Gaseous solubilities of carbon dioxide (1), hydrogen sulfide (2), and their binary mixture (x(2) approximate to 0.2, 0.5, 0.8) have been measured in the ionic liquid 1-octyl-3-methylimidazolium bis(trifluoromethyl)sulfonylimide ([C(8)mim][Tf2N]) at temperatures ranging from (303.15 to 353.15) K and at pressures under 2 MPa. The observed PTx solubility data were used to obtain Henry's law constants and correlated by three models: (1) the simple Krichevsky-Kasarnovsky (KK) equation, (2) a model comprised of the extended Henry's law and the Pitzer's virial expansion for the excess Gibbs free energy, and (3) the generic Redlich-Kwong (RK) cubic equation of state proposed for gas ionic liquid systems. The correlations from the three models show quite good consistency with the experimental data for IL/CO2 and IL/H2S binary mixtures within experimental uncertainties. For IL/CO2/H2S ternary mixtures, the RK model shows the best correlation with the experimental data. The comparison showed that the solubility of H2S is about two times as great as that of CO2 in the ionic liquid studied in this work. It was further found, by comparison of the experimental data of this study with those of previous reports, that the solubility of H2S in [C(n)mim][Tf2N] ILs increases as the number of carbon atoms in the alkyl substituent of methylimidazolium cation, n, increases. In addition, quantum chemical calculations at DFT/B3LYP level of theory using 6-311+G(d) and 6-311++G(2d,2p) basis sets were performed on the isolated systems studied in this work to provide explanations from a molecular point of view for the observed experimental trends.