Solubility ternary solution equilibria

Many different types of phase behaviour are encountered in ternary systems that consist of water and two solid solutes. For example, the system KNO3—NaNC>3— H20 which does not form hydrates or combine chemically at 323 K is shown in Figure 15.6, which is taken from Mullin 3 . Point A represents the solubility of KNO3 in water at 323 K (46.2 kg/100 kg solution), C the solubility of NaN(>3 (53.2 kg/100 kg solution), AB is the composition of saturated ternary solutions in equilibrium with solid KNO3 and BC... 

The Isothermal Diagram.—For the representation of the isothermal relations in a ternary system, various methods can be employed. One may, in the first place, employ the triangular diagram, the use of which has already been explained (p. 204). Where we are dealing with the equilibria between aqueous solutions and two salts with the same ion, a simple two-branched curve, ach (Fig. 116), will be obtained if the two salts do not form any double salt. In this diagram, a represents the solubility of the salt A, h the solubility of the salt B, while the curves ac and he represent ternary solutions in equilibrium with solid salt A and solid salt B respectively. At c we have an invariant system in which the solution is in equilibrium with both salts as solid phases. 

The activities of acetone in the two binary solutions are plotted, as in Fig. 3.18. Ignoring the mutual solubility of water and chloroform in the ternary mixtures, equilibrium concentrations of acetone in the two layers are estimated by reading concentrations at equal values of acetone activity, as follows ... 

Figure 26 shows the ternary phase diagrams (solubility isotherms) for three types of solid solution. The solubilities of the pure enantiomers are equal to SA, and the solid-liquid equilibria are represented by the curves ArA. The point r represents the equilibrium for the pseudoracemate, R, whose solubility is equal to 2Sd. In Fig. 26a the pseudoracemate has the same solubility as the enantiomers, that is, 2Sd = SA, and the solubility curve AA is a straight line parallel to the base of the triangle. In Figs. 26b and c, the solid solutions including the pseudoracemate are, respectively, more and less soluble than the enantiomers. 

General solvent extraction practice involves only systems that are unsaturated relative to the solute(s). In such a ternary system, there would be two almost immiscible liquid phases (one that is generally aqueous) and a solute at a relatively low concentration that is distributed between them. The single degree of freedom available in such instances (at a given temperature) can be construed as the free choice of the concentration of the solute in one of the phases, provided it is below the saturation value (i.e., its solubility in that phase). Its concentration in the other phase is fixed by the equilibrium condition. The question arises of whether or not its distribution between the two liquid phases can be predicted. 

The maximum additive concentration (MAC) is defined as the maximum amount of solubilisate, at a given concentration of surfactant, that produces a clear solution. Different amounts of solubilisates, in ascending order, are added to a series of vials containing the known concentration of surfactant and mixed until equilibrium is reached. The maximum concentration of solubilisate that forms a clear solution is then determined visually. This same procedure can be repeated for the different concentrations of surfactant in a known amount of solubilisate in order to determine the optimum concentration of surfactant (Figure 4.24). Based on this information, one can construct a ternary phase diagram that describes the effects of three constituents (i.e., solubilisate, surfactant, and water) on the micelle system. Note that unwanted phase transitions can be avoided by ignoring the formulation compositions near the boundary. In general, the MAC increases with an increase in temperature. This may be due to the combination of the increase of solubilisate solubility in the aqueous phase and the micellar phase rather than an increased solubilization by the micelles alone. 

In the preceding chapter we have been considering the equilibrium of two phases of the same substance. Some of the most important cases of equilibrium come, however, in binary systems, systems of two components, and we shall take them up in this chapter. Wo can best understand what is meant by this by some examples. The two components mean simply two substances, which may be atomic or molecular and which may mix with each other. For instance, they may be substances like sugar and wrater, one of which is soluble in the other. Then the study of phase equilibrium becomes the study of solubility, the limits of solubility, the effect of the solute on the vapor pressure, boiling point, melting point, etc., of the solvent. Or the components may be metals, like copper and zinc, for instance. Then we meet the study of alloys and the whole field of metallurgy. Of course, in metallurgy one often has to deal with alloys with more than two components—ternary alloys, for instance, with three components—but they arc considerably more complicated, and we shall not deal with them. 

The combination of Eqs. (24)-(27) with the equation for the solid-liquid equilibrium provides a relation for the solubility of a solute forming a dilute solution in a ternary mixture. 

A recently developed model for the S-L-V equilibrium (63) utilizes the PMVF of the solvent in a binary mixture and the solute solubility at a reference pressure. This approach uses Eq. (50) to predict the ternary liquid mole fractions for the S-L equilibrium at different CO2 mole fractions corresponding to different pressures and at a fixed temperature. Next the pressure is adjusted to satisfy the isofugacity criterion for the L-V equilibrium, to permit the prediction of the vapor phase composition at which all three (S-L-V) phases coexist. This is repeated for other temperatures to obtain the P-T trace of the S-L-V equilibrium. The P-T trace for the constant liquid phase composition of the... 

If the alcohol in the ternary soap system is replaced by a fatty acid, yet another type is obtained. Here, as in the previous main type, there are the five mesophases B, C, D, E, and F and the two regions, Lh and L2, with homogeneous solutions. In this case, however, no water is needed to make soap and fatty acid mutually soluble. This is illustrated in Figure 28, which shows the phase equilibrium in the sodium caprylate-caprylic acid-water system. Here L2 extends to the caprylate-caprylic acid axis, and in the other direction far into the water comer. This is obviously caused by the ability of the soap and fatty acid to form molecular compounds with one another—the familiar acid soaps, which can also exist in the solid crystalline form. 

Curve LRPEK is the binodal solubility curve, indicating the change in solubility of the A- and B-rich phases upon addition of C. Any mixture outside this curve will be a homogeneous solution of one liquid phase. Any ternary mixture underneath the curve, such as M, will form two insoluble, saturated liquid phases of equilibrium... 

Vapor-liquid equilibrium (VLE) data and gas solubilities for binary or ternary polymer solutions... 

When considerable quantities of a soluble impurity are present in, or deliberately added to, a binary solution, the system may be assessed better in terms of three components, expressing the data on a triangular ternary equilibrium diagram (see section 4.6). 

---