Solubility-molar Volume Relationships

Solubility-Molar Volume Relationships The correlation between aqueous solubility at room temperature and the molar volume has been studied by McAuliffe [5] for different hydrocarbon classes. He discusses linear relationships, presented as graphs, describing the decrease in solubility with increasing molar volume for the homologous series of alkanes, alkenes, alkandienes, alkynes, and cycloalkanes. 

Similar relationships have been derived using other descriptors that are generally collinear with log P for non-polar non-specific toxicants, such as water solubility, molar volume and topological indices (Table 5.6), which may be applied if the log cannot be estimated and may also be used to cross-check the predictions obtained, especially if there is reasonable doubt about the correctness of the respective log P values. 

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

The plot between Henry s law constant and molar volume (Figure 1.7.4) is more scattered. Figure 1.7.5 shows the often-reported inverse relationship between octanol-water partition coefficient and the supercooled liquid solubility. 

While the solubility parameter can be used to conduct solubility studies, it is more informative, in dealing with charged polymers such as SPSF, to employ the three dimensional solubility parameter (A7,A8). The solubility parameter of a liquid is related to the total cohesive energy (E) by the equation 6 = (E/V) 2, where V is the molar volume. The total cohesive energy can be broken down into three additive components E = E j + Ep + Ejj, where the three components represent the contributions to E due to dispersion or London forces, permanent dipole-dipole or polar forces, and hydrogen bonding forces, respectively. This relationship is used... 

The correlation between aqueous solubility and molar volume discussed by McAuliffe [5] for hydrocarbons, and the importance of the cavity term in the solvatochromic approach, indicates a significant solubility dependence on the molecular size and shape of solutes. Molecular size and shape parameters frequently used in quantitative structure-water solubility relationships (QSWSRs) are molecular volume and molecular connectivity indices. Moriguchi et al. [33] evaluated the following relationship to estimate Cw of apolar compounds and a variety of derivatives with hydrophilic groups ... 

Air-water partition coefficients and Flenry s law constants are strongly temperature dependent because of the temperature dependencies of vapor pressure and of solubility. FI is also slightly dependent on the temperature dependence of water density and, hence, molar volume. The constants may be concentration dependent because of variations in yw, although the effect is believed to be negligible at low concentrations of non-associating solutes. Noted that these simple relationships break down at high concentrations, i.e., at mole fractions in excess of approximately 0.01. For most environmental situations, the concentrations are (fortunately) usually much lower. For thermodynamic purposes, H is usually preferred, whereas for environmental purposes, H is more convenient. 

Kqw is Ywvw/Yovo where v is molar volume and subscripts w and o refer to the water and octanol phases (Mackay, 1991). A plot of log Kow versus log solubility is thus expected to have a slope of approximately -1, and this is observed. Numerous further studies have explored and refined this relationship (e.g., Miller et al., 1985 Chiou et al., 1977, 1982 Valvani et al., 1981 Yalkowsky and Valvani, 1979 Yalkowsky et al., 1983a, 1983b Banerjee et al., 1980). 

The effect of temperature, pressure and density on solute retention (k1) in supercritical fluid chromatography (SFC) has been well studied.(1-6) Retention in SFC depends upon both solute solubility in the fluid and solute interaction with the stationary phase. The functional relationship between retention and pressure at constant temperature has been described by Van Wasen and Schneider. ( 1 ) The trend in retention is seen to depend on the partial molar volume of... 

Equation 11 should be the relationship between retention-solubility and pressure at constant temperature for infinitely dilute solutions. The RHS of eq. 11 consists of three terms, the first term will be a constant whose value depends on the partial molar volume of the solute in the stationary phase. The second term is the solubility of the solute in the supercritical fluid mobile phase. 

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. 

Other molecular properties have been also proposed to model the hydrophobic interactions. The parachor, which is related to the surface tension of a compound (139, 140) represents mainly the intermolecular interactions in a liquid. The Hildebrand-Scott solubility parameter, 6, (141) is related to intermolecular van der Waals forces and the closely related molar attraction constant, F, is obtained by multiplying 6 by the molar volume (142). The partition coefficient between two solvents can be obtained from the solubility parameters and the molar volumes of the solute and the solvents (193). This relationship is based on regular solution theory (194) and the assumption that the partial molar volumes of the solute is not different from its molar volume. Recently this has been criticized and a new derivation was proposed (195) in which the partial molar volumes are taken into account. The molar refractivity, MR, is related to dispersion forces and can be obtained as a sum of the partial molar refractivi-ties assigned to atoms and bonds (140, 143). These parameters have been compared (144) to establish their relative applicability to correlations with biological activity. The conclusion was that logP and molecular refractivity were the best parameters. Parameters obtained from high pressure liquid chromatography (144,... 

Conventionally, a relationship between gas solubility and molar volume has been considered. Of course, the molar volume correlates to the fluctuation of electrons around the molecules, i.e. electronic polarizability. Table 1.2 summarizes gas (He, H2,02, N2, and C02) solubility to various solvents. Here, the solvents are arranged in the order of their refractive indices. One may find the lower the refractive indices of the solvents (columns upward) or the higher the refractive indices of the gas (rows rightward), the higher the gas solubility. These trends are consistent with the like dissolves like rule. 

Correlations of Solubility with Molecular Parameters. The aqueous solubility of aromatic hydrocarbons has been shown by Klevens (25) to be related to carbon number, molar volume, and molecular length. These parameters along with the molar solubilities (expressed as — In S) of the compounds studied are presented in Table XIII. Figures 5 through 7 demonstrate the relationship between each of these parameters and solubility. These figures show that there are several compounds whose anomalous behavior makes accurate extrapolations of solubility from these relationships impossible. For example, anthracene and phenanthrene are structural isomers. They, therefore, have identical carbon numbers and very similar molar volumes. However, their aqueous solubilities differ by more than a factor of 20. Phenanthrene, fluoranthene, pyrene, and triphenylene all have very similar molecular lengths but their respective aqueous molar solubilities at 25°C are 5.6 X 10 6, 1.0 X 10"6, 6.8 X 10"7, and 2.8 X 10 8. 

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... 

Zeller (13 1) reviewed graphical three-dimensional solubility parameter estimation methods (12,14,49,55,172,173) as applied to solvent swelling of crosslinked elastomers. In general, the graphical method (Eqs. B22 and B23) does not account for the known influence of molar volume and crosslink density of solubility, and incorrectly assumes a linear relationship between the solubility parameter difference and solubility. An improved method used the Flory-Rehner equation to modify the interaction parameter for the effects of crosslink density (132). 

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