Predictive regular solution theory

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). 

The solubihty parameter is therefore a measure of the energy density hoi ding the molecules in the hquid state. Note that regular solution theory can only predict positive AH. Thus, with this approach, prediction of solubihty involves matching the solute and solvent solubihty parameters as closely as possible to minimize AH. As a very rough mle of thumb 1— 21 must be less than 2 Q/cm ) for solubihty. 

For a given reaction studied in a series of solvents, (8r- 8 f) is essentially constant, and most of the change in In k will come from the term — AV (8j — 8s)". If AV is positive, an increase in 8s (increase in solvent internal pressure) results in a rate decrease. If AV is negative, the reverse effect is predicted. Thus reactivity is predicted by regular solution theory to respond to internal pressure just as it does to externally applied pressure (Section 6.2). This connection between reactivity and internal pressure was noted long ago," and it has been systematized by Dack. -" ... 

Equation 1 has proved to be a better predictor of the equilibrium which exists between monomer and micelles for mixed surfactant systems than is the regular solution theory model. It also predicts well the mixture CMC and shows the heat of mixing to be smaller than that predicted by the regular solution theory in agreement with the experiment (13). The purpose of this paper is to further explore... 

Ruelle, R, M. Buchmann, H. Nam-Tran, andU.W. Kesselring. 1992. The mobile order theory versus UNIFAC and regular solution theory-derived models for predicting the solubility of solid substdftbasn. Res.9 788-791. 

Example 4-1 Qualitative prediction using Regular Solution Theory. 

Baner, A.L., Piringer, O. Prediction of solute partition coefficients between polyolefins and alcohols using the regular solution theory and group contribution methods. Ind. Eng. Chem. Res. 1991, 30 1506-1515. 

Regular solution theory, the solubility parameter, and the three-dimensional solubility parameters are commonly used in the paints and coatings industry to predict the miscibility of pigments and solvents in polymers. In some applications quantitative predictions have been obtained. Generally, however, the results are only qualitative since entropic effects are not considered, and it is clear that entropic effects are extremely important in polymer solutions. Because of their limited usefulness, a method using solubility parameters is not given in this Handbook. Nevertheless, this approach is still of some use since solubility parameters are reported for a number of groups that are not treated by the more sophisticated models. 

Additional approaches to understand and predict solubilities in mixed solvents are based on estimation of the activity coefficient, logy, in Eq. (1). Martin, Chertkoff, and Restaino investigated the use of regular solution theory, as developed by Hildebrand and Scott, to predict the solubilities of organic solutes in various solvent mixtures ... 

Azizian, S. Pour, A. H. Solubility of 2-naphthol in organic nonelectrolyte solvents. Comparison of observed versus predicted values based upon mobile order and regular solution theories./. Chem. Res.-S. 2003, 7, 402-404. 

The activity coefficient has to be estimated for nonideal solutions. There is no general method for predicting activity coefficients of solid solutes in liquid solvents. For nonpolar solutes and solvents, however, a reasonable estimate can frequently be made with the regular solution theory, or the Scatchard-Hildebrand relation. 

For the prediction of solubility of polar solutes in polar solvents, the regular solution theory, Eq. (17), has been modified to take into account the additional interactions between the solvent and the solute. Some of these modified methods are discussed by Prausnitz et al. (16). 

Knowing the thermal stability of clathrates permits the prediction of experimental conditions for polymerization (8). A detailed analysis of this problem requires the examination of all the involved phases, particularly the solid and liquid phases. Equations for phase equilibria were derived from within the framework of the regular solution theory they contain an interaction parameter W, (whose value is always positive or zero for ideal solutions), which measures the tendency of host and guest to segregate in the liquid phase. The melting or decomposition point is very sensitive to the value of W, especially when it exceeds 2 RT, i.e. when a miscibility gap is observed in the liquid phase. For this reason the PHTP-hydrocarbon clathrates melt congruently between 115 and 180 C, whereas the urea-hydrocarbon... 

This expanded liquid EOS model in conjunction with the regular solution theory model predicted the solute solubilities of naphthalene and phenanthrene in toluene with CO2 reasonably well at both high and low pressures (56). 

The temperature-dependent miscibility of fluorous biphasic systems [1] can be predicted by use of the Hildebrand-Scratchard or regular solution theory [2, 9]. According to this theory the critical temperature (T). above which the two liquids of a biphasic system mix in all ratios is dose to the phase-separation temperature of a biphasic system consisting of equal volumes of each phase ... 

Barton"" " provides empirical methods based on solubility parameters for ternary solvent systems. All these methods provide only a qualitative idea on miscibility. The combination of regular solution theory and solubility parameters has been employed for predicting the partition coefficients of organic compounds between water and polystyrene and between alcohols and polyolefins. The results are useful to a first approximation. 

Since the solubility parameters of all the components are similar, regular solution theory predicts essentially ideal solution behavior, even though, for example, the water-aromatic hydrocarbon mixtures are highly nonideal. This is an example of how bad the regular solution theory predictions can be when used for mixtures for which it is not appropriate. 

These are usually heat effects during dissolution of solids (and liquids) in solvents, and the ideal solution relation is modified by an energy term that takes into account heats of mixing. The term modifies the ideal solution equation to give the regular solution theory prediction of solubility... 

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. 

Compare the regular solution theory predictions for the activity coefficients of the benzene-... 

Figure 9.6-1 The regular solution theory predictions for the activity coefficients of the benzene-2,2,4-trimethyl pentane mixture. The points indicated by o are the experimental data.

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