Three different variants of the crossover Soave-Redlich-Kwong equation of state are applied to describe the equilibrium behaviour of 72 common non-associating fluids - 27 hydrocarbons (including the first 10 n-alkanes), 36 halogenated refrigerants, 5 cryogenics (fluorine, oxygen, nitrogen, argon and carbon monoxide) and 4 other industrially important inorganic fluids (carbon dioxide, sulfur dioxide, nitrous oxide and sulfur hexafluoride). The model contains six compound dependent parameters. Two of them (a(0) and b of the classical part) are adjusted on the critical experimental temperature and the critical pressure. In a first model denoted as model A, the four remaining parameters are fitted to describe the saturated liquid and vapour densities and vapor pressures as well as PVT data at pressures up to P=3 x P-c. In the second model (model B), the dispersion softness m is expressed as a function of the acentric factor omega and a relation between two of the crossover parameters is employed; the number of fitted parameters is thus reduced to two. Based on model B, we suggested our final Model C, in which all the parameters can be determined from the critical point, acentric factor or rectlinear diameter. This model is superior to the classical Soave-Redlich-Kwong equation of state because it improves considerably the description of the liquid densities over the whole coexistence region. Contrary to equations of state optimized to reproduce the liquid densities at low temperatures, the crossover equation does not overpredict the critical temperature and pressure. Model C is applied to describe the equilibrium behaviour of two compounds not included in the parameterization, hexafluoropropene (HFO1216) and hexafluoropropene oxide (HFPO). (C) 2015 Elsevier B.V. All rights reserved.