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Evaluation of the excess chemical potential of a component i in the solution is generally a complex task, but in the HNC approximation, it actually can be done really easily (Phys Rev A 1977, 16, 2153-2168):
with the sum going over all components of the mixture. The short-ranged direct correlation function is the same as used for the evaluation of the isothermal compressibilities. Exponentiation of
yields directly the activity coefficient
.
Mean activity coefficients
Remeber that the chemical potential can be written as a sum of ideal part and excess part (involving activity coefficient .
The activity coefficient of ion i is then
It is not experimentally possible to measure the activity coefficient of an individual ion (the whole system has to be electrically neutral). As a solution to this problem, the so called mean activity coefficients were introduced, combining the contribution of an anion and a cation at the same time.
For a binary electrolyte, we can write
with being the respective stoichiometric coefficient describing the dissociation of the salt. This leads to the well know expression for the mean activity coefficient of a symmetric binary electrolyte.
pyOZ is currently capable of evaluating excess chemical potentials/activity coefficient only when using the HNC closure relation.
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