The Chain-of-rotators equation of state in a simplified form is extended to polar substances with modifications of parameters a and b. New parameter values are reported for 67 polar and associating substances and 38 non-polar substances. Two sets of mixing rules are investigated to apply the equation of state to mixtures : the van der Waals mixing rules and the free energy matching mixing rules. Examples are presented of calculated vapor-liquid phase diagrams for various mixture combination of polar, non-polar, and associating substances.