Regular solutions, thermodynamic propertie

A theory of regular solutions leading to predictions of solution thermodynamic behavior entirely in terms of pure component properties was developed first by van Laar and later greatly improved by Scatchard [109] and Hildebrand [110,1 11 ]. It is Scatchard-Hildebrand theory that will be briefly outlined here. Its point of departure is the statement that It is next assumed that the volume... 

Determination of transformation enthalpies in binary systems. Just as consistent values of for elements can be obtained by back-extrapolation from binary systems, so it is possible to obtain values of by extrapolating the enthalpy of mixing vs composition in an alloy system where the phase has a reasonable range of existence. The archetypal use of this technique was the derivation of the lattice stability of f.c.c. Cr from the measured thermodynamic properties of the Ni-based f c.c. solid solution (7) in the Ni-Cr system (Kaufman 1972). If it is assumed that the f.c.c. phase is a regular solution, the following expression can be obtained ... 

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. 

It was found that the humic material ion exchange properties can be explained by a regular solution model similar to that of Truesdell and Christ (16) for clays. The thermodynamic constants for the exchange reactions studied were found to be different for each ionic strength. Changes in the configurations of the organic molecules could cause the observed variations. Other evidence (17,... 

A thermodynamic method, more fitting to this chapter, has been proposed by Nauman et al. They claim a process for the separation of a physically mixed solid polymers by selective dissolution. They rely on the different polymer solubility characteristics. Tables of this property have been reported and are based on regular solution theory and Hildebrand solubility parameters. The core of the Nauman invention is to find suitable solvents to dissolve particular polymers under defined temperature and pressure conditions. A mixture of polymers is first added to one solvent, at a given temperature, in order to dissolve a particular polymer. The remaining polymer mixture is then treated at a higher temperature with the same solvent or with a different solvent. For clarity, two examples are taken from the patent."... 

Most real solutions are neither ideal nor regular. As a result a realistic description of their thermodynamic properties must consider the fact that both the excess enthalpy of mixing, and excess entropy, are non- zero. Wilson... 

Most of the recent theories of liquid solution behavior have been based on well-defined thermodynamic or statistical mechanical assumptions, so that the parameters that appear can be related to the molecular properties of the species in the mixture, and the resulting models have some predictive ability. Although a detailed study of the more fundamental approaches to liquid solution theory is beyond the scope of this book, we consider two examples here the theory of van Laar, which leads to regular solution theory and the UNIFAC group contribution model, which is based on the UNIQUAC model introduced in the previous section. Both regular solution theory and the UNIFAC model are useful for estimating solution behavior in the absence of experimental data. However, neither one is considered sufficiently accurate for the design of a chemical process. 

The experimental data for the partial solubility of perfluoro-n-heptane in various solvents has been plotted as a function of both mole fraction and volume ftaction in Fig. 11.2-3. It is of interest to notice that these solubility data are almost symmeuic functions of the volume fraction and nonsymmetric functions of the mole fraction. Such behavior has also been found with other thermodynamic mixture properties these observations suggest the use of volume fractions, rather than mole fractions or mass fractions, as the appropriate concentration variables for describing nonideal mixture behavior. Indeed, this is the reason that volume fractions have been used in both the regular solution model and the Wohl expansion of Eq. 94-8 for liquid mixtures. 

In Chapter 4, methods based on equations of state were presented for predicting thermodynamic properties of vapor and liquid mixtures. Alternatively, as developed in this chapter, predictions of liquid properties can be based on correlations for liquid-phase activity coefficients. Regular solution theory, which can be applied to mixtures of nonpolar compounds using only properties of the pure components, is the first type of correlation presented. This presentation is followed by a discussion of several correlations that can be applied to mixtures containing polar compounds, provided that experimental data are available to determine the binary interaction parameters contained in the correlations. If not, group-contribution methods, which have recently undergone extensive development, can be used to make estimates. All the correlations discussed can be applied to predict vapor-liquid phase equilibria and some, as discussed in the final section of this chapter, can estimate liquid-liquid equilibria. 

In this chapter, we apply some of the general principles developed heretofore to a study of the bulk thermodynamic properties of nonelectrolyte solutions. In Sec. 11-1 we discuss conventions for the description of chemical potentials in nonelectrolyte solutions and introduce the concept of an ideal component. In Sec. 11-2, we demonstrate how the concept of solution molecular weight can be introduced into thermodynamics in a natural fashion. Section 11-3 is devoted to a study of the properties of ideal solutions. In Sec. 11-4, we discuss the properties of solutions that can be considered to be ideal when they are dilute but are not necessarily ideal when they are more concentrated. In Sec. 11-5, regular solutions are defined and some of their properties are derived. Section 11-6 is devoted to a study of some of the approximations that prove useful in the derivation of the properties of real solutions. Finally, in Sec. 11-7, some of the experimental techniques utilized for the measurement of chemical potentials and activity coefficients of components in solution are described. 

Exact form of the distribution function and following from it thermodynamical properties of linear pol5meric chain conformation are strictly determined in the SARW statistics for ideal diluted [28 and concentrated [29] solutions. Here this approach is spread on the regular polymeric stars in diluted and concentrated solutions with the description of their thermo-d5mamical and dynamical properties. 

It is convenient to think of the excess property as a mathematical operator that removes the ideal-solution part from a thermodynamic property. It is a linear operator and can be combined with other operators, such as the partial molar differentiation. Expressions that can be written between regular properties may be written for the excess and for the partial molar excess properties. For example, starting with the fundamental relationship... 

When a polymer bears ionic groups regularly appended on its chain, it is called a polyelectrolyte. The parameter which controls its thermodynamic properties in solution is the charge parameter X proportional to the linear charge density, introduced in the polyelectrolyte theory proposed by Katchalsky [6] and later by Manning [7]. It is expressed as ... 

We ha c developed a model for the thermodynamic properties of ideal and regular solutions. Two components A and B will tend to mix because of the favorable entropy resulting from the many different ways of interspersing A and B particles. The degree of mixing also depends on w hether the. 46 attractions are stronger or weaker than the AA and BB attractions. In the next chapters we will apply this model to the properties of solutions. 

Powell and Powell (197 ). In order to calibrate a clinopyroxene -olivine geothermometer, the authors use ternary regular solution theory (Wohl, 19 6 Prigogine and Defay, 195 ) to represent the thermodynamic mixing properties of Mg-Fe -Al (=A1+Ti+Cr+Fe3+) clinopyroxene. Olivine is assumed to be ideal. The crystallization temperatures of several intrusions, xenoliths and lavas are estimated on the basis of the model and known pressures. 

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