An Interesting Algebraic Rearrangement of Semi-empirical Gaseous Equations of State. Partitioning of the Compressibility Factor into Attractive and Repulsive Parts

The general semi-empirical gaseous equation of state can be rearranged to produce an expression for the compressibility factor, z, which is partitioned into two unitless factors, one due to attractive molecular forces and the other due to occluded molecular volumes, hence to repulsions. This idea may prove useful in introductory physical chemistry courses when students are learning to conceptualize non-ideal behavior. The expressions for pressure correction presented in equations by van der Waals, Berthelot, Clausius, Redlich-Kwong and Dieterici are reviewed. Compressibility factors are calculated for 24 van der Waals gases at various temperatures and pressures.