The vdW EOS suggests that for all pure substances the critical compressibility factor is a constant (=0.375). This, however, is contrary to experience. Indeed, although similar in magnitude, the value of Z_C is specific to a pure substance. For example, for methane it is 0.286, while for helium 0.302. This indicates that although an improvement over ideal gas EOS, the vdW EOS does not reflect the specificity needed to predict the behaviour of all substances at high pressures. 

To bridge this gap several other cubic EOS of higher accuracy have been advanced, the three most widely used of which are:

• Redlich-Kwong (RK) EOS (Otto Redlich and J. N. S. Kwong, Chem. Rev.,vol. 44, pp. 233-244, 1949)
• Soave-Redlich-Kwong (SRK) EOS (G. Soave, Chem. Eng. Sci., vol. 27, pp. 1197-1203, 1972.)
• Peng-Robinson (PR) EOS (D. Y. Peng and D. B. Robinson, Ind. Eng. Chem. Fundam., vol. 15, pp. 59-64, 1976.)

All the above EOSs including that due to van der Waals may be expressed by a single equation of the following form: