Solvents, mixed aqueous molar volume

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. 

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 Kirkwood—Buff formalism was used to derive an expression for the composition dependence of the Henry s constant in a binary solvent. A binary mixed solvent can be considered as composed of two solvents, or one solvent and a solute, such as a salt, polymer, or protein. The following simple expression for the Henry s constant in a binary solvent (H2t) was obtained when the binary solvent was assumed ideal In = [In f2,i(ln V — In V ) + In i 2,3(ln Vj — In V)]/ (In — In V ). In this expression, i 2,i and i 2,3 are the Henry s constants for the pure single solvents 1 and 3, respectively V is the molar volume of the ideal binary solvent 1—3 and and Vs are the molar volumes of the pure individual solvents 1 and 3. The comparison with experimental data for aqueous binary solvents demonstrated that the derived expression provides the best predictions among the known equations. Even though the aqueous solvents are nonideal, their degree of nonideality is much smaller than those of the solute gas in each of the constituents. For this reason, the ideality assumption for the binary solvent constitutes a most reasonable approximation even for nonideal mixtures. 

Eq. (2) does not contain any adjustable parameter and can be used to predict the gas solubility in mixed solvents in terms of the solubilities in the individual solvents (1 and 3) and their molar volumes. Eq. (2) provided a very good agreement [9] with the experimental gas solubilities in binary aqueous solutions of nonelectrolytes a somewhat modified form correlated well the gas solubilities in aqueous salt solutions [17]. The authors also derived the following rigorous expression for the Henry constant in a binary solvent mixture [9] (Appendix A for the details of the derivation) ... 

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. 

In order to verify the applicability of Eq. (23) combined with the nonideal molar volume of a mixed solvent to the solubility of a drug in an aqueous mixed solvents, 32 experimental sets were selected. Most of them were taken from the paper of... 

Eq. (28) thus obtained can be used to represent the solubility of poorly soluble drugs in aqueous mixed solvents if information about the properties of the binary solvent (composition, phase equilibria and molar volume), the nonideality parameters and the constant A is available. These parameters can be considered as adjustable, and determined by fitting the experimental solubilities in the binary solvent. We applied such a procedure to the solubilities of caffeine in water/AW-dimethylformamide (Herrador and Gonzalez, 1997) and water/1,4-dioxane (Adjei et al., 1980), of sulfamethizole in water/1,4-dioxane (Reillo et al., 1995) as well as of five solutes in water/ propylene glycol (Rubino and Obeng, 1991). It was shown that Eq. (28) provides accurate correlations of the experimental data. 

The following equations Ml) Equation9with ideal molar volume, M2) Equation 9 with the molar volume expressed via Equation 11, M3) Equation 7 combined with Equations 5, 12—14, and M4) Equation 7 combined with Equations 5, 15—17 will be tested for the solubilities of the HOP in aqueous mixed solvents. 

From the experimental solubilities in binary solvents and molar volumes of the individual constituents. The calculation procedure is the same as above, with the exception that the solubilities of naphthalene in the binary subsystems 1 and 11 were obtained from experiment. The calculation of the solubilities in binary aqueous solvents was described in detail in previous sections. It should be noted that the water/ methanol/ 1-butanol mixed solventand the binary subsystem water/1-butanol are not completely miscible. Only the homogeneous regions of mixed solvents were considered in this paper. 

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. 

Many characteristics of a protein in aqueous solvents are connected to its preferential solvation (or preferential hydration). The protein stability is a well-known example. Indeed, the addition of certain compounds (such as urea) can cause protein denaturation, whereas the addition of other cosolvents, such as glycerol, sucrose, etc. can stahihze at high concentrations the protein stiucture and preserve its en2ymatic activity [4-7]. The analysis of literature data shows that as a rule Ffor the former and r23 " <0 for the latter compounds. Recently, the authors of the present paper showed how the excess (or deficit) number of water (or cosolvent) molecules in the vicinity of a protein molecule can be calculated in terms of F2 the molar volume of the protein at infinite dilution and the properties of the protein-free mixed solvent [8]. The protein solubility in an aqueous mixed solvent is another important quantity which can be connected to the preferential solvation (or hydration) [9-13] and can help to understand the protein behavior [9-17]. 

Equations 3 and 5 allow one to calculate the Kirkwood-Buff integrals G12 and G23 using experimental data regarding the preferential binding parameters r2 and the partial molar volume of a protein at infinite dilution in a mixed solvent 49-50,52 jjjg Kirkwood—Buff integrals Gn and Go can be evaluated on the basis of the properties of protein-free mixed solvent water + cosolvent. It should be mentioned that recently the Kirkwood—Buff theory was used to analyze the effects of various cosolvents on the properties of aqueous protein solutions. " ... 

Marcus Y (2005a) BET nodehng of solid-liquid phase diagrams of common ion binary stilt hydrate mixtures. 1. The BET parameters. J Sol Chem 34 297-306 Marcus Y (2006) On the molar volumes and viscosities of electrolytes. J Sol Chem 35 1271-1286 Marcus Y (2007) Gibbs energies of transfer of anions from water to mixed aqueous organic solvents. Chem Rev 107 3880-3897... 

However, Equation 10.30 cannot provide the maximum in the solubility versus mixed solvent composition, which was frequently observed in the solubility of drugs in aqueous mixed solvents (Jouyban-Gharamaleki et al. 1999, and references therein). To accommodate this feature of the solubility curve, the molar volume of the mixed solvent is replaced in Equation 10.30 by... 

This critical and extensive review deals with both the volume changes asso dated with the mixing of binary mixtures of liquids and partial molar volumes at Infinite dilution of various solvent systems, aqueous and non aqueous. The temperature range cited is that at which the experimental measurements have been performed. Included Is a detailed discussion of the experimental methods used for measurements and associated theoretical developments. The coverage... 

Similar cases of specific interactions have been found also for the partial molar volumes of electrolytes (ions) in mixed solvents. The reports concerning the partial molar volumes of electrolytes in mixed solvents generally do no pertain to dilute solutions of the cosolvent, but on the contrary, most such studies cover the entire composition range. The curves tend to be very asymmetric in the solvent composition and changes in direction are often encountered, as shown, for example, in Figure 6.1 for some electrolytes in aqueous DMSO according to Letellier et al. [30]. In a few cases were very dilute solutions were studied, so that pair-interaction parameters could be... 

FIGURE 6.1 Representative partial molar volumes of electrolytes in mixed aqueous DMSO solvents NaBr ( ), KBr (a), Me NBr (t) with lOOcm -mol" deducted, and Bu NBr ( ) with... 

The standard partial molar volumes of electrolytes in mixed solvents can be modeled, as can those in neat solvents, in terms of the sum of the intrinsic volumes of the ions and their electrostriction. It is assumed that the intrinsic volumes, that is, the volumes of the ions proper and including the voids between ions and solvent molecules, are solvent independent, so that they do not depend on the natures of the solvents near the ions. Then, if no preferential solvation of the ions by the components of the solvent mixture takes place, the electrostriction can be calculated according to Marcus [32] as for neat solvents (Section 4.3.2.5), with the relevant properties of the solvents prorated according to the composition of the mixture. This appeared to be the case for the ions Li+, Na", K+, CIO ", AsE , and CFjSOj in mixtures of PC with MeCN, in which V (P,PC+MeCN) is linear with the composition over nearly the entire composition range. This is the case also for Me NBr in W+DMSO, as shown in Figure 6.1. Similarly, in aqueous methanol mixtures, smooth curves result for the ions Li", Na ", K+, Cs", CF, Br", and I" like those shown in Figure 6.1 for NaBr and KBr. However, when preferential solvation occurs, the... 

Because molarity is defined in terms of the volume of the solution, not the volume of solvent used to prepare the solution, the volume must be measured after the solutes have been added. The usual way to prepare an aqueous solution of a solid substance of given molarity is to transfer a known mass of the solid into a volumetric flask, dissolve it in a little water, fill the flask up to the mark with water, and then mix the solution thoroughly by tipping the flask end over end (Fig. G.8I. 

Many investigators have studied substitution at iron(II)-diimine complexes in binary aqueous mixed solvents and other investigators in aqueous salt solutions. Some years ago the results of addition of salts and a cosolvent were assessed, for [Fe(5N02phen)3] in water, t-butyl alcohol, acetone, dimethyl sulfoxide, and acetonitrile mixtures containing added potassium bromide or tetra-n-butylammonium bromide. " Now the effects of added chloride, thiocyanate, and perchlorate on dissociation and racemization rates of [Fe(phen)3] in water-methanol mixtures have been established. The main explanation is in terms of increasing formation of ion pairs as the methanol content of the medium increases, but it is somewhat spoiled by the (unnecessary) assumption of a mechanism involving interchange within the ion pairs. Kip values (molar scale) of 11,18, and 25 were estimated for perchlorate, chloride, and thiocyanate in 80% (volume) methanol at 298.2 K. These values may be compared with values of 20, 7, and 4 for association between [Fe(phen)3] and iodide, " [Fe(bipy)3] and iodide, " and [Fe(phen)3] and cyanide " " in aqueous solution (at 298.2,... 

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