  Accuracy of the mean activity coefficient expression
(Hansen-Vieillefosse-Belloni equation), valid within the hypernetted chain
(HNC) approximation, was tested in a wide concentration range against new Monte
Carlo (MC) data for +1:-1 and +2:-2 primitive model electrolytes. The
expression has an advantage that the excess chemical potential can be obtained
directly, without invoking the time consuming Gibbs-Duhem calculation. We found
the HNC results for the mean activity coefficient to be in good agreement with
the machine calculations performed for the same model. In addition, the
thermodynamic consistency of the HNC approximation was tested. The mean
activity coefficients, calculated via the Gibbs-Duhem equation, seem to follow
the MC data slightly better than the Hansen-Vieillefosse-Belloni expression.
For completeness of the calculation, the HNC excess internal energies and
osmotic coefficients are also presented. These results are compared with the
calculations based on other theories commonly used to describe electrolyte
solutions, such as the mean spherical approximation, Pitzer's extension of the
Debye-H\"uckel theory, and the Debye-H\"uckel limiting law.
