Combinatorial Entropy of Mixing for Molecules Differing in Size and Shape

In reducing experimental vapour–liquid equilibrium data it is common to calculate the Gibbs energy of mixing in excess of that for a solution whose entropy of mixing is given by one of two expressions; ideal entropy or Flory–Huggins entropy. The first of these is proper for a mixture of small molecules of similar size and the second one is proper for a mixture of monomer and chain polymer. This paper considers intermediate cases where there are significant differences in molecular shape as well as size. An expression is derived for the combinatorial entropy of mixing; this expression has Flory's result as the leading term but also contains corrections for molecular bulkiness. The combinatorial entropy of mixing depends on characteristic parameters reflecting both molecular size and shape. Methods are given for simple evaluation of these parameters and illustrations for representative mixtures are presented. In some case, the corrections for bulkiness can be very large.