Solubility regular solution

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). 

Regular solutions, the solubility parameter and Scatchard-Hildebrand theory... 

Solubility parameters are generally tabulated, together with the corresponding liquid molar volumes, only at 25°C. Although solubility parameters are themselves temperature-dependent, the combination of quantities in Eq. 70 is not. Differentiating Eq. 70 with respect to temperature gives — the excess entropy, a quantity which has been assumed to be zero in accord with the definition of a regular solution. Thus only data at 25°C are needed. Solubility parameters may be... 

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. 

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. 

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] ... 

Still, the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74) ... 

The solubility parameter concept was established in the 1930s by the work of Hildebrand and Scatchard. The original concept covers regular solutions, i.e., solutions that do not show an excess entropy effect on mixing. The solubility parameter concept offers the following interesting features ... 

Given a nonionic solute that has a relatively low solubility in each of the two liquids, and given equations that permit estimates of its solubility in each liquid to be made, the distribution ratio would be approximately the ratio of these solubilities. The approximation arises from several sources. One is that, in the ternary (solvent extraction) system, the two liquid phases are not the pure liquid solvents where the solubilities have been measured or estimated, but rather, their mutually saturated solutions. The lower the mutual solubility of the two solvents, the better can the approximation be made. Even at low concentrations, however, the solute may not obey Henry s law in one or both of the solvents (i.e., not form a dilute ideal solution with it). It may, for instance, dimerize or form a regular solution with an appreciable value of b(J) (see section 2.2). Such complications become negligible at very low concentrations, but not necessarily in the saturated solutions. 

If Z9b(ai) can be equated with P calculated from the entries in Table 2.5, then Z9b(a2) in any other solvent Ab can be estimated from Eq. (2.62). Equation (2.62) is actually a combination of four expressions of the form of Eq. (2.8) (see section 2.2.2), two for water and solvent Ai and two for water and solvent A2, presuming them to be immiscible pairs of liquids. It employs concentrations on the mole fraction scale, and assumes that the systems behave as regular solutions (which they hardly do). This eliminates the use of the solubility parameter 8 of water, which is a troublesome quantity (see Table 2.1). Solvent Ai need not, of course, be 1-octanol for Eq. (2.62) to be employed, and it suggests the general trends encountered if different solvents are used in solvent extraction. 

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.)...

One of the approaches to calculating the solubility of compounds was developed by Hildebrand. In his approach, a regular solution involves no entropy change when a small amount of one of its components is transferred to it from an ideal solution of the same composition when the total volume remains the same. In other words, a regular solution can have a non-ideal enthalpy of formation but must have an ideal entropy of formation. In this theory, a quantity called the Hildebrand parameter is defined as ... 

Equation (4.7) is the non-ideal part of the solubility and can be added to Equation (4.3) to obtain an expression for the solubility of a regular solution. 

The mole fraction solubilities of ten copper(II) and five chromium(III) P-diketo-nates were measured in SCCO2 with a spectroscopic technique and found to vary over four orders of magnitude. Observed trends indicate that the solubility in supercritical carbon dioxide is strongly dictated by the character of the hydrocarbon or fluorocarbon shell surrounding the central metal atom. A regular solutions approach was used for Cr(acac)°3 to quantitatively attempt to predict the solubility in SCCO2. Solubility... 

The solubility of a gas is an integral part for the prediction of the permeation properties. Various models for the prediction of the solubility of gases in elastomeric polymers have been evaluated (57). Only a few models have been found to be suitable for predictive calculations. For this reason, a new model has been developed. This model is based on the entropic free volume activity coefficient model in combination with Hildebrand solubility parameters, which is commonly used for the theory of regular solutions. It has been demonstrated that mostly good results are obtained. An exception... 

The solubility parameter is therefore a measure of the energy density holding the molecules in the liquid state. Note that regular solution theory can only predict positive AH. Thus, with this approach, prediction of solubility involves matching the solute and solvent solubility parameters as closely as possible to minimize AH. As a very rough mle of thumb 61 — 62 must be less than 2 (f/cm3)1 /2 for solubility. 

The factors that cause solutions of iodine to deviate from die behavior of regular solutions are illustrated in Fig. 3. in which values of the left hand member of Eq. (7) are plotted against those of the right for iodine solutions at 25°C ai is tire activity of solidiodine Xy denotes measured solubility Vy is the extrapolated molal volume of liquid iodine. 59 cra3 i is the volume fraction of the solvent, 1.0 62 = 14.1 1 is the solubility parameter of the solvent. Illustrative values of xi and 6] are given in accompanying table. 

A key feature of this model is that no data for mixtures are required to apply the regular-solution equations because the solubility parameters are evaluated from pure-component data. Results based on these equations should be treated as only qualitative. However, mixtures of nonpolar or slightly polar, nonassociating chemicals, can sometimes be modeled adequately (1,3,18). Applications of this model have been limited to hydrocarbons (qv) and a few gases associated with petroleum (qv) and natural gas (see Gas, natural) processing, such as N2, H2, C02, and H2S. Values for 8 and JV can be found in many references (1—3,7). 

According to Hildebrand et al. (1970), the simpliLed solubility equation (assuming the difference in heat capacity of the crystalline and the hypothetical molten forms of the solute is negligible) for a crystalline solute in a regular solution is... 

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. 

A better estimate of all attractive forces surrounding a molecule was found in the use of the solubility parameter [32,33], Hancock et al. [34] has reviewed the use of solubility parameters in pharmaceutical dosage form design. The solubility parameter is used as a measure ofthe internal pressures ofthe solvent and solute in nonideal solutions. Cosolvents that are more polar have larger solubility parameters. The square root ofthe cohesive energy density, that is, the square root of the energy of vaporization per unit volume of substance, is known as the solubility parameter and was developed from Hildebrand s Regular Solution Theory in the Scatchard-Hildebrand... 

Other attempts at characterizing the deviation from ideal solubility theory have been made. Anderson et al. [50] showed that solubilities that could not be rationalized from the regular solution theory could be rationalized by assuming the formation of speciLc solute-solvent complexes. Yalkowsky et al. [51,52] showed that the deviation from the ideal solubility equation could be expressed in terms of interfacial tension and surface area. In equation form,... 

When gas solubility data are lacking or are unavailable at the desired temperature, they can be estimated using available models. The method of Prausnitz and Shair (1961), which is based on regular solution theory and thus has the limitations of that theory. The applicability of regular solution theory is covered in detail by Hildebrand et al. (1970). A more recent model, now widely used, is UNIFAC, which is based on structural contributions of the solute and solvent molecular species. This model is described by Fredenslund et al. (1977) and extensive tabulations of equilibrium data, based on UNIFAC, have been published by Hwang et al. (1992) for aqueous systems where the solute concentrations are low and the solutions depart markedly from thermodynamic equilibrium. 

There already exists a substantial literature devoted to the estimation of various material properties with the help of additive structual increments (Reid et. al, 1987, Van Krevelen, 1990). The regular solution theory in combination with additive structural increments has a wide application for estimating the relative solubilities of organic substances in polymers and the solubility of polymers in various solvents (Barton, 1983) and will be described later in this chapter. When estimating partition coefficient values, one is quickly confronted with this method s application limits, particularly with polar and non-polar structures, for example the partitioning of substances between polyolefins and alcohol (Baner and Piringer, 1991). 

The solubility parameter is valid only for regular solutions (where the excess entropy is equal to zero) and mainly for nonpolar classes of substances. Of the numerous suggested improvements that have been made, the one by Hansen is worth mentioning. Here the solubility parameter is the sum of three parts (Barton, 1983) corresponding to a nonpolar or pure dispersive (8,/), polar (8P) and hydrogen bonding (8/,) based interactions ... 

According to the regular solution theory, polymers are as a rule soluble in solvents if their solubility parameters are similar to those of the corresponding solvent. The upper limit for good solubility is defined to he a difference (AS) of 6 units between solubility parameters ... 

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