On the abundances of noble and biologically relevant gases in Lake Vostok, Antarctica

Motivated by the possibility of comparing theoretical predictions of Lake Vostok's composition with future in situ measurements, we investigate the composition of clathrates that are expected to form in this environment from the air supplied to the lake by melting ice. In order to establish the best possible correlation between the lake water composition with that of air clathrates formed in situ, we use a statistical thermodynamic model based on the description of the guest-clathrate interaction by a spherically averaged Kihara potential with a nominal set of potential parameters. We determine the fugacities of the different volatiles present in the lake by defining a "pseudo" pure substance dissolved in water owning the average properties of the mixture and by using the Redlich-Kwong equation of state to mimic its thermodynamic behavior. Irrespective of the clathrate structure considered in our model, we find that xenon and krypton are strongly impoverished in the lake water (a ratio in the 0.04--0.1 range for xenon and a ratio in the $\sim$0.15--0.3 range for krypton), compared to their atmospheric abundances. Argon and methane are also found depleted in the Lake Vostok water by factors in the 0.5--0.95 and 0.3--0.5 ranges respectively, compared to their atmospheric abundances. On the other hand, the carbone dioxide abundance is found substantially enriched in the lake water compared to its atmospheric abundance (by a factor in the 1.6--5 range at 200 residence times). The comparison of our predictions of the CO$_2$ and CH$_4$ mole fractions in Lake Vostok with future in situ measurements will allow disentangling between the possible supply sources.