Phase Diagrams of Nonideal Mixtures

An azeotropic mixture is sometimes called a constant-boiling mixture, since it distills without any change in composition. It is impossible to distill from one side of an azeotrope to the other. For example, ethanol and water at 1.00 atm have an azeotrope at an ethanol mole fraction equal to 0.90. Any mixture of ethanol and water can be distilled to this composition, but no further. 

000 atm the boiUng temperature of water is 100°C and that of ethanol is 78.3°C. The azeotrope boils at 78.17°C at this pressure. 

Tie line areas (one vapor phase, one liquid phase) 

Two coexisting / Tie line liquid states / region-two liquids 

Rgure 6.15 Temperature-Composition Phase Diagram of a System with Liquid-Liquid Phase Separation (Schematic). 

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Solid-fluid phase diagrams of binary hard sphere mixtures have been studied quite extensively using MC simulations. Kranendonk and Frenkel [202-205] and Kofke [206] have studied the solid-fluid equilibrium for binary hard sphere mixtures for the case of substitutionally disordered solid solutions. Several interesting features emerge from these studies. Azeotropy and solid-solid immiscibility appear very quickly in the phase diagram as the size ratio is changed from unity. This is primarily a consequence of the nonideality in the solid phase. Another aspect of these results concerns the empirical Hume-Rothery rule, developed in the context of metal alloy phase equilibrium, that mixtures of spherical molecules with diameter ratios below about 0.85 should exhibit only limited solubility in the solid phase [207]. The simulation results for hard sphere tend to be consistent with this rule. However, it should be noted that the Hume-Rothery rule was formulated in terms of the ratio of nearest neighbor distances in the pure metals rather than hard sphere diameters. Thus, this observation should be interpreted as an indication that molecular size effects are important in metal alloy equilibria rather than as a quantitative confirmation of the Hume-Rothery rule. 

Since few liquid mixtures are ideal, vapor-liquid equilibrium calculations are somewhat more complicated than for the cases in the previous section, and the phase diagrams for nonideal systems can be more structured than Figs. 10.1-1 to 10.1-6. These complications arise from the (nonlinear) composition dependence of the species activity coefficients. For example, as a result of the composition dependence of yt, the vapor-liquid equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction, so that no.nideal solutions exhibit deviations from Raoult s law. However, all the calculational methods discussed in the previous section for ideal mixtures, including distillation column design, can be used for nonideal mix-, tures, as long as the composition dependence of the activity coefficients is taken into account. 

Figure 1.2. Phase equilibrium of binary mixtures (a) ideal mixture (b) nonideal mixture (c) tangential azeotropic mixture (xi. Az = 1) (d) azeotropic mixture (e) mixture with internal tangential azeotrope (0 < xi, Az < 1) (f) urixture with two azeotropes Azi and Az2, (g) heteroazeotropic mixture and (h) azeotropic mixture with two liquid phases (y — x, T — x — y, and K — x diagrams). Az, azeotropic or heteroazeotropic point x i and x 2, compositions of liquid phases.

The furfural-cyclohexane phase diagram (Fig. 146) shows that you can have mixtures that exhibit nonideal behavior, without having to form an azeotrope. In sum, without the phase diagram in front of you, you shouldn t take the distillation behavior of any liquid mixture for granted. 

Determination of T y. In the formulation of the phase equilibrium problem presented earlier, component chemical potentials were separated into three terms (1) 0, which expresses the primary temperature dependence, (2) solution mole fractions, which represent the primary composition dependence (ideal entropic contribution), and (3) 1, which accounts for relative mixture nonidealities. Because little data about the experimental properties of solutions exist, Tg is usually evaluated by imposing a model to describe the behavior of the liquid and solid mixtures and estimating model parameters by semiempirical methods or fitting limited segments of the phase diagram. Various solution models used to describe the liquid and solid mixtures are discussed in the following sections, and the behavior of T % is presented. 

The PT diagram of Fig. 12.6 is typical for mixtures of nonpolar substance such as hydrocarbons. An example of a diagram for a highly nonideal syster methanol/benzene, is shown in Fig. 12.8. The nature of the curves in this figu suggests how difficult it can be to predict phase behavior, particularly for sped so dissimilar as methanol and benzene. 

In general, the steps of this separations system synthesis method for nonideal mixtures involving azeotropes include examination of the RCM representation (overlaid with vapor-liquid equlibria (VLE) pinch information, liquid-liquid equlibria (LLE) binodal curves and tie lines, and. solid-liquid equlibria (SLE) phase diagrams if appropriate) determination of the critical thermodynamic features to be avoided (e.g., pinched regions), overcome (e.g., necessary distillation... 

The cell theory plus fluid phase equation of state has been extensively applied by Cottin and Monson [101,108] to all types of solid-fluid phase behavior in hard-sphere mixtures. This approach seems to give the best overall quantitative agreement with the computer simulation results. Cottin and Monson [225] have also used this approach to make an analysis of the relative importance of departures from ideal solution behavior in the solid and fluid phases of hard-sphere mixtures. They showed that for size ratios between 1.0 and 0.7 the solid phase nonideality is much more important and that using the ideal solution approximation in the fluid phase does not change the calculated phase diagrams significantly. 

In 8.4.5 we described the stability conditions that, when violated, can cause a one-phase liquid mixture to separate into two liquid phases. We also showed in Figure 8.20 an isobaric, liquid-liquid, Txx diagram on which one-phase states divide into stable, metastable, and unstable states. Liquid-liquid separations occur in nonideal mixtures that have strong positive deviations from ideal-solution behavior in such mixtures the activity coefficients become much greater than unity. This occurs when attractive forces between molecules of the same species are stronger than those between molecules of different species. Liquid-liquid separations have never been observed in mixtures that are negative deviants over the entire composition range. 

Figure 10.3. The AG/x plots of a few imaginary mixtures to show the contributions of enthalpy (a) and entropy (b) to binary phase diagrams. Top left an ideal mixture (AH = 0) at some temperature (T > 0). Top right a nonideal mixture (AH > 0) also with an entropy term. Bottom right an ideal mixture at nonzero temperature, where A and B have a different crystal structure. ...

Classification of Binary Phase Diagrams. Figure 2 shows a classification of binary phase diagrams suggested by Scott and Van Konynenburg (19), with examples of each class. This classification is based on the presence or absence of three-phase lines and the way critical lines connect with these this is best seen on a P,T projection. In classes I, II and VI the two components have similar critical temperatures, and the gas-liquid critical line passes continuously between the pure component critical points class II and VI mixtures differ from class I in that they are more nonideal and show liquid-liquid immiscibillty. Class II behavior is common, whereas class VI, in which closed solubility... 

Next, we specify the x, between 0 and 1, and estimate the total pressure P and yx from Eq. (1.193) to prepare the total pressure and equilibrium compositions shown in Table 1.10. In Figure 1.9, we can compare both the Tyx and Pyx diagrams obtained from Raoult s law and the NRTL model using the Aspen Plus simulator. As we see, ideal behavior does not represent the actual behavior of the acetone-water mixture, and hence we should take into account the nonideal behavior of the liquid phase by using an activity coefficient model. 

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