  We have investigated the time scale for formation of molecular clouds by
examining the conversion of HI to H2 using a time-dependent model. H2 formation
on dust grains and cosmic ray and photo destruction are included in
one-dimensional model slab clouds which incorporate time-independent density
and temperature distributions. We calculate 21cm spectral line profiles seen in
absorption against a background provided by general Galactic HI emission, and
compare the model spectra with HI Narrow Self-Absorption, or HINSA, profiles
absorbed in a number of nearby molecular clouds. The time evolution of the HI
and H2 densities is dramatic, with the atomic hydrogen disappearing in a wave
propagating from the central, denser regions which have a shorter H2 formation
time scale, to the edges, where the density is lower and the time scale for H2
formation longer. The model 21cm spectra are characterized by very strong
absorption at early times, when the HI column density through the model clouds
is extremely large. The minimum time required for a cloud to have evolved to
its observed configuration, based on the model spectra, is set by the
requirement that most of the HI in the outer portions of the cloud, which
otherwise overwhelms the narrow absorption, be removed. The characteristic time
that has elapsed since cloud compression and initiation of the HI to H2
conversion is a few x 10^{14} s or ~ 10^7 yr. This sets a minimum time for the
age of these molecular clouds and thus for the star formation that may take
place within them.
