Thermodynamic phase-equilibrium ideal mixture behavior

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. 

Chapters 17 and 18 use thermodynamics to describe solutions, with nonelectrolyte solutions described in Chapter 17 and electrolyte solutions described in Chapter 18. Chapter 17 focuses on the excess thermodynamic properties, with the properties of the ideal and regular solution compared with the real solution. Deviations from ideal solution behavior are correlated with the type of interactions in the liquid mixture, and extensions are made to systems with (liquid + liquid) phase equilibrium, and (fluid -I- fluid) phase equilibrium when the mixture involves supercritical fluids. 

Ideal Adsorbed Solution Theory. Perhaps the most successful general approach to the prediction of multicomponent equilibria from single-component isotherm data is ideal adsorbed solution theory. In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equilibrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equilibrium pressure for the pure component at Ike same spreading pressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption. Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, are not consistent with an ideal adsorbed phase and there is no way of knowing a priori whether or not a given system will show ideal behavior. 

The classical thermodynamic approach has been applied to liquid phase adsorption by Larionov and Myers and by Minka and Myers. It was shown that for sorption of carbon tetrachloride-isooctane and benzene-carbon tetrachloride on aerosil the adsorbed solutions show approximately ideal behavior whereas adsorbed mixtures of benzene, ethyl acetate, and cyclohexane on activated carbon showed appreciable deviations from ideality. However, it is shown that the activity coefficients and hence the adsorption equilibrium data for the ternary systems may be successfully predicted, by classical methods, from data for the constituent binaries. 

The DME-water binary system exhibits two liquid phases when the DME concentration is in the 34% to 93% range [2]. However, upon addition of 7% or more alcohol, the mixture becomes conpletely miscible over the complete range of DME concentration. In order to ensure that this non-ideal behavior is simulated correctly, it is recommended that binary vapor-liquid equilibrium (VLE) data for the three pairs of components be used in order to regress binary interaction parameters (BIPs) for a UNIQUAC/UNIFAC thermodynamics model. If VLE data for the binary pairs are not used, then UNIFAC can be used to estimate BIPs, but these should be used only as preliminary estimates. As with all non-ideal systems, there is no substitute for designing separation equipment using data regressed from actual (experimental) VLE. 

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