= Solution
The usual major carbon/oxygen reservoirs in a hydrogen-rich <hot Jupiter> are \b[<water>, <carbon monoxide> and <methane>], with their relative importance set by <thermochemical equilibrium>. This is not a universal ranking for every temperature and composition: nitrogen molecules or <carbon dioxide> can exceed a strongly depleted member of this trio.
At about one bar, the useful net reaction is
$$
\mathrm{CO}+3\mathrm{H}_2\rightleftharpoons\mathrm{CH}_4+\mathrm{H}_2\mathrm O.
$$
The rightward reaction is exothermic. Cooler gas favors <methane> and <water>; warming favors <carbon monoxide> and suppresses <methane>. The CO/CH4 crossover is of order $10^3\,\mathrm K$ and shifts with pressure, elemental inventory and metallicity; it is not a universal temperature. <Water> remains an important oxygen reservoir for oxygen-rich compositions but can dissociate at sufficiently high temperature.
Increasing the <atmospheric metallicity of a giant planet> raises the available carbon and oxygen. In a dilute, H2-dominated regime, major CO and H2O abundances roughly increase with the enrichment factor, and cool-regime CH4 does likewise. CO2 can rise faster, approximately quadratically in suitable warm regimes. At very high enrichment, the H2 fraction and <mean molecular weight> also change, invalidating simple linear scalings.
At high temperature and <atmospheric carbon-to-oxygen ratio> below unity, CO binds much of the carbon, leaving excess oxygen for H2O. As C/O approaches or exceeds one, CO consumes nearly all available oxygen and \b[H2O is strongly depleted]; excess carbon enhances CH4, <hydrogen cyanide> and <acetylene>. Cooler CH4-dominated chemistry uses less oxygen in CO and can leave more <water> even at the same elemental ratio. These trends are <carbon partition and atmospheric water abundance>, and assume equilibrium rather than vertical or horizontal quenching.
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