  Investigating the reliability of the assumption of instantaneous chemical
equilibrium (ICE) for calculating the CO number density in the solar atmosphere
is of crucial importance for the resolution of the long-standing controversy
over the existence of `cool clouds' in the chromosphere, and for determining
whether the cool gas owes its existence to CO radiative cooling or to a
hydrodynamical process. Here we report the first results of such an
investigation in which we have carried out time-dependent gas-phase chemistry
calculations in radiation hydrodynamical simulations of solar chromospheric
dynamics. We show that while the ICE approximation turns out to be suitable for
modeling the observed infrared CO lines at the solar disk center, it may
substantially overestimate the `heights of formation' of strong CO lines
synthesized close to the edge of the solar disk, especially concerning vigorous
dynamic cases resulting from relatively strong photospheric disturbances. This
happens because during the cool phases of the hydrodynamical simulations the CO
number density in the outer atmospheric regions is smaller than what is
stipulated by the ICE approximation, resulting in decreased CO opacity in the
solar chromosphere. As a result, the cool CO-bearing gas which produces the
observed molecular lines must be located at atmospheric heights not greater
than 700 km, approximately. We conclude that taking into account the
non-equilibrium chemistry improves the agreement with the available on-disk and
off-limb observations, but that the hydrodynamical simulation model has to be
even cooler than anticipated by the ICE approximation, and this has to be the
case at the `new' (i.e. deeper) formation regions of the rovibrational CO
lines.
