The Theory of Ionic Solutions

The virial development for the osmotic pressure of a solution may be used, if the potentials of average force of the solute molecules at infinite dilution are known, to compute the deviations from perfect solution behavior. The expression for the logarithm of the activity coefficient can thus be obtained as a sum of coefficients multiplied by powers of the concentration. For an ionic solution, with 1/R² forces, the series is only conditionally convergent. By summing certain additive terms occurring in the coefficients over all powers of concentration convergence can be attained. The integrations necessary to obtain terms correct up to and including $c^{\frac{3}{2}}$ are performed. The results are given in terms of certain functions which can readily be computed.