The recent discovery and initial characterization of sub-Neptune-sized exoplanets that receive stellar irradiance of approximately Earths raised the prospect of finding habitable planets in the coming decade, because some of these temperate planets may support liquid water oceans if they do not have massive H2/He envelopes and are thus not too hot at the bottom of the envelopes. For planets larger than Earth, and especially planets in the 1.7-3.5 R_Earth population, the mass of the H2/He envelope is typically not sufficiently constrained to assess the potential habitability. Here we show that the solubility equilibria vs. thermochemistry of carbon and nitrogen gases results in observable discriminators between small H2 atmospheres vs. massive ones, because the condition to form a liquid-water ocean and that to achieve the thermochemical equilibrium are mutually exclusive. The dominant carbon and nitrogen gases are typically CH4 and NH3 due to thermochemical recycling in a massive atmosphere of a temperate planet, and those in a small atmosphere overlying a liquid-water ocean are most likely CO2 and N2, followed by CO and CH4 produced photochemically. NH3 is depleted in the small atmosphere by dissolution into the liquid-water ocean. These gases lead to distinctive features in the planets transmission spectrum, and a moderate number of repeated transit observations with the James Webb Space Telescope should tell apart a small atmosphere vs. a massive one on planets like K2-18 b. This method thus provides a way to use near-term facilities to constrain the atmospheric mass and habitability of temperate sub-Neptune exoplanets.
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