Abstract: This paper proposes that a critical compressibility factor Zc can be used as a fourth parameter for corresponding states, as a result of the analysis of the relationship between Zc and acentric factor w. Two formulas used in the Patel-Teja equation of state for expressing molecular characteristics can be improved by using Zc. Excellent results are obtained with these two new formulas for predicting certain polar molecules not included in the process of fitting parameters. Bhirud equation, which is only adoptable for saturated liquid volumes of non-polar molecules, has been successfully extended for polar molecules. For polar molecules, no definite relationship does exist between Zc and w. It is assumed, therefore, that Zc would probably serve as a good correction factor for some formulas in which w is used as the third parameter for corresponding states.