  We study molecular hydrogen formation in and on solids. We construct a model
with surface sites and bulk sites capable of describing (1) the motion and
exchange of H and H_2 between surface and bulk, (2) the recombination of H and
dissociation of H_2 in and on the solid, and (3) the injection of H from the
gas phase and the loss of H and H_2 from the solid. The basic physical
processes include thermally activated reactions, collisionally induced
reactions, and tunneling reactions. Our main application is to the astronomical
problem of H_2 formation on grains in space but the model has more general
applicability. We investigate the steady-state H and H_2 concentrations in and
on the solid when gas phase atoms or ions stick to the surface or penetrate the
body of the grain. The model identifies ranges of physical parameters for which
the solid becomes saturated (surface and/or bulk) with particles (H and/or H_2)
and facilitates the calculation of the efficiency of molecule formation (the
fraction of the gas phase atoms that leave as molecules). These solutions are
highly degenerate in the sense that they depend only on a small number of
dimensionless parameters. We find that a variety of recombination pathways
operate under a broad range of conditions. As an example we study H_2 formation
in and on carbon grains.
