  The faint CO gases in debris disks are easily dissolved into C by UV
irradiation, while CO can be reformed via reactions with hydrogen. The
abundance ratio of C/CO could thus be a probe of the amount of hydrogen in the
debris disks. We conduct radiative transfer calculations with chemical
reactions for debris disks. For a typical dust-to-gas mass ratio of debris
disks, CO formation proceeds without the involvement of H$_2$ because a small
amount of dust grains makes H$_2$ formation inefficient. We find that the CO to
C number density ratio depends on a combination of
$n_\mathrm{H}Z^{0.4}\chi^{-1.1}$, where $n_\mathrm{H}$ is the hydrogen nucleus
number density, $Z$ is the metallicity, and $\chi$ is the FUV flux normalized
by the Habing flux. Using an analytic formula for the CO number density, we
give constraints on the amount of hydrogen and metallicity for debris disks. CO
formation is accelerated by excited H$_2$ either when the dust-to-gas mass
ratio is increased or the energy barrier of chemisorption of hydrogen on the
dust surface is decreased. This acceleration of CO formation occurs only when
the shielding effects of CO are insignificant. In shielded regions, the CO
fractions are almost independent of the parameters of dust grains.
