In this paper we present a thermodynamic model for asymmetric solutions with a special emphasis on solute–solvent interactions. The new “COSMOSAC-LANL” activity coefficient model is rooted in first principles calculations based on the COSMO model where the microscopic information passes to the macroscopic world via a dielectric continuum solvation model followed by a post statistical thermodynamic treatment of self-consistent properties of the solute particle. To model the activity coefficient at infinite dilution for the binary mixtures, a 3-suffix Margules (3sM) function is introduced to model asymmetric interactions and, for the combinatorial term, the Staverman–Guggenheim (SG) form is used. The new “COSMOSAC-LANL” activity coefficient model has been used to calculate the solubility of CO₂ in room temperature ionic liquids and to model the selectivity between CO₂ and CH₄ gases. We have shown improved solubility and selectivity prediction of CO₂ and CH₄ gas in room temperature ionic liquids using the ADF-COSMOSAC-2013 model with the new “LANL” activity coefficient model. The calculated values have been compared with experimental results where they are available.