  We use the moving mesh code AREPO coupled to a time-dependent chemical
network to investigate the formation and destruction of molecular gas in
simulated spiral galaxies. This allows us to determine the characteristics of
the gas that is not traced by CO emission. Our extremely high resolution AREPO
simulations allow us to capture the chemical evolution of the disc, without
recourse to a parameterised `clumping factor'. We calculate H2 and CO column
densities through our simulated disc galaxies, and estimate the CO emission and
CO-H2 conversion factor. We find that in conditions akin to those in the local
interstellar medium, around 42% of the total molecular mass should be in
CO-dark regions, in reasonable agreement with observational estimates. This
fraction is almost insensitive to the CO integrated intensity threshold used to
discriminate between CO-bright and CO-dark gas, as long as this threshold is
less than 10 K km/s. The CO-dark molecular gas primarily resides in extremely
long (>100 pc) filaments that are stretched between spiral arms by galactic
shear. Only the centres of these filaments are bright in CO, suggesting that
filamentary molecular clouds observed in the Milky Way may only be small parts
of much larger structures. The CO-dark molecular gas mainly exists in a
partially molecular phase which accounts for a significant fraction of the
total disc mass budget. The dark gas fraction is higher in simulations with
higher ambient UV fields or lower surface densities, implying that external
galaxies with these conditions might have a greater proportion of dark gas.
