Research of a Thermodynamic Function \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\): Temperature Dependence and Relation to Properties at Infinite Dilution

In this work, we propose the idea of considering \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\) as an infinite dilution thermodynamic function. Our research shows that \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\) as a thermodynamic function is closely related to temperature, with the relation being simply expressed as: \({\ln \left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}=\frac{A}{T}+B}\). Then, we use this equation to correlate the isothermal vapor–liquid equilibrium (VLE) data for 40 systems. The result shows that the total average relative deviation is 0.15%, and the total average absolute deviation is 3.12%. It indicates that the model correlates well with the experimental data. Moreover, we start from the total pressure expression, and use the Gibbs–Duhem equation to re-derive the relationship between \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\) and the infinite dilution activity coefficient (\({\gamma^{\infty}}\)) at low pressure. Based on the definition of partial molar volume, an equation for \({\left(\frac{\partial p}{\partial x}\right)_{T,x \rightarrow 0}}\) and gas solubility at high pressure is proposed in our work. Then, we use this equation to correlate the literature data on the solubility of nitrogen, hydrogen, methane, and carbon dioxide in water. These systems are reported at temperatures ranging from 273.15 K to 398.15 K and pressures up to 101.325 MPa. The total average relative deviation of the predicted values with respect to the experimental data is 0.08%, and the total average absolute deviation is 2.68%. Compared with the Krichevsky–Kasarnovsky equation, the developed model provides more reliable results.