Regular-solution theory

Regular solution theory employs simple statistical arguments to capture the nature of phase equilibria of solutions. Although simple, it has been used widely to predict the existence of phases and phase transitions. It has been used to explain different first-order transition phenomena, such as ferromagnetism and gas adsorption on solid surfaces. [Pg.182]

Consider a system of N molecules of species 1 and N2 molecules of species 2, as illustrated in Fig. 10.5. The species can be different chemical moieties or different phases of the same substance. Assume that the molecules are positioned at the N = N - - N2 sites of a regular three-dimensional lattice. Each lattice site is assumed to occupy the same volume Vo, so that the total volume of the system is F = Nvo. The coordination number z is the number of sites neighboring each lattice site. Each molecule is assumed to interact only with its z nearest neighbors. [Pg.182]

The potential energy of interaction is en, 22, and 12 between molecules in neighboring sites, depending on the type of molecules. [Pg.184]

If molecules are randomly distributed on lattice sites, then the probability that a molecule of species i occupies any specific lattice site is equal to the molar fraction x/, [Pg.184]

The probability that species j occupies a neighboring site of a specific lattice site is simply zxj. Consequently the average energy between neighboring molecules is [Pg.184]

Because of the importance of distillation processes, first it was the objective to develop models only for the prediction of VLE. The first predictive model with a wide range of applicability was developed by Hildebrand and Scatchard [48]. The so-called regular solution theory is based on considerations of van Laar, who was a student of van der Waals and used the van der Waals equation of state to derive an expression for the excess Gibbs energy [49]. Since the two parameters a and b of the van der Waals equation of state can be obtained from critical data, it should be possible to calculate the required activity coefficients using critical data. However, the results were strongly dependent on the mixing rules applied. [Pg.290]

Hildebrand and Scatchard [48] showed that better results are obtained, if instead of the van der Waals constants a and b molar volumes v, and so-called solubility parameters 8i are used instead. For binary systems the following relations are obtained for the activity coefficients [Pg.290]

The solubility parameter 5/ can be calculated using values for the enthalpy of vaporization and the molar volume v, at 298.15 K [Pg.290]

For regular solutions the solubility parameters 5j and molar volumes vi can be assumed to be constant for a larger temperature range. For a few compounds the parameters are given in Table 5.16. [Pg.290]

The regular solution theory is not limited to binary systems. It can directly be applied for the calculation of activity coefficients in multicomponent systems [Pg.291]

Generally, the activity coefficients are 1 when polar interactions are important, with a resulting increase in solubility of compounds compared with the ideal solubility. The opposite is often true in nonpolar systems where dispersion forces are important, with the activity coefficients being 1. A variety of methods are used to calculate activity coefficients of solid solutes in solution. A frequently used method is that of Scatchard-Hildebrand, which is also known as regular solution theory (Prausnitz et al. 1999). [Pg.13]

In electrolytic solutions we were concerned with electrostatic interactions between ions in the solution and with the solvent (water). In solutions of nonelectrolytes we will be concerned with molecule-solvent interactions due to electrostatic forces, dispersion forces, and chemical forces. [Pg.13]

Even though a solution contains no ions, electrostatic interactions can still be significant. This is because of a property called polarity. An electrically neutral molecule can have a dipole moment that is due to an asymmetric distribution of its electrical charge. This means that one end of the molecule is positive and the other end is negative. The dipole moment is defined by [Pg.13]

V2 = molar volume of the subcooled liquid solute 62 = solubility parameter of the subcooled liquid 61 = solubility parameter of the solvent = volume fraction, or the solvent defined by [Pg.13]

TABLE 1.9 Solubility of Napthalene in Various Solvents by UNIFAC and Scatchard-Hildebrand Theory [Pg.14]

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). [Pg.61]

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. [Pg.435]

Regular Solution Theory. The key assumption in regular-solution theory is that the excess entropy, is zero when mixing occurs at constant volume (3,18). This idea of a regular solution (26) leads to the equations ... [Pg.236]

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. ... [Pg.413]

Recall that regular solution theory deals with nonpolar solvents, for which the dispersion force is expected to be a major contributor to intermolecular interactions. The dispersion energy, from Eq. (8-15), is for 1-2 interactions... [Pg.414]

We encountered the quantity AE ap/V in Eq. (8-35) it is the cohesive energy density. The square root of this quantity plays an important role in regular solution theory, and Hildebrand named it the solubility parameter, 8. [Pg.415]

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. -" ... [Pg.416]

Strictly speaking Eq. (8-51) should be applied only to reacting systems whose molecular properties are consistent with the assumptions of regular solution theory. This essentially restricts the approach to the reactions of nonpolar species in nonpolar solvents. Even in these systems, which we recall do not exhibit a marked solvent dependence, correlations with tend to be poor. - pp Nevertheless, the solubility parameter and its partitioning into dispersion, polar, and H-bonding components provide some insight into solvent behavior that is different from the information given by other properties such as those in Tables 8-2 and 8-3. [Pg.418]

The solubility parameter 5 of a pure solvent defined initially by Hildebrand and Scott based on a thermodynamic model of regular solution theory is given by Equation 4.4 [13] ... [Pg.73]

The micellization and adsorption properties of industrial sulfonate/ ethoxylated nonionic mixtures have been assessed in solution in contact with kaolinite. The related competitive equilibria were computed with a simple model based on the regular solution theory (RST). Starting from this analysis, the advantage of adding a hydrophilic additive or desorbing agent to reduce the overall adsorption is emphasized. [Pg.275]

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). [Pg.276]

Comparison Theoretical Equilibrium Calculations and Results of Circulation Tests in Porous-Media To make this interpretation more quantitative, the regular solution theory (RST) was applied to sulfonate/desorbent dynamic equilibria reached inside porous media by using the approach described above. In so doing, we assumed that the slugs injected were sufficiently large and that a new equilibrium was reached at the rear of micellar slug in the presence of desorbent. [Pg.288]

It is notified in the work [15], that the swelling of some coal does not agree with the thesis of regular solutions theory that is why, it is not allowed to calculate the parameter for them. Authors explain this fact by the presence of oxygen atoms in the investigated coal. But also the molecular weight of separate sections (clusters) between the points of crossing for methylated or acetylated samples of this coal is equal only to 300 - 600 in accordance with the calculations (that is unreal). [Pg.54]

The Flory-Huggins interaction parameter, x Is the sum of enthalpic (xH) and entropic (x ) contributions to the polymer-solute interactions (28). xs is an emPitical constant related to the coordination of the polymer subunits (29). Chiou et al. (20) have selected a value of 0.25 for xs of humlc matter. From regular solution theory, xq is given by... [Pg.199]

Other LAS homolog structural effects on wettability and soil removal were found when the data were analyzed using the cohesive energy ratio, R, the regular solution theories of the... [Pg.263]

Fig. 4. 23 Application of the regular solution theory for correlation of distribution constants for ZnA2 and CuA2 with solvent properties (solubility parameters) the numbers refer to the solvents listed in Table 4.10. (From Ref. 22.)...

J.7.I Topological features of phase diagrams calculated using regular solution theory... [Pg.72]

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 ... [Pg.9]

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) ... [Pg.13]

Equations 3 and 4 are derived from Equation 5 (31) which has been Found to be invalid For the systems oF interest. However, Equations 3 and 4 have been shown to accurately describe mixture CMC values and monomer-micelle equilibrium. The resolution is that Equations 3 and 4 should be considered as valuable empirical equations to describe these nonideal systems. The Fact that they were originally derived From regular solution theory is a historical coincidence. [Pg.13]

Only one model to describe nonideal micelle Formation was described here. Regular solution theory in a diFFerent Form than that used here has been applied to these systems ( ). Alternative models have been proposed based on statistical mechanics (37.50). the... [Pg.13]

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... [Pg.32]

It was recently ascertained that the behavior of the adsorbed film of two surfactants in equilibrium with their micelle can be explained by assuming both the surface region and the micelle particle to be mixtures of the surfactants (1 - ) - Further, the application of the regular solution theory to the mixtures was shown to be useful to describe the nonideal behavior of ionic surfactants ( - ) However, the above treatments are incomplete from the thermodynamic viewpoint, because they do not consider the dissociation of surfactants and ignore the presence of solvent (T). In addition, it is impossible to suppose that the regular solution theory is applicable to both the adsorbed film and the micelle of ionic surfactants accompanied by the electrical double layer ( ). [Pg.163]

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. [Pg.302]

The regular solution theory may be applied to surface adsorption and micelle formation of mixed nonaethoxylated fatty alcohols with Gaussian distribution In hydrophobic chain length. Such a system can be treated as an Ideal mixture,... [Pg.311]

Model Development. There is vast opportunity for development of fundamentally based models to describe the thermodynamics of mixed micelle formation. As discussed in Chapter 1, regular solution theory has yielded useful relations to describe monomer—mi cel 1e equilibrium. [Pg.328]

However, the thermodynamic assumptions behind regular solution theory are incorrect for these systems. [Pg.328]

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