  Observations of spiral galaxies show a strong linear correlation between the
ratio of molecular to atomic hydrogen surface density R_mol and midplane
pressure. To explain this, we simulate three-dimensional, magnetized
turbulence, including simplified treatments of non-equilibrium chemistry and
the propagation of dissociating radiation, to follow the formation of H_2 from
cold atomic gas. The formation time scale for H_2 is sufficiently long that
equilibrium is not reached within the 20-30 Myr lifetimes of molecular clouds.
The equilibrium balance between radiative dissociation and H_2 formation on
dust grains fails to predict the time-dependent molecular fractions we find. A
simple, time-dependent model of H_2 formation can reproduce the gross behavior,
although turbulent density perturbations increase molecular fractions by a
factor of few above it. In contradiction to equilibrium models, radiative
dissociation of molecules plays little role in our model for diffuse radiation
fields with strengths less than ten times that of the solar neighborhood,
because of the effective self-shielding of H_2. The observed correlation of
R_mol with pressure corresponds to a correlation with local gas density if the
effective temperature in the cold neutral medium of galactic disks is roughly
constant. We indeed find such a correlation of R_mol with density. If we
examine the value of R_mol in our local models after a free-fall time at their
average density, as expected for models of molecular cloud formation by
large-scale gravitational instability, our models reproduce the observed
correlation over more than an order of magnitude range in density.
