Assessing the validity and limits of linear density models for predicting dissociation–association equilibria in supercritical water

A linear relationship between the logarithms of solute dissociation constants, log ( K ) , and the density of water, log ( ρ H 2 O ), has empirically been demonstrated for decades and raised hope for an universal formalism to describe solute thermodynamic properties over wide ranges of temperature and density at supercritical conditions. Yet, neither a theoretical foundation nor an assessment of the ranges of validity have been presented. Here, we use classical molecular dynamics (MD) simulations as a complementary tool to assess the validity of this linear relationship for the example of NaCl and reveal its limits at water densities below ca. 0.3 g cm −3 . The derivative ∂ log ( K ) / ∂ log ( ρ H 2 O ) is calculated based on the volume of reaction and water compressibility derived from the simulations performed in the isothermal–isobaric ensemble at 673 K. Our results corroborate the linear dependence of log ( K ) vs. log ( ρ H 2 O ) in the experimentally studied density range and suggest that the linear dependence also extends to higher densities. However, towards lower densities, log ( K ) decreases and takes on values that are lower than would be expected by simply extrapolating the linear behavior. This decrease is consistent with earlier theoretical predictions for the behavior of log ( K ) at vapor-like densities but questions the relevance of some indirect experimental evidence obtained at low temperatures. Although the function described by log ( K ) vs log ( ρ H 2 O ) is non-linear in the low density range, it can be considered well-behaved even at near critical conditions.