Solvents, mixed aqueous activity coefficients

In principle, Gibbs free energies of transfer for trihalides can be obtained from solubilities in water and in nonaqueous or mixed aqueous solutions. However, there are two major obstacles here. The first is the prevalence of hydrates and solvates. This may complicate the calculation of AGtr(LnX3) values, for application of the standard formula connecting AGt, with solubilities requires that the composition of the solid phase be the same in equilibrium with the two solvent media in question. The other major hurdle is that solubilities of the trichlorides, tribromides, and triiodides in water are so high that knowledge of activity coefficients, which indeed are known to be far from unity 4b), is essential (201). These can, indeed, be measured, but such measurements require much time, care, and patience. 

The pH of an aqueous solution, where the concentration of the solute is not very high, is a good measure of the proton-donating/accepting ability of the solvent. But unfortunately this is no longer true in concentrated solutions because activity coefficients are no longer at unity. A measurement of solvent acidity is needed which works in concentrated solutions and applies to mixed solvents as well. This is established in the Hammett acidity function (Ho)10,11- This function is used for acidic solvents of high dielectric constants Hq is... 

Studies of the solution properties of heteropoly acids have been somewhat spares despite the general interest in these compounds for many years. Deterents to such studies have been primarily the instability of the compounds and the uncertainty concerning their composition. Conductivity and pH measurements on the heteropoly acids H4[PMonVO40] and H5[PMoi0V2O40] in aqueous solutions and mixed solvents has already been discussed. The acids are strong 1-4 and 1-5 electrolytes, respectively. Activity coefficients of ammonium 6-heteropolymolybdates have been reported and shown these to be 1 3 electrolytes197. ... 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

The problems involved in the measurement of acidities or relative acidities of weak acids are illustrated by the widely different estimates which have been given for the acidity of substituted acetylenes. Two different approaches have been used for measuring the equilibrium acidity of carbon acids which do not ionize in the pH range. In one approach, the ionization of a carbon acid is studied in mixed solvents containing base. Some of these solutions are more basic than aqueous solutions and by varying the solvent mixture the ionization of acids with pK values in the range 12—25 can be studied. Values at the low end of the pK range are directly compared with aqueous p/iC values. It is assumed that ratios of the activity coefficients (f) for the ionized (S-) and unionized acids (SH) are the same for all the acids studied and an acidity function (86)... 

In this paper, the Kirkwood—Buff formalism was used to relate the Henry s constant for a binary solvent mixture to the binary data and the composition of the solvent. A general equation describing the above dependence was obtained, which can be solved (analytically or numerically) if the composition dependence of the molar volume and the activity coefficients in the gas-free mixed solvent are known. A simple expression was obtained when the mixture of solvents was considered to be ideal. In this case, the Henr/s constant for a binary solvent mixture could be expressed in terms of the Henry s constants for the individual solvents and the molar volumes of the individual solvents. The agreement with experiment for aqueous solvents is better than that provided by any other expression available, including an empirical one involving three adjustable parameters. Even though the aqueous solvents considered are nonideal, their degrees of nonideality are much lower than those of the solute gas in each of the constituent solvents. For this reason, the assumption that the binary solvent behaves as an ideal mixture constitutes a reasonable approximation. 

In a previous paper regarding the gas solubility in mixtures of two nonelectrolytes, the ideality approximation for the binary solvent was employed to obtain an expression for the gas solubility. The ideality of the mixed solvents constituted a good approximation because usually the nonideality of the mixture of two nonelectrolytes is much lower than those between each of them and the gas. A similar assumption can be made for dilute aqueous salt solutions. Indeed, the data regarding the activity coefficient of water (yw) in dilute aqueous solutions of sodium chloride indicate that 1(9 In 7w/9xw)p,tI 0.01 for a molality of sodium chloride smaller than 0.8. Considering, in addition, that (Ai2 - A2s)4=o is independent of composition, eq 13 becomes... 

The Kirkwood-Buff theory of solutions for ternary mixtures was used to analyze the gas solubility in a mixed binary solvent composed of a high molecular weight and a low molecular weight cosolvent, such as the aqueous solutions of water soluble polymers. A rigorous expression for the composition derivatives of the gas activity coefficient in ternary solution was used to derive the composition dependence of the Henry constant under isobaric and isothermal conditions. The obtained expressions as well as the well-known Kri-chevsky equation were tested for the solubilities of Ar, CH4, C2H6 and C3H8 in the aqueous solutions of PPG-... 

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... 

Another method suggested by the authors for predicting the solubility of gases and large molecules such as the proteins, drugs and other biomolecules in a mixed solvent is based on the Kirkwood-Buff theory of solutions [18]. This theory connects the macroscopic properties of solutions, such as the isothermal compressibility, the derivatives of the chemical potentials with respect to the concentration and the partial molar volumes to their microscopic characteristics in the form of spatial integrals involving the radial distribution function. This theory allowed one to extract some microscopic characteristics of mixtures from measurable thermodynamic quantities. The present authors employed the Kirkwood-Buff theory of solution to obtain expressions for the derivatives of the activity coefficients in ternary [19] and multicomponent [20] mixtures with respect to the mole fractions. These expressions for the derivatives of the activity coefficients were used to predict the solubilities of various solutes in aqueous mixed solvents, namely ... 

The present paper deals with the application of the fluctuation theory of solutions to the solubility of poorly soluble drugs in aqueous mixed solvents. The fluctuation theory of ternary solutions is first used to derive an expression for the activity coefficient of a solute at infinite dilution in an ideal mixed solvent and, further, to obtain an equation for the solubility of a poorly soluble solid in an ideal mixed solvent. Finally, this equation is adapted to the solubility of poorly soluble drugs in aqueous mixed solvents by treating the molar volume of the mixed solvent as nonideal and including one adjustable parameter in its expression. The obtained expression was applied to 32 experimental data sets and the results were compared with the three parameter equations available in the literature. 

The main difficulty in predicting the solid solubility in a mixed solvent consists in calculating the activity coefficient of a solute in a ternary mixture In this paper, the Kirkwood-Buff (KB) theory of solutions (or fluctuation theory) (Kirkwood and Buff, 1951) is employed to analyze the solid (particularly drug) solubility in mixed (mainly aqueous) solvents. The analysis is based on results obtained previously regarding the composition derivatives of the activity coefficients in ternary solutions (Ruckenstein and Shulgin, 2001). These equations were successfully applied to gas solubilities in mixed solvents (Ruckenstein and Shulgin, 2002 Shulgin and Ruckenstein, 2002). 

The Flory-Huggins and Wilson equations for the activity coefficients of the components of the mixed solvent were employed to correlate 32 experimental data sets regarding the solubility of drugs in aqueous mixed solvents. The results were compared with the models available in literature. It was found that the suggested equation can be used for an accurate and reliable correlation of the solubilities of drugs in aqueous mixed binary solvents. It provided slightly better results than the best literature models but has also the advantage of a theoretical basis. 

In a previous paper (Ruckenstein and Shulgin, 2003), the Kirkwood-Buff theory of solutions (Kirkwood and Buff, 1951) was employed to obtain an expression for the solubility of a solid (particularly a drug) in binary mixed (mainly aqueous) solvents. A rigorous expression for the composition derivative of the activity coefficient of a solute in a ternary solution (Ruckenstein and Shulgin, 2001) was used to derive an equation for the activity coefficient of the solute at infinite dilution in an ideal binary mixed solvent and further for the solubility of a poorly soluble solid. By considering that the excess volume of the mixed solvent depends on composition, the above equation was modified empirically by including one adjustable parameter. The modified equation was compared with the other three-parameter equations available in the literature to conclude that it provided a better agreement. 

The paper is organized as follows first, an equation for the activity coefficient of a solute at infinite dilution in a binary nonideal mixed solvent (Ruckenstein and Shulgin, 2003) is employed to derive an expression for its solubility in terms of the properties of the mixed solvent. Second, various expressions for the activity coefficients of the cosolvents are inserted into the above equation. Finally, the obtained equations are used to correlate the drug solubilities in binary aqueous mixed solvents and the results are compared with experimental data and other models available in the literature. 

In this paper, the fluctuation theory of solutions was applied to the solubility of drugs in aqueous mixed solvents. A rigorous expression for the activity coefficient of a solute at infinite dilution in a real mixed solvent was used to derive an equation for the sol-... 

First, a rigorous expression for the activity coefficient of a solid solute at infinite dilution in an ideal multicomponent solvent was derived using the fluctuation theory of solution. Second, the obtained expression was used to express the solubility of a poorly soluble solid in an ideal multicomponent solvent in terms of the solubilities of this solid in two subsystems of the multicomponent solvent and their molar volumes. Finally, the developed procedure was used to predict the drug solubilities in ternary and quaternary aqueous mixed solvents using the drug solubilities in the constituent binary aqueous mixed solvents. The predicted solubilities were compared with the experimental ones and good agreement was found. 

The infinite dilution approximation implies that the activity coefficients in Eqs. (l)-(3) can be replaced by their values at infinite dilution of the solute y2 °°, and However, the solubilities of drugs in aqueous mixed solvents are not always very low. While the solubilities of various drugs in water (only poorly soluble drugs are considered in the present paper) do not exceed l-2mol%, the solubilities of the same drugs in the popular cosolvents ethanol and 1,4-dioxane can reach 5-20 mol%, and the solubilities in the water/l,4-dioxane and water/ethanol mixtures are often appreciable and can reach 8-30 mol%. Therefore, the effect of the infinite dilution approximation on the accuracy of the predictions of the solubilities of poorly soluble drugs deserves to be examined. 

The prediction of the solubility of poorly soluble substances of environmental significance in multicomponent (ternary and higher) aqueous mixed solvents is a difficult task because it requires the knowledge of the activity coefficient of a solute in a multicomponent mixed solvent. The method most often used for the solubility of a solid in ternary and multicomponent mixed solvents is the combined nearly ideal binary solvent/Redlich - Kister equation (33). That equation was applied to the solubility of a solid in ternary... 

In the present paper the Kirkwood-Buff theory of ternary solutions was apphed to infinitely dilute proteins in aqueous mixed solvents. Novel expressions for the Kirkwood-Buff integrals G]2, G23, and G]3, and the preferential binding parameter r23 have been derived and used to calculate the various properties of infinitely dilute proteins in aqueous mixed solvents. In particular, the Kirkwood-Buff integrals Gi2 and G23, the excess (or deficit) of water and cosolvent, and the derivatives of the activity coefficients of a protein and cosolvent were calculated for five different mixtures involving infinitely dilute proteins in various aqueous mixed solvents. 

The present paper is devoted to the derivation of a relation between the preferential solvation of a protein in a binary aqueous solution and its solubility. The preferential binding parameter, which is a measure of the preferential solvation (or preferential hydration) is expressed in terms of the derivative of the protein activity coefficient with respect to the water mole fraction, the partial molar volume of protein at infinite dilution and some characteristics of the protein-free mixed solvent. This expression is used as the starting point in the derivation of a relationship between the preferential binding parameter and the solubility of a protein in a binary aqueous solution. 

A relationship between the derivative of the activity coefficient of the protein with respect to the mole fraction of water at infinite dilution of protein and the preferential binding parameter was used to connect the solubility of a protein in an aqueous mixed solvent to the preferential binding parameter. This relation was used to examine the salting-in and salting-out effect of various compounds on the protein solubility in water and to predict the protein solubility. 

We have seen many successful industrial applications of applied electrolyte thermodynamics models. In particular, the electrolyte NRTL activity coefficient model of Chen and Evans has proved to be the model of choice for various electrolyte systems, aqueous and mixed-solvent. However, there are unmet needs that require further development. 

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