The fundamental flaws inherent in Maxwell's equal area rule are analyzed. Using an alternative principle that overcomes the limitations of Maxwell's rule, general equations are derived for determining the saturation pressure and other properties associated with the liquid-vapor phase transition given an arbitrary equation of state. The equivalence of the equation for saturation pressure to those available in the literature is proved. It is found that the alternative principle predicts saturation pressures that are significantly different from those calculated using Maxwell's rule. These results are based on numerical studies on three different equations of state and fifteen substances. Similar results are obtained for the vaporization entropy as well.