown that the production efficiency strongly
depends on the grain composition and temperature as well as on its size. In
this paper we present a formula which provides the total production rate of
H$_2$ per unit volume in the cloud, taking into account the grain composition
and temperature as well as the grain size distribution. The formula agrees very
well with the master equation results. It shows that for a physically relevant
range of grain temperatures, the production rate of H$_2$ is significantly
enhanced due to their broad size distribution.
