Thermodynamic Modeling of the H₂O–Na⁺, K⁺ || HPO₄^2–, PO₄^3– System

A comprehensive thermodynamic model for aqueous solutions containing sodium and potassium monohydrogen phosphates has been developed based on the Pitzer–Simonson–Clegg formalism for excess properties, the Helgeson–Kirkham–Flowers equation of state for standard-state properties, and the IAPWS formulations for pure water. The model accounts explicitly for acid–base equilibria among H2PO4–, HPO42–, and PO43– species and includes all necessary ion–ion and ion–neutral interactions to accurately describe solution properties over a wide temperature range. Thermodynamic parameters were evaluated using critically selected literature data on osmotic coefficients, water activity, solubility, enthalpies of dilution, and heat capacities. Solubility products of relevant solid phases, including multiple hydrates of Na2HPO4 and K2HPO4, were parametrized. The resulting model reproduces experimental phase equilibria and thermodynamic properties with high accuracy from the crystallization to the boiling point of saturated solutions. The model forms a foundation for the future inclusion of dihydrogen phosphate species and enables the consistent prediction of multicomponent phosphate solution behavior across wide concentration and temperature ranges.