A binary system of benzene and hexafluorobenzene is known as a system with famous double azeotropes (minimum-and-maximum pressure azeotropes at the isothermal VLE (vapor-liquid equilibrium)). In order to understand how these azeotropic behaviors will be affected by interactions with an ionic liquid, solubility experiments for benzene + ionic liquid, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [emim][Tf2N], and hexafluorobenzene + [emim][Tf2N] systems have been made at temperatures of about 283, 298, and 318 K. Both binary systems show immisciblity gaps with concentration ranges from about 77 to 100 and from about 65 to 100 mole % for benzene and hexafluorobenzene systems, respectively. The observed solubility data have been used to develop equation-of-state (EOS) models (with a generic Redlich-Kwong cubic equation) for these binary systems. As for the binary system of benzene and hexafluorobenzene, VLE data in the literature have been employed to develop the EOS model. Thus, binary and ternary phase diagrams for the present three components have been constructed using the present binary interaction parameters. Then, extractive separations of the azeotropes are discussed based on the present EOS model.