In this work, it is assessed the capability of a cubic equation of state and the Huron-Vidal-NRTL mixing rules to describe the liquid-liquid equilibria of binary mixtures formed by a polar aprotic solvent and alkanes. N,N-dimethylacetamide, 1-methylpirrolidin-2-one, propanenitrile, nitrobenzene and nitromethane are selected as polar aprotic solvents and mixtures including alkanes between butane and hexadecane are studied. For each solvent and the n-alkanes series, generalized expressions are developed for the binary interaction parameters (BIPs) as function of the RTc/Pc ratio of alkanes. All the generalized expressions are obtained by fitting liquid-liquid equilibria experimental data. To validate the proposed model, liquid-liquid, vapor-liquid equilibria and some liquid molar volumes predictions are performed. In total, 35 binary mixtures are analyzed. For the type of mixtures analyzed, it is shown that using the parameters of the pure substances required for the cubic EoS and the critical point of n-alkanes, it is possible to obtain satisfactory description of liquid-liquid and vapor-liquid equilibria at low pressure (below 1 Atm) using a simple thermodynamic model.