The Ionization Constant of Water over Wide Ranges of Temperature and Density

A semitheoretical approach for the ionization constant of water, $KW,$ is used to fit the available experimental data over wide ranges of density and temperature. Statistical thermodynamics is employed to formulate a number of contributions to the standard state chemical potential of the ionic hydration process. A sorption model is developed for calculating the inner-shell term, which accounts for the ion–water interactions in the immediate ion vicinity. A new analytical expression is derived using the Bragg–Williams approximation that reproduces the dependence of a mean ion solvation number on the solvent chemical potential. The proposed model was found to be correct at the zero-density limit. The final formulation has a simple analytical form, includes seven adjustable parameters, and provides good fitting of the collected $KW$ data, within experimental uncertainties, for a temperature range of $0–800 °C$ and densities of $0–1.2 g cm−3.$