## Theory: thermodynamic properties-excess chemical potential

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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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