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THERMODYNAMIC FOUNDATIONS OF ACTIVITY COEFFICIENTS OF ELECTROLYTES IN ELECTROSTATIC THEORIES
Janez Cerar1
e-mail: janez.cerar@fkkt.uni-lj.si
1Faculty of Chemistry and Chemical Technology, University of Ljubljana,
Večna pot 113, SI-1000 Ljubljana, Slovenia
Activity coefficients provide a measure of the non-ideality introduced by a species in a system. In electrolyte solutions, strong electrostatic interactions often cause ionic activity coefficients to deviate substantially from unity, even at low concentrations. Although the century-old Debye–Hückel theory1 successfully predicts activity coefficients in dilute solutions, only recently has a thermodynamic decomposition of these contributions been achieved2.
Within the Debye–Hückel framework, it can be demonstrated that the energetic contributions of induced repulsive electrostatic interactions and entropy are each exactly half the magnitude—but opposite in sign—to that of the direct attractive electrostatic interaction between the central ion and its ionic atmosphere. This decomposition not only deepens our understanding of how ions influence their surroundings but also establishes a direct link between activity coefficients and the microscopic behaviour of individual ions.
This work explores potential extensions of the approach to other electrostatic theories, including the non-linear Poisson–Boltzmann equation, the Hypernetted Chain (HNC) equation, and the incorporation of non-Coulombic terms. Furthermore, its applicability to polyelectrolyte solutions—of both spherical and cylindrical symmetry—is considered. Finally, the approach enables the validation of such thermodynamic dissections, ensuring consistency across theoretical frameworks.
Keywords: electrolyte solutions, entropy, attractive interactions, induced repulsive interactions.
References:
(1) Debye, P.; Hückel, E. Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung
und verwandte Erscheinungen. Phys. Z., 1923, 24, 185-206.
(2) Cerar, J. Thermodynamic decomposition of Debye–Hückel activity coefficients: resolving attractive, repulsive, and entropic components. Phys. Chem. Chem. Phys., 2026, 28, 16841-16850.