A modified version of the Peng–Robinson equation of state (EoS) is developed to describe the thermodynamic properties of polar and non-polar substances. The modified EoS is obtained after replace the alpha function of Soave by the alpha function of Heyen in the pressure–volume–temperature relationship of the Peng–Robinson EoS. The parameters of the EoS are correlated in terms of the critical temperature, the critical pressure, the acentric factor and the polar factor of Halm-Stiel to obtain generalized expressions by fitting two vapor pressure data for 67 polar compounds and 23 n-alkanes. To validate the EoS, vapor pressures are calculated for 178 polar and 81 non –polar compounds. The average absolute relative deviation calculated is 1.51%. In total, 8440 vapor pressure data are calculated for polar substances and 2281 for gases and hydrocarbons. The modified EoS is compared with a modified Patel–Teja equation that requires substance-dependent parameters, the Peng–Robinson EoS and a generalized version of the Peng–Robinson–Stryjek-Vera EoS. The calculated deviations are 6.17%, 6.68% and 1.27% for the PR, the gPRSV and the PTH EoSs. Additionally, to improve liquid densities estimations, the modified EoS is translated in volume by fitting one saturated liquid volume. The translation-parameter is generalized for gases and hydrocarbons and it is estimated and reported for 179 polar compounds. Saturated liquid densities are calculated for 259 substances. The calculated average absolute relative deviation is 1.70%. This value is practically the same calculated with the PTH EoS. Also, single-phase density calculations including pressures above 100 MPa are performed for some gases, alkanes and polar substances. It has be found that results are better with the proposed model, especially for heavy hydrocarbons. For example, the deviations for n-tetracosane are 6.2% and 13% for the modified and the PTH EoSs. Similar results are obtained for other compounds like n-eicosane and n-octacosane. On the other hand, heat capacity at constant pressure for the saturation curve and the single phase region is predicted with the modified, the PR and the PTH EoSs for 20 compounds. Results show that average absolute relative deviations for all the models are similar and their values are around 5.0% for the saturated liquid, 7.0% for saturated vapor and 4.0% for the single phase region. Finally, the modified EoS is used to predict the vapor pressure, the saturated liquid volume and the heat capacity in the single phase region of water. In general, results can be considerate adequate taking in account the simplicity of the proposed EoS. Calculated deviations are 0.75%, 4.34% and 5.17% for the three properties selected.