Margules equations, binary ternary

Broul et al. (13) and Hala (14) developed a correlation scheme for systems containing two solvents and one salt, which they applied to several salt concentrations, not just to the saturation level as in the studies mentioned above. They utilized the binary VLE data for the three binaries (solvent 1-salt solvent 2-salt and solvent 1-solvent 2) along with the ternary data to correlate successfully the ternary results. They employed the Margules equation (15) with the addition of a term to account for the coulombic interactions. 

Because of the limitations of the Margules equation—especially in predicting multicomponent VLE data—the Wilson, NRTL, and LEMF (16) equations are employed in this study. The experimental data on the systems presented in Table I were used in this work. These are the only systems for which both binary and ternary data could be found in the literature. As a matter of fact, uncertainties do exist about the accuracy of the two HgC systems. The maximum boiling... 

In both solid and gaseous solutions, virial equation-based Raoultian coefficients have often been proposed. For example, the Margules equations, often used in binary and sometimes in ternary solid solutions and which have a virial equation basis, were proposed originally for gaseous solutions. However, there is no satisfactory general model for Raoultian coefficients in multi-component solid solutions, and the tendency in modeling has been to treat these solutions as ideal (i.e., to use the mole fraction of a solid solution component as its activity see Equation (3.13)). 

These equations can be solved for the coefficients c, d 0, c, and d 0 in terms of the infinite-dilution activity coefficients (which are binary-system properties), but the solution will not be unique. Equation 5.48d, connecting the ternary second-order Margules expansion coefficients to the binary infinite-dilution activity coefficients, shows that a constant (say, c0) can be added to any c and c[Pg.202]

The paper is organized as follows first, the thermodynamic relations for the solubility of poorly soluble solids in pure and multicomponent mixed solvents are written. Second, an equation for the activity coefficient of a solute at infinite dilution in a binary nonideal mixed solvent [23) is employed to derive an expression for its solubility in terms of the properties of the mixed solvent. Third, various expressions for the activity coefficients of the cosolvents, such as Margules and Wilson equations [19), are inserted into the above equation for the solubility. The obtained equations are used to correlate the HOP solubilities in binary aqueous mixed solvents and the results are compared with experiment. Finally, the case of an ideal multicomponent solvent is considered and used for ternary and higher mixed solvents. 

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