Classical fluid theories do not describe the long-range fluctuations that occur in the vicinity of a pure component or mixture's critical point. The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is extended with a renormalization group theory for mixtures. The theory accounts for the long-range density fluctuations and the results reduce to the results of the classical PC-SAFT equation of state away from the critical point. Two approximation methods, the isomorphic approximation and phase-space cell approximation, are used for the renormalization group corrections of mixtures. The two variants are evaluated by comparison to experimental vapor-liquid data for systems of alkalies, carbon dioxide and hydrogen sulfide. Overall, the considered implementation of the phase-space cell approximation is slightly superior to the isomorphic approximation for the mixtures investigated here. The phase-space cell approximation tends to overestimate the renormalization corrections for some cases but generally leads to good agreement with experimental data for binary mixtures.