  We present a comprehensive study of the abundance of carbon dioxide in
exoplanetary atmospheres in hot, hydrogen-dominated atmospheres. We construct
novel analytical models of systems in chemical equilibrium that include carbon
monoxide, carbon dioxide, water, methane and acetylene and relate the
equilibrium constants of the chemical reactions to temperature and pressure via
the tabulated Gibbs free energies. We prove that such chemical systems may be
described by a quintic equation for the mixing ratio of methane. By examining
the abundances of these molecules across a broad range of temperatures
(spanning equilibrium temperatures from 600 to 2500 K), pressures (via
temperature-pressure profiles that explore albedo and opacity variations) and
carbon-to-oxygen ratios, we conclude that carbon dioxide is subdominant
compared to carbon monoxide and water. Atmospheric mixing does not alter this
conclusion if carbon dioxide is subdominant everywhere in the atmosphere.
Carbon dioxide and carbon monoxide may attain comparable abundances if the
metallicity is greatly enhanced, but this property is negated by temperatures
above 1000 K. For hydrogen-dominated atmospheres, our generic result has the
implication that retrieval studies may wish to set the subdominance of carbon
dioxide as a prior of the calculation and not let its abundance completely roam
free as a fitting parameter, because it directly affects the inferred value of
the carbon-to-oxygen ratio and may produce unphysical conclusions. We discuss
the relevance of these implications for the hot Jupiter WASP-12b and suggest
that some of the previous results are chemically impossible. The relative
abundance of carbon dioxide to acetylene is potentially a sensitive diagnostic
of the carbon-to-oxygen ratio.
