Systems of Limited Liquid-Phase Miscibility

A general formulation of the problem of solid-liquid phase equilibrium in quaternary systems was presented and required the evaluation of two thermodynamic quantities, By and Ty. Four methods for calculating Gy from experimental data were suggested. With these methods, reliable values of Gy for most compound semiconductors could be determined. The term Ty involves the deviation of the liquid solution from ideal behavior relative to that in the solid. This term is less important than the individual activity coefficients because of a partial cancellation of the composition and temperature dependence of the individual activity coefficients. The thermodynamic data base available for liquid mixtures is far more extensive than that for solid solutions. Future work aimed at measurement of solid-mixture properties would be helpful in identifying miscibility limits and their relation to LPE as a problem of constrained equilibrium. 

At the molecular level, appreciable negative deviations from Raoult s law reflect stronger forces of intermolecular attraction in the liquid phase between unlike than between like pairs of molecules. Conversely, appreciable positive deviations result for solutions in which intermolecular forces between like molecules are stronger than between unlike. In this latter case the forces between like molecules may be so strong as to prevent complete miscibility, and the system then forms two separate liquid phases over a range of compositions. Systems of limited miscibility are treated in Sec. 13.9. 

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. 

Miscibility with the Feed Components. In a solute—solvent system exhibiting strong positive deviations from Raoult s Law, the solute has only limited solubility in the solvent. Above a certain solute concentration, two liquid phases are formed. The presence of two liquid phases on the plates of a distillation column leads to instability and operational problems. It is therefore necessary to ensure that the solute concentration in the liquid phase never exceeds its solubility limit. This solubility limit gives a minimum feasible solvent concentration in the section below the solvent addition plate of the primary column. 

B. Systems Formed of Two Liquid Phases only. Solutions of Liquids in Liquids. Partial or limited miscibility. Phenol and water. Methylethylketone and water. Triethylamine and water. General form of the concentration-temperature curve. Influence of pressure on the critical solution temperature. Influence of foreign substances on the critical solution temperature. Presence of vapour phase. 

Since recirculating stills are unsatisfactory for measuring vapour-liquid equilibrium in systems of limited miscibility, various flow methods have been developed. In the flow method a steady stream of boiling liquid or preheated vapour of constant and known composition is fed into an equilibrium cell. The liquid and the vapour phase are then separated and analysed. A good example of this type of instrument has been described by Vilim et al., and is shown in... 

The Pb-Sn system has a eutectic. Look at the Pb-Sn phase diagram (Fig. AT. 26). Above i27°C., liquid lead and liquid tin are completely miscible, that is, the one dissolves in the other completely. On cooling, solid first starts to appear when the lines (or boundaries) which limit the bottom of the liquid field are reached. 

A phase is defined as a state of matter that is uniform throughout in terms of its chemical composition and physical state in other words, a phase may be considered a pure substance or a mixture of pure substances wherein intensive properties do not vary with position. Accordingly, a gaseous mixture is a single phase, and a mixture of completely miscible liquids yields a single hquid phase in contrast, a mixture of several solids remains as a system with multiple solid phases. A phase rule therefore states that, if a limited number of macroscopic properties is known, it is possible to predict additional properties. 

Building on earlier work in these laboratories (8) we have overcome the typical mass transfer limitations of phase transfer catalysis for propylene oxidation by the use of 3-component liquid phases based on CO2 expanded liquids (CXLs). For the application to oxidations by aqueous H2O2, the organic component of the CXL is chosen because it is miscible with both dense CO2 and water. In this way, homogeneous systems are produced which decrease mass-transfer limitations and intensify chemical reactions. Previous reports using CXL systems have shown that they enhance the oxidation of the substrate and improve the selectivity at moderate reaction temperatures and pressures (3, 8, 9). 

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. 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

The compositions of the vapor and liquid phases in equilibrium for partially miscible systems are calculated in the same way as for miscible systems. In the regions where a single liquid is in equilibrium with its vapor, the general nature of Fig. 13.17 is not different in any essential way from that of Fig. I2.9< Since limited miscibility implies highly nonideal behavior, any general assumption of liquid-phase ideality is excluded. Even a combination of Henry s law, valid for a species at infinite dilution, and Raoult s law, valid for a species as it approaches purity, is not very useful, because each approximates real behavior only for a very small composition range. Thus GE is large, and its composition dependence is often not adequately represented by simple equations. However, the UNIFAC method (App. D) is suitable for estimation of activity coefficients. 

Figure 5.7 exhibits the prediction of the SS-LMBW/RISM-KHM theory for the site density profiles of the liquid/Iiquid interface in the binary system with partially miscible n-hexane and methanol at ambient conditions. The bulk limiting values of the n-hexane density in the phase rich in n-hexane (z —oo) and of the methanol density... 

The partitioning of a substance between two liquid phases (multistage partitioning, partition chromatography) and the extraction of solids require similar properties of a solvent [50-55]. When a substance has to be partitioned, a solvent system with limited miscibility of the components is required in order that the substance dissolves to a different extent in the two phases. The greater the chemical differences between any two solvents, the more limited their miscibility. Other requirements that the solvent system must fulfil are, inter alia, a favorable partition coefficient (the average partition coefficient of the component mixture should be between ca. 0.2 and 5), as high a separation... 

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