Solute-solvent interactions mole fractional solubility

When the only effects that have to be taken into account are those of cavity formation in the solvent and the dispersion interactions, i.e., when both the solvent and the solute are non-polar, then Hildebrand s solubility parameter concept (Hildebrand and Scott 1950) provides good estimates of the solubility. The mole fraction of a gaseous solute, x2, in a solution in equilibrium at a partial pressure p2 of this gas, can be estimated from the following expression ... 

It is known from physical chemistry that the equilibrium vapour pressure is smaller over solutions than over pure water. In the case of ideal solutions this vapour pressure decrease is proportional to x0, the mole fraction of the solvent (Raoult s law). If the solution is real, the interaction of solvent and solute molecules cannot be neglected. For this reason a correction factor has to be applied to calculate the vapour pressure lowering. This correction factor is the so-called osmotic coefficient of water (g ). We also have to take into account that the soluble substance dissociates into ions, forming an electrolyte. 

FIGURE 10.5 Comparison between experimental (o) and calculated (solid lines) solubilities of paracetamol (S is the mole fraction of paracetamol) in the mixed solvent water/ethanol is the mole fraction of ethanol) at room temperature. The solubility was calculated using Equation 10.29. 1-activity coefficients expressed via the Flory-Huggins equation, 2-activity coefficients expressed via the Wilson equation. (From S. Romero, A. Reillo, B. Escalera, and P. Bustamante, 1996, The Behavior of Paracetamol in Mixtures of Amphiprotic and Amphiprotic-Aprotic Solvents. Relationship of Solubility Curves to Specific and Nonspecific Interactions, Chemical and Pharmaceutical Bulletin, 44, 1061. Reprinted from E. Ruckenstein, and I. L. Shulgin, 2003c, Solubility of Drugs in Aqueous Solutions. Part 2 Binary Nonideal Mixed Solvent, International Journal of Pharmaceutics, 260, 283, With permission from Elsevier.)... 

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