Binary systems graphical representation

For binary systems, graphical representation is typically plotted (Figure 3.7(a)) as the vapor-phase mole fraction of the more volatile component (y.4) vs liquid-phase mole fraction (xa). The y = x diagonal line is included for reference. The data are usually plotted for a constant total pressure. 

Experimental data on only 26 quaternary systems were found by Sorensen and Arlt (1979), and none of more complex systems, although a few scattered measurements do appear in the literature. Graphical representation of quaternary systems is possible but awkward, so that their behavior usually is analyzed with equations. To a limited degree of accuracy, the phase behavior of complex mixtures can be predicted from measurements on binary mixtures, and considerably better when some ternary measurements also are available. The data are correlated as activity coefficients by means of the UNIQUAC or NRTL equations. The basic principle of application is that at equilibrium the activity of each component is the same in both phases. In terms of activity coefficients this... 

Related Calculations. Graphic representation of liquid-liquid equilibrium is convenient only for binary systems and isothermal ternary systems. Detailed discussion of such diagrams appears in A. W. Francis, Liquid-Liquid Equilibrium, Interscience, New York, 1963. Thermodynamic correlations of liquid-liquid systems using available models for liquid-phase nonideality are not always satisfactory, especially when one is trying to extrapolate outside the range of the data. 

For mixtures containing more than two species, an additional degree of freedom is available for each additional component. Thus, for a four-component system, the equilibrium vapor and liquid compositions are only fixeci if the pressure, temperature, and mole fractions of two components are set. Representation of multicomponent vapor-liquid equilibrium data in tabular or graphical form of the type shown earlier for binary systems is either difficult or impossible. Instead, such data, as well as binary-system data, are commonly represented in terms of K values (vapor-liquid equilibrium ratios), which are defined by... 

In this Chapter, we define partial molar properties and describe their application. We then discuss their relationship with the change of properties of a system on mixing. Finally, we examine the graphical representation of partial molar properties for binary mixtures. 

Covering chemical phenomena of 1,2, 3, 4, and multiple component systems, this standard work on the subject (Nature, London), has been completely revised and brought up to date by A. N. Campbell and N. O. Smith. Brand new material has been added on such matters as binary, tertiary liquid equilibria, solid solutions in ternary systems, quinary systems of salts and water. Completely revised to triangular coordinates in ternary systems, clarified graphic representation, solid models, etc. gth revised edition. Author, subject indexes. 236 figures. 505 footnotes, mostly bibliographic, xii -f- 494pp. 536 x 8. 

P-T-X diagram A three-dimensional graphic representation of the phase relationships in a binary system by means of the pressure, temperature, and concentration variables. 

The phase behavior of mixtures forms the basis of industrial separations. What makes such separation possible is the fact that when a mixture is brought into a region of multiple coexisting phases, each phase has its own composition. Understanding the phase behavior of multicomponent systems is very important in the calculation of separation processes. In this chapter we review graphical representations of the phase behavior of binary and ternary systems. Since we are dealing with several independent variables, pressure, temperature, and composition, special conventions are used in order to represent information in two-dimensional graphs. 

The interpretation of equation (k) for a ternary or higher-order solution is no more difficult in principle than the interpretation already given for a binary solution. However, every additional component requires the addition of one compositional variable to the free energy of mixing function, and therefore one additional dimension in free energy - composition space. The graphical depiction of a binary system thus requires two dimensions (Gip, X2) that of a ternary system, three dimensions (G, X2, X3), and so on. The graphical representation of multicomponent solutions with c > 3 is virtually impossible, except in projection, and it becomes necessary to rely on strictly fimctional treatments of the properties of state. 

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