|Be aware that the conventional consistency tests do not work.
Activity coefficients determined using accurate VLE data must satisfy the Gibbs–Duhem (GD) equation. However, the slope methods or point tests have the practical disadvantage that it is difficult to draw accurate tangents. Therefore, the slope method is limited at best to a rough measure of the thermodynamic consistency [ref. 1]. Meanwhile, integral methods or area tests have the disadvantage that the cancellation of errors may occur due to the lack of a point-by-point test of the data.
If the activity coefficient equations are used for correlating the VLE data, point tests and area tests must be satisfied. The deviation from the Gibbs-Duhem equation, (AAD)GD, usually ranges from 10-5 to 10-8, because the significant figures are insufficient. Using software, (AAD)GD = 10-90 can be established, if the significant figure is set at 100. That is, if the conventional activity coefficient equations are used, the Gibbs-Duhem equation is always satisfied, no matter how serious the experimental errors are involved in the data. Therefore, these conventional consistency tests cannot be used for eliminating inaccurate VLE data.
Be aware that the TC line provides useful consistency tests for the VLE data..
As shown using a numerical analysis [ref. 2], deviations from the Gibbs-Duhem equation, (AAD)GD, are related to the systematic error involved in the liquid phase mole fraction of component 1, Δx1, as follows:
(AAD)GD = k (Δx1)2
where k denotes a constant. The equation clearly shows that the only way to satisfy the Gibbs-Duhem equation is to remove the experimental errors. A possible method for removing errors is to establish a high-precision correlation using data obtained by different researchers using different equipment and methods. The TC line is a high-precision correlation established using the VLE and LLE data of binaries. Therefore, it can be a core standard of the data consistency tests. Furthermore, universal correlations, the PPM, enable us to eliminate the error involved in VLE data.
1) J. M. Prausnitz, Molecular Thermodynamics of Fluid Phase Equilibria, Prentice-Hall, Upper Saddle River, NJ, 1969.
2) S. Kato, Fluid Phase Equilibria, 297 (2010), 192-199.