The Redlich-Kister (RK) three-coefficient expansion for gE is investigated geometrically and its global phase diagram is presented. The azeotropy and stability conditions yield surfaces (envelopes) in the three-dimensional azeotropy space and stability space respectively, whose axes represent variables determined from Henry's constants, pure substance vapor pressures and the highest-order RK coefficient. Zeotropy, single, double, triple, and tangent azeotropy (or saddle-point azeotropy), as well as stability, are identified in regions of the azeotropy and stability spaces. The connection between the two spaces is established. Envelopes for gE = 0 and dgE/dx=0 are also constructed in the azeotropy or stability spaces, to indicate the gE shape. Some results regarding the shape of gE are transferable to hE and vE when these are described independently by three-coefficient Redlich-Kister expansions. The analysis is applied to eleven actual mixtures, whose state is represented in the azeotropy and stability space. Fitting temperature-dependent RK coefficients allows to estimate the continuous path the mixture follows in both spaces at varying temperature, revealing possible intermediate states and the mixture tendency at the extreme temperatures.
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