Regular solution binary

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

Colloidal crystals . At the end of Section 2.1.4, there is a brief account of regular, crystal-like structures formed spontaneously by two differently sized populations of hard (polymeric) spheres, typically near 0.5 nm in diameter, depositing out of a colloidal solution. Binary superlattices of composition AB2 and ABn are found. Experiment has allowed phase diagrams to be constructed, showing the crystal structures formed for a fixed radius ratio of the two populations but for variable volume fractions in solution of the two populations, and a computer simulation (Eldridge et al. 1995) has been used to examine how nearly theory and experiment match up. The agreement is not bad, but there are some unexpected differences from which lessons were learned. 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

The corresponding monomer/micelle equilibria can be dealt with by the regular solution theory (RST), as shown in particular by Rubingh in 1979 (1). The application of this theory to numerous binary surfactant systems (2 - 4) has followed and led to a set of coherent results (5). 

The equations for the regular solution model for a binary mixture with two sublattices are quite similar to the equations derived for a regular solution with a single lattice only. The main difference is that the mole fractions have been replaced by ionic fractions, and that while the pair interaction is between nearest neighbours in the single lattice case, it is between next nearest neighbours in the case of a two sub-lattice solution. 

Consideration of the thermodynamics of nonideal mixing provides a way to determine the appropriate form for the activity coefficients and establish a relationship between the measured enthalpies of mixing and the regular solution approximation. For example, the excess free energy of mixing for a binary mixture can be written as... 

The regular solution approximation is introduced by assuming definition) that the excess entropy of mixing is zero. This requires that the excess free energy equal the excess enthalpy of mixing. For binary mixtures the excess enthalpy of mixing is ordinarily represented by a function of the form... 

Both the Muggianu and Kohler equations can be considered symmetrical as they treat the components in the same way and do not differentiate between them. This is true for another method suggested by Colinet (1967) which is derived differently than either the Kohler or Muggianu equations but which can be reduced to the Muggianu equation (Hillert 1980). Toop s equation (1965) is essentially different in that it considers one of the binary systems does not behave in the same way as the others and the extrapolation is based essentially on two of the binaries having identical mole-fraction products with the mole-fiaction products of the third being different. For a sub-regular solution Toop s equation breaks down to (Hillert 1980)... 

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 ... 

I-f the interactions between sur-factants in the mixed micelle can be described by regular solution theory, the -following equations apply -for a binary system ... 

Regular Solution Theory. I-F the sur-Factant mixing in the micelle obeys regular solution theory, the -Following relationships are valid -For a binary sur-Factant system (45) ... 

Recently, Rubingh ll) and Scamehorn et al. (9) have shown that the activity coefficients obtained by fitting the mixture CMC data can be correlated by assuming the mixed micelle to be a regular solution. This model proposed by Rubingh for binary mixtures has been extended to include multicomponent surfactant mixtures by Holland and Rubingh (10). Based on this concept Kamrath and Frances (11) have made extensive calculations for mixed micelle systems. 

By analogy with the treatment of mixed micelles, we now assume that the free energy of mixing of the surface phase can be calculated using the standard regular solution expression for the activity coefficients in a binary mixture ... 

By extending regular solution theory for binary mixtures of AEg in aqueous solution to the adsorption of mixture components on the surface (3,4), it is possible to calculate the mole fraction of AEg, Xg, on the mixed surface layer at tt=20, the molecular interaction parameter, 6, the activity coefficients of AEg on the mixed surface layer, fqg and f2s and mole concentration of surfactant solution, CTf=20 3t surface pressure tt=20 mn-m l (254p.l°C). The results from the following equations are shown in Table I and Table II. 

The interaction parameter, ft, is a fitting parameter in the regular solution model that can be found from liquid-solid equilibrium data (93). With the DLP model, the interaction parameter is calculated from the lattice parameters of the binary compounds. For a compound semiconductor AiJB C, ft is computed from the lattice constants aAC and aBC of the binary compounds from the following expression... 

The A-B binary system conforms to regular solution behaviour and the interaction parameter 2 is 17,400 J/mol. Find the critical temperature Tc below which phase separation occurs. Calculate the compositions of a and a in equilibrium at 900K. 

For the A-B binary regular solution, we have seen in the section 2.3.5 that RTlny a=QN RTlnyB=QN ... 

The Scatchard-Hildebrand regular-solution model expresses the liquid activity coefficients y in a binary mixture as... 

Thus, the total Gibbs energy of the binary system, as given by the regular solution model, is ... 

Further elaboration requires a model. We shall consider the Bragg-Williams approximation (sec. I.3.8d) in which only the enthalpic part of G is accounted for, the entropy is assumed to remain ideal. For gas adsorbates this leads to the FFG isotherm II.3.8.17] and A1.5a] and in solutions it gives rise to the Regular Solution model, both models being fairly widely applicable. For this approximation, for a binary solution we derived I.3.8.25]... 

---