The singularities of the integrals in Mayer's ionic solution theory

The terms of the expression previously obtained by Friedman for the cluster integral sum in Mayer's theory are examined as to order in total ion concentration, c, at the limit, c = 0. The order of the singularity at c = 0 is calculated for several of those terms of the irreducible cluster integrals that correspond to graphs of low connectivity but with an arbitrary number of vertices. On the basis of these calculations and two postulates concerning the relation of the singularities of these integrals to others, it is concluded that the terms of the cluster integral sum, when arranged in order of increasing index, are also in increasing order of concentration, and that the first term, κ ³/12π, has a lower order than any other. The order in concentration of the higher terms depends on whether the third moment of the concentration of charge types, σc₈z₈ ³, vanishes, as it does in solutions of electrolytes of symmetrical charge type.