In this paper, vapor–liquid equilibrium (VLE) data of binary mixtures containing gases such as carbon dioxide (CO2), methane, ethane, propane, or butane in the ionic liquid 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate ([emim][FAP]) have been modeled using the Peng–Robinson equation of state (PR-EoS), combined with quadratic mixing rules. The calculations were performed at various temperatures. All calculations were performed with only one adjustable binary interaction parameter except in the system with CO2. In that case, two adjustable binary interaction parameters were used. The results showed a temperature dependence of the adjustable parameters. In all cases, the calculated results have been found to be in good agreement with the experimental data. A total absolute average deviation in the bubble-point pressures of less than 3% was established over a wide temperature range (293–363 K) and pressures up to 11 MPa.