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.

Accurate prediction of infinite dilution activity coefficient (γ ∞ ) is essential for the calculation of phase equilibria, solubility, and related properties in molecular thermodynamics. Here, we propose a new model to accurately predict the value of γ ∞ . It is applicable to calculate γ ∞ for compounds in aqueous solution at different temperatures. The model is based on the relationship of (∂p/∂x) T,x→0 with γ ∞ and temperature at low pressure. First, we introduce the new idea of using the group contribution method to estimate (∂p/∂x) T,x→0 and then obtain the activity coefficient of a solute at infinite dilution in water based on the relationship between (∂p/∂x) T,x→0 and γ ∞ . The accuracy of this model is verified using experimental data from 46 systems and more than 450 data points. The result shows that the total average relative deviation of the predicted values from the experimental values for training data is 4.73%. Besides, we test the applicability of the model using solutes that are not part of the training data set. The result shows that the model is satisfactory for the prediction of testing data. Compared with other models, the results prove that the developed model outperforms the UNIFAC model, the modified UNIFAC model, and previous predictive models for aqueous systems. The final equation with only simple arithmetic is more easily applied in engineering practices.

No abstract