Solubility, infinite dilution coefficient

Zielenjiewicz, W., Golankiewicz, B., Perlovich, G.L., and Kozbial, M. Aqueous solubilities, infinite dilution activity coefficients and octanol-water partition coefficients of tricyclic analogs of acyclovir. /. Solution Chem., 28(6) 731-745,1999. 

Tsonopoulos and Pransnitz (27) have reported that the hydrocarbon infinite dilution coefficient, y00, is the appropriate quantity for correlating the aqueous solubilities of hydrocarbons. They, along with Leinonen et al. (23) and Pierotti et al. (28) have successfully correlated y00 with carbon number, molar volume, and degree of branching. Recently MacKay and Shiu (26) have correlated the hydrocarbon infinite dilution coefficients of 32 aromatic hydrocarbons (using the supercooled standard state) with carbon number. From this relationship, they derived a... 

The activity coefficients may be regarded as a measure of the deviation of a real system from the idealized behaviour of an arbitrarily chosen reference state. For a solute of limited solubility, infinite dilution is chosen as the reference state, for completely miscible liquids the single components and for gases and vapours the fugacity / = 1 at standard temperature. In all these cases y< = 1 for the reference state [19]. 

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). 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

Haines, R.L.S., Sandler, S.L. (1995) Aqueous solubilities and infinite dilution activity coefficients of several polycyclic aromatic hydrocarbons. J. Chem. Eng. Data 40, 835-836. 

This equation has the expected behavior that AG< becomes more positive with decreasing solubility of the solute. However, free energies of solvation for different solutes cannot be related to their relative solubilities unless the vapor pressures of the different solutes are similar or one takes account of this via Equation 76. Furthermore, if the solubility is high enough that Henry s law does not hold, then one must consider finite-concentration activity coefficients, not just the infinite-dilution limit. 

A wide range of values (one decade ) could be obtained using correlations as well as using different experimental methods [34, 38, 43]. As for solubility, diffusion coefficient at infinite dilution should be determined experimentally using the real liquid phase. Experimental methods are, however, more complex to carry out and correlations are widely used. 

Table 5.3 Solute and solvent solubility isotope effects for (benzene-water) solutions at 306.2 K obtained from IE s on Henry s Law coefficients, Ki and Kn- [Isotope effects on free energies of transfer, ideal gas to solution in the limit of infinite dilution] (Dutta-Choudhury, M., Miljevic, N.

Wright, D.A., Sandler, S.I., and DeVoll, D. Infinite dilution activity coefficients and solubilities of halogenatedhydrocarbons in water at ambient temperature, iinviron. Sci. Tec/mo/., 26(9) 1828-1831, 1992. 

For an ionic solute dissociating into v ions, the temperature coefficient is 1/v times the right-hand side of Eq. (2.60). Again, it is assumed that the solubility is sufficiently low for the mean ionic activity coefficient to be effectively equal to unity and independent of the temperature. When this premise is not met, then corrections for the heat of dilution from the value of the solubility to infinite dilution must be added to Asoi //°b in Eq. (2.60). 

Calorimetric measurements are time consuming and very expensive because of the amount of the IL taken to the experiment. The results usually show the same type of interaction as in other experiments as the activity coefficients at the infinite dilution or solubility measurements. Prom calorimetric measurements it can be observed that the molar heat capacities depend linearly on the temperature and increase proportionally to the alkyl chain length of the cation. 

For low miscibility, the solubility of a substance in water is often estimated as the inverse of the chemical s infinite dilution activity coefficient ... 

The accurate prediction of the aqueous solubility of drugs and drug-like compounds is much further away from a satisfactory solution because the existing QSAR- or group-contribution-based solubility prediction models exhibit quite limited predictive power for new drug classes. Why is it that the extremely important problem of the prediction of aqueous solubility much less solved than the prediction of less important partition coefficients The answer is that the development of prediction models for logarithmic partition coefficients is much simpler, because the molecule X under consideration only acts as a solute at infinite dilution in the two phases. Hence the task is only to calculate the free energy of... 

For a more soluble (or completely miscible) pollutant (i.e., ethanol), a Henry s law constant can be similarly estimated by using its tabulated infinite dilution activity coefficient measured at Tx, by extrapolation using P2sat, from to T2 ... 

Since the initial work of Smidsrod and Guillet numerous investigators have used I.G.C. to determine physicochemical parameters characterising the interaction of small amounts of volatile solutes with polymers Baranyi has shown that infinite dilution weight fraction activity coefficients, interaction parameters and excess partial molar heats of mixing can be readily determined with this technique. Partial molar heats and free energies of mixing, and solubility parameters of a wide variety of hydrocarbons in polystyrene and poly(methyl methacrylete) have been determined The temperature dependence of the interaction parameter between two polymers has also been studied... 

Larachi, R, Leroux, M., Hamoudi, S., Bemis, A., Sayari, A. (2000) Solubility and infinite dilution activity coefficient for 5-chlorovanilhn and 4-chloroguaiacol in water over the temperature range 280 to 363 K. J. Chem. Eng. Data 45, 404-408. 

At temperatures above Fg, or for a semicrystalline polymer, the magnitude of the retention volume is a direct measure of the solubility of the probe in the polymer. At infinite dilution of the solute the relation between the bulk retention volume and the activity coefficient is (5,37,38)... 

Solubilitiesattemperaturesand pressures above the critical values of the solvent liave important applications for supercritical separation processes. Examples are extraction of caffeine from coffee beans and separation of asplraltenes from heavy petroleum fractions. For a typical solid/vapor equilibrium (SVE) problem, tire solid/vapor saturation pressure P is very small, and the saturated vapor is for practical purposes an ideal gas. Hence 0 for pure solute vapor at this pressure is close to unity. Moreover, exceptfor very low values of the system pressure P, the solid solubility yj is small, and can be approximated by j, the vapor-phase fugacity coefficient of the solute at infinite dilution. Finally, since is very small, the pressure difference P — in the Poyntingfactor is nearly equal to P at any pressure where tins factor... 

Many nonionizable organic solutes in water are described thermodynamically on the mole fraction scale, although their solubilities may commonly be reported in practical units, for example, molality. [Refer to Schwarzenbach et al. (1993) and Klotz (1964) for detailed discussion of such aqueous solutions.] Here, the standard state is the pure liquid state of the organic solute, that is, Xj = 1. The reference state is Xi - 1, that is, a solution in which the organic solute molecules interact with one another entirely. Activity coefficients of solute molecules in dilute aqueous solutions are generally much greater than unity for this reference state choice, jc, 1. For example, with this reference state, aqueous benzene has an experimental infinitely dilute solution activity coefficient, T nzeno of 2400 for an infinite dilution reference state, jc, - 0, the activity coefficient would be approximately 1 (Tanford, 1991). 

From Eqs. (9) and (10) one can see, that the calculation of the solubilities of solids in a SCF in the presence of an entrainer (cosolute or cosolvent) requires information about the properties of the pure components, the fugacity coefficients at infinite dilution and the values of K p. 

Equation 14 allows one to calculate the fugacity coefficient of a solute at infinite dilution in the binary mixture of two SC fluids, in terms of the fugacity coefficients of the solute at infinite dilution for each of the SC fluids. This expression will be used in the next section to derive an expression for the solubility of a solid in a gaseous mixture of two SC fluids. 

Expression for the Solubility of a SoUd in a Gaseous Mixture Formed of Two SC Fluids. Assuming that the solute solubilities are very small and that the fugacity coefficients have the same values as those at infinite dilution, eqs 1—3 can be recast as... 

As already mentioned, the Krichevsky equation (eq 1) is valid when the binary mixtures 1—2 and 2—3 (gas solute/pure solvents) and the ternary mixture 1—2—3 are ideal. However, these conditions are often far from reality. Let us consider, for example, the solubility of a hydrocarbon in a water—alcohol solvent (for instance, water—methanol, water—ethanol, etc.). The activity coefficient of propane in water at infinite dilution is 4 X 10 , whereas the activity coefficients of alcohols and water in aqueous solutions of simple alcohols seldom exceed 10. It is therefore clear that the main contribution to the nonideality of the ternary gas-binary solvent mixture comes from the nonidealities of the gas solute in the individual solvents, which are neglected in the Krichevsky equation. 

The present paper is concerned with mixtures composed of a highly nonideal solute and a multicomponent ideal solvent. A model-free methodology, based on the Kirkwood—Buff (KB) theory of solutions, was employed. The quaternary mixture was considered as an example, and the full set of expressions for the derivatives of the chemical potentials with respect to the number of particles, the partial molar volumes, and the isothermal compressibility were derived on the basis of the KB theory of solutions. Further, the expressions for the derivatives of the activity coefficients were applied to quaternary mixtures composed of a solute and an ideal ternary solvent. It was shown that the activity coefBcient of a solute at infinite dilution in an ideal ternary solvent can be predicted in terms of the activity coefBcients of the solute at infinite dilution in subsystems (solute + the individual three solvents, or solute + two binaries among the solvent species). The methodology could be extended to a system formed of a solute + a multicomponent ideal mixed solvent. The obtained equations were used to predict the gas solubilities and the solubilities of crystalline nonelectrolytes in multicomponent ideal mixed solvents. Good agreement between the predicted and experimental solubilities was obtained. 

Solubility of a Solid. For the solubilities of poorly soluble crystalline nonelectrolytes in a multicomponent mixed solvent, one can use the infinite-dilution approximation and consider that the activity coefficient of a solute in a mixed solvent is equal to the activity coefficient at infinite dilution. Therefore, one can write the following relations for the solubility of a poorly soluble crystalline nonelectrolyte in a ternary mixed solvent and in two of its binaries i2,i3... 

Generally speaking, the thermodynamic properties of these complex mixtures (solute-i-multicomponent aqueous solvent) depend on many factors such as the chemical natures of the solute and of the constituents of the mixed solvent, the intermolecu-lar interactions between the components in these mixtures, the mixture composition and the pressure and temperature. In the present paper only low soluble solutes are considered. Therefore, the solutions can be considered as dilute and the intermolecu-lar interactions between the solute molecules can be neglected. Thus, the properties of a solute-free mixed solvent and the activity coefficient of the solute at infinite dilution can describe the behavior of such dilute mixtures. 

The application of UNIFAC to the solid-liquid equilibrium of sohds, such as naphthalene and anthracene, in nonaqueous mixed solvents provided quite accurate results [11]. Unfortunately, the accuracy of UNIFAC regarding the solubility of solids in aqueous solutions is low [7-9]. Large deviations from the experimental activity coefficients at infinite dilution and the experimental octanol/water partition coefficients have been reported [8,9] when the classical old version of UNIFAC interaction parameters [4] was used. To improve the prediction of the activity coefficients at infinite dilution and of the octanol/water partition coefficients of environmentally significant substances, special ad hoc sets of parameters were introduced [7-9]. The reason is that the UNIFAC parameters were determined mostly using the equihbrium properties of mixtures composed of low molecular weight molecules. Also, the UNIFAC method cannot be applied to the phase equilibrium in systems containing... 

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