The equation of state of multipolar gases

Abstract

The equation of state in the approximation of the second virial coefficient B is discussed theoretically for gases consisting of unlike multipolar molecules. A molecule of species i is assumed to posses a permanent 2n-pole moment M(n)i, as well as a 2n-pole moment P(n)i induced in it by the electric field F(n)i of order n of a neighbouring molecule of species j having the permanent 2m-pole electric moment M(m)j. Tensor formalism is used for deriving general expressions for the potential energy of electrostatic and inductional interaction of two multipolar molecules of species i and j. These energies then serve for computing two contributions to B: the one, of inductional type, is obtained in the first approximation and contains, in addition to terms with dipolar polarizability, terms accounting for the quadrupolar polarizability induced in the molecule by the molecular electric field gradient; the other, which is purely electrostatic, is obtained in the second approximation of the theory. Moreover, cross contributions to B between the electrostatic and inductional energies as well as contributions from dipolar anisotropy of dispersional-type interactions are computed. In computing the mean values of the respective powers of rij (the distance between the two molecules), a general Lennard-Jones (s-t)-type potential is applied. The theoretically derived non-central contributions to B are valid in general for molecules of arbitrary symmetry and arbitrary electrical structure; the expressions are applied to cases of axially symmetric, tetrahedral and octahedral molecules. For methane, the theoretical formulas allowed to determine numerically the octopole moment from experimental data on B to be ΩCH4 = 5 × 10−34 e.s.u. cm3.