Phase Equilibrium and G Minimum Displacements of the Equilibrium Under External Parameters M. DeurnY and 0. Henri-Rousseau Universite de Perpignan, Avenue de Villeneuve 66025 Perpignan cedex, France K. Boulii and 6. Bwlil Universite d'Oran, Es Senia, Algerie In the study of liquid-gas phase equilibriums, i t is necessary to distinguish the total pressure from the ~ a r t i a and l this purpose ~ e r o n a 'has vapor pressures of the gas. proposed in this Journal a useful approach bv considering in the-system to he studied an inert gas that cannot be condensed. Then, for fixed pressure and temperature i t is found that the phase equilibrium of the compound of interest only corresponds to a minimum of the Gibhs free energy when its partial pressure equals its vapor pressure. However, application of the above treatment to more general situations that take into account some external parameters like the temperature, the total pressure, the addition of a solute or of an inert gas is not given. These typical situations are studiedin textbooksin different and specificad hoc fashions, intrinsically good but neither very clear nor general from a physical pointbf view. s em on st rations of the Clausius-Clapeyron equation or of the ebulliometric Raoult law are for instance usually performed in the simplified situation of a one-compound system. As a consequence, total, partial, and vapor messures are undistinguishable when such a svstem is'in ihermal and mechanical equilibrium. Thus, the ~hvsicalreasons of the vaDor pressure chanee with the variation of an external parametkr (e.g., total-pressure P a t T fixed) may then not appear clearly. The object of this paper is therefore to treat the displacements of a phase equilibrium with respect to changes in pressure, temperatuke, amount of solute, and amoun; of an inert gas, in the framework of the Perona approach and in a similar wav as that was used t o discuss in this JournaPsome chemical equilibriums in terms of minimum of G.
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The General System and the Bask Conditions of the Eaullibriurn Depicted in Figure 1is the general system that allows the study of the phase equilibrium changes under external perturbations: total, partial, and vapor pressures are distinguished in this rigid and insulated container C surmounted by a mobile piston that keeps the C inside under the surrounding pressure P and encloses three compounds A, Y, and Z. I t will be assumed that: rhegas phase (fortheranyeoftotalpressureP and temperature T ronsidpred~and cannot be condensed. On the other hand, A is present in the vapor (Ag) and in the liquid (Al) phases, its total number of moles, n ~heing ~ ,constant. (2) Z is a solute dissolved in the liquid phase of A, which cannot
Figure 1. The general system.
be vaporized. In the following, we shall consider that the solution is diluted, i.e., nz"
