Determination of partial molar volumes at critical end points

There has been considerable interest in the volumetric behavior of supercritical binary (and higher) fluid mixtures near the solvent critical point. It is in the vicinity of this critical point that supercritical extraction processes are generally considered to be most effective. In the case of a solvent + solute system that exhibits liquid-liquid-vapor (llg) partial miscibility, properties of the dense gas phase near an ll = g upper critical end point are most interesting. The partial molar volumes of the solvent and solute at these conditions are difficult to measure directly. In this note, we show that the solvent and solute partial molar volumes of the critical phase of a binary critical end point are readily determined from the associated three-phase liquid-liquid-vapor (llg) volume-composition data.