  We have determined the temperature dependence of the solvation behavior of a
large collection of light gases in imidazolium-based Ionic Liquids (ILs) with
the help of extensive molecular dynamics simulations. The solubility of
molecular hydrogen, oxygen, nitrogen, methane, krypton, argon, neon and carbon
dioxide in the imidazolium based ILs of type 1-n-alkyl-3-methylimidazolium
bis(trifluoromethylsulfonyl)imide ([C$_n$mim][NTf$_2$]) with varying chain
lengths $n\!=\!2,4,6,8$ are computed for a temperature range between
$300\,\mbox{K}$ and $500\,\mbox{K}$ at $1\,\mbox{bar}$. By applying Widom's
particle insertion technique and Bennet's overlapping distribution method, we
are able to determine the temperature dependent solvation free energies for
those selected light gases in simulated imidazolium based ILs with high
statistical accuracy. Our simulations show that the magnitude of the solvation
free energy of a gas molecule at a chosen reference temperature and its
temperature-derivatives are intimately related with respect to oneanother. We
conclude that this "universal" behavior is rooted in a solvation
entropy-enthalpy compensation effect, which seems to be a defining feature of
the solvation of small molecules in Ionic Liquids. We argue that this feature
is based on a hypothesized funnel-like shape of the free energy landscape of a
solvated gas molecule. The observations lead to simple analytical relations,
determining the temperature dependence of the solubility data based on the
absolute solubility at a certain reference temperature, which we call
"solvation funnel" model. By comparing our results with available experimental
data from many sources, we can show that the "solvation funnel" model is
particularly helpful for providing reliable estimates for the solvation
behavior of very light gases, such as hydrogen, where conflicting experimental
data exist.
