A linear relationship between the logarithms of solute dissociation constants, log(K), and the density of water, log (ρH2O), 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. 0.3gcm−3. The derivative ∂log(K)/∂log(ρH2O) is calculated based on the volume of reaction and water compressibility derived from the simulations performed in the isothermal–isobaric ensemble at 673K. Our results corroborate the linear dependence of log(K) vs. log(ρH2O) 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(ρH2O) is non-linear in the low density range, it can be considered well-behaved even at near critical conditions.

中文翻译：

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评估线性密度模型在预测超临界水中解离-缔合平衡的有效性和局限性


几十年来，溶质解离常数的对数 log（K） 和水的密度 log （ρH2O） 之间的线性关系已经被实证证明，这为在超临界条件下在很宽的温度和密度范围内描述溶质热力学性质的通用形式带来了希望。然而，既没有提出理论基础，也没有对有效性范围的评估。在这里，我们使用经典分子动力学 （MD） 模拟作为补充工具来评估这种线性关系的有效性，例如 NaCl，并揭示其在水密度低于约 0.3gcm-3 时的极限。导数 ∂log（K）/∂log（ρH2O） 是根据在 673K 下在等温-同压集合中进行的模拟得出的反应体积和水压缩率计算得出的。我们的结果证实了 log（K） vs. log（ρH2O） 在实验研究的密度范围内的线性依赖性，并表明线性依赖性也延伸到更高的密度。然而，对于较低的密度，log（K） 会降低并呈现低于通过简单地推断线性行为所预期的值。这种降低与早期对 log（K） 在类似蒸汽密度下的行为的理论预测一致，但质疑在低温下获得的一些间接实验证据的相关性。尽管 log（K） 与 log（ρH2O） 描述的函数在低密度范围内是非线性的，但即使在接近临界条件下，也可以认为它表现良好。