Mutual solubility partial

Best ternary predictions are usually obtained for mixtures having a very broad two-phase region, i.e., where the two partially miscible liquids have only small mutual solubilities. Fortunately, this is the type of ternary that is most often used in commercial liquid-liquid extraction. 

For all calculations reported here, binary parameters from VLE data were obtained using the principle of maximum likelihood as discussed in Chapter 6, Binary parameters for partially miscible pairs were obtained from mutual-solubility data alone. 

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

For systems that are only partially miscible in the liquid state, the activity coefficient in the homogeneous region can be calculated from experimental values of the mutual solubility limits. The methods used are described by Reid et al. (1987), Treybal (1963), Brian (1965) and Null (1970). Treybal (1963) has shown that the Van-Laar equation should be used for predicting activity coefficients from mutual solubility limits. 

Partial mutual solubility in the solid state. Fig. 2.9 shows different examples of binary systems for which there is still a complete miscibility in the liquid state, but only a limited mutual solubility in the solid state, depending on the temperature. The Ni-Au system, for instance, still has complete mutual solid solubility but only at high temperature, that is, by decreasing the temperature, de-mixing... 

A similar behaviour (complete mutual solubility in the liquid state and partial solubility in the solid state) is presented also by the Pt-Au and Ba-Ca systems (Fig. 2.9(b) and (c)). Notice in the Pt-Au diagram the closeness (mainly for compositions near 40 at.% Au) between the melting and the de-mixing equilibria. 

The Ba-Ca diagram has a different appearance because Ca (in its high-temperature form) and Ba are completely mutually soluble, while only a partial solid solubility is observed for Ba in the low-temperature modification of Ca. 

Figure 2.10. Examples of binary systems characterized by complete mutual solubility in the liquid state and, depending on temperature and/or composition, partial solubility in the solid state and presenting (in certain composition ranges) an invariant (three-phase) reaction (eutectic in the Cu-Ag, peritectic in the Ru-Ni and Re-Co and eutectoidal in Ti-W (one) and in Th-Zr (two)).

The mutual solubility of two liquids A and B depends, in general, on how much the molecules of each liquid tend to attract those of its own kind, relative to their tendency to attract those of the other. This tendency is measured by the excess Gibbs energy of mixing of the two liquids (see section 2.4), Am gL, which is related to the partial vapor pressures p/ and of the two liquids A and B in the mixture. If the composition of the system is given by and Wb moles of the respective components in a given phase, their mole fractions in this phase are... 

If the original liquids are again partially miscible, and the added component soluble in either the mutual solubility may be increased if so the interfacial tension will probably diminish whatever may be the effect on the surface tensions of the two pure liquids. Clearly, if sufficient of the third component be added to make the two phases completely soluble the interfacial tension must disappear altogether. 

On a ternary equilibrium diagram like that of Figure 14.1, the limits of mutual solubilities are marked by the binodal curve and the compositions of phases in equilibrium by tielines. The region within the dome is two-phase and that outside is one-phase. The most common systems are those with one pair (Type I, Fig. 14.1) and two pairs (Type II. Fig. 14.4) of partially miscible substances. For instance, of the approximately 1000 sets of data collected and analyzed by Sorensen and Arlt (1979), 75% are Type I and 20% are Type II. The remaining small percentage of systems exhibit a considerable variety of behaviors, a few of which appear in Figure 14.4. As some of these examples show, the effect of temperature on phase behavior of liquids often is very pronounced. 

CONSOLUTF TEMPERATURE. The upper convolute temperature for two partially miscible liquids is the critical temperature above which the two liquids are miscible in all proportions. In some systems where the mutual solubility decreases with increasing temperature over a certain temperature range, the lower convolute temperature corresponds to the critical temperature below which the two liquids are miscible in all proportions. Some systems such as mclhylclhyl ketone and water have both upper and lower consolute temperatures. 

In the study of miscibility of partially miscible liquid pairs, the external pressure is kept constant and, therefore, the vapour phase is ignored. The mutual solubilities are represented by means of temperature-composition diagram. 

Since the partial entropy contains a term — i lnA this entropy will always become large and positive for very small concentrations, so that a small mutual solubility will necessarily occur. Complete miscibility thus only occurs when AF can still... 

Related Calculations. This illustration outlines the procedure for obtaining coefficients of a liquid-phase activity-coefficient model from mutual solubility data of partially miscible systems. Use of such models to calculate activity coefficients and to make phase-equilibrium calculations is discussed in Section 3. This leads to estimates of phase compositions in liquid-liquid systems from limited experimental data. At ordinary temperature and pressure, it is simple to obtain experimentally the composition of two coexisting phases, and the technical literature is rich in experimental results for a large variety of binary and ternary systems near 25°C (77°F) and atmospheric pressure. Example 1.21 shows how to apply the same procedure with vapor-liquid equilibrium data. 

Some typical phase behavior that can be exhibited by ternary mixtures is shown in Fig. 3.11. Let us consider a situation where binary mixtures of component 1 and component 2 are only partially miscible, where two coexisting liquid phases may be formed one rich in 1 and the other rich in 2. This is represented by the base of the ternary phase diagram shown in Fig. 3.11a. In addition, let us assume that components 1 and 3 are completely miscible and components 2 and 3 are also completely miscible. For this case, one might expect that if enough of component 3 is added to the system, then components 1 and 2 can be made to mix with each other, due to their mutual solubility with component 3. This is type I phase behavior. 

Liquid-liquid extraction may be represented by a three-component system forming two liquid phases. The solvent and the feed are two essentially immiscible liquids with possible partial mutual solubility. The extract component or solute, to be extracted from the feed by the solvent, is soluble in both phases. 

For the UNIQUAC equation, there are two adjustable equation parameters for each binary. For the binary that is partially miscible, the best way to determine the two binary parameters is to fit the mutual solubility data. For the completely miscible binaries, useful interaction parameters can be obtained from vie data. However, fitting vie data to within experimental accuracy does not uniquely determine the binary parameters. The choice of a particular set of parameters can have a significant effect on the representation of the ternary lie. For the ternary system of chloroform, water, and acetone at 333°K, for example, the two binary parameters are first determined from mutual solubility data for chloroform and water and then the other binary parameters for the two miscible binaries. Somewhat improved predictions occur by fitting binary parameters to the miscible binaries. Similar predictions have also been found for ternary systems of ethyl acetate, ethanol, and water. 

To calculate phase equilibria for ternary mixtures of Type II, we require mutual solubility data for the two partially miscible bienries and vapor-liquid equilibrium data for the completely miscible binary. From such data we can obtain bienry parameters as required in some expression for molar excess Gibbs energy g for the ternary. 

So far we have considered liquid-liquid equilibrium only for binary mixtures. We next consider multicomponent mixtures. When two solvents are partially miscible (rather than immiscible), their mutual solubility will be affected by the addition of a third component. In this case the equilibrium conditions are... 

The discussion in this section has been concerned with the distribution of a solute between two liquid, phases whose equilibrium is unaffected by the added solute. This will occur if the amount of added solute is very small, or if the solvents are essentially immiscible at all conditions. However, if the amount of dissolved solute is so large as to affect the miscibility of the solvents, the solute addition can have a significant effect on the solvents, including the increase (salting in) or decrease (saltin out) of the mutual solubility of the two solvents, as was discussed in Sec. 11.2. It is important to emphasize that such situations are described by the methods in Sec. 11.2 as a multicomponent liquid-liquid equilibrium problem, in contrast to the procedures in this section, which are based on the assumption that the partial or complete immiscibility of the solvents is imaffected by the addition of the partitioning solute. 

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