It is shown in this paper that for pure substances obeying the van der Waals (VdW) equation of state (EOS) or Redlich–Kwong (RK) type equations of state below the critical temperature, it is possible to obtain with the help of the Maxwell equal areas rule the vapour pressure curve, the difference between the molar volume of the vapour and of the liquid, and the difference between the molar entropies of vapour and liquid; each property is obtained in the first step as a dimensionless expression, function of a dimensionless temperature. Any particular property of a particular fluid obeying VdW EOS or one type of RK EOS can be obtained from the corresponding dimensionless expression by multiplying it with a dimension unit which is a function of the particular temperature-dependent parameter a(T) of the EOS considered for the fluid. In the cases of VdW and the original RK (EOS), the dimensionless functions are unique for all the pure fluids that obey the EOS under consideration. A comparison of VdW, RK and RK–Soave (SRK) predictions with experimental vapour pressure data is exemplified for carbon dioxide.