This work reports predictions from molecular simulation results for the solubility of the single gases carbon dioxide, carbon monoxide, and hydrogen in the ionic liquid 1-N-butyl-3-methyl-imidizolium hexafluorophosphate ([bmim][PF6]) at temperatures from 293 to 393 K and at pressures up to 9 MPa, The predictions are achieved by Gibbs ensemble Monte Carlo simulations at constant pressure and temperature (NpT-GEMC). The intermolecular forces are approximated by effective pair potentials for the pure gases and by a quantum-chemistry-based pair potential for [bmim][PF6]. The interactions between unlike group, are described using common mixing rules without any adjustable binary interaction parameter. The simulation results for the solubility of hydrogen agree within their statistical uncertainty with experimental data, whereas the results for carbon monoxide and carbon dioxide reveal somewhat larger deviations.