Margules Equations Applied to PAH Solubilities in Alcohol−Water Mixtures

Solubilities of phenanthrene, pyrene, and perylene were determined in aqueous solutions containing either methanol, ethanol, or propanol at alcohol volume fractions ranging from zero to nearly 1, at 25 °C and atmospheric pressure. These data, and data from the literature on naphthalene were compared to various forms of two- and three-suffix Margules equations and UNIFAC predictions. For each solute−solvent−cosolvent ( i.e ., PAH−water−alcohol) system examined, the solubility ( S ) of each PAH increased with increasing alcohol volume fraction ( v 3 ). The UNIFAC model poorly estimated solubilities at cosolvent volume fractions near 0.5. Analysis of the data with various forms of the Margules equations shows that, in addition to solute−solvent and solute−cosolvent interaction terms, inclusion of solvent−cosolvent ( i.e., water−alcohol) and solute−solvent−cosolvent interaction terms in the model improves predic tions, particularly at cosolvent volume fractions near 0.5. A simplified three-suffix Margules model is proposed, which includes terms for all these interactions and accurately estimates the experimental data with a consistent set of interaction parameters. All sets of interaction parameters involving solute molecules were regressed against each solute's respective log octanol−water partition coefficient, K ow . Solubilities of other PAH compounds in similar alcohol−water mixtures, obtained from the liturature, were estimated accurately with these relationships and knowledge of each solute's K ow value and enthalpy of fusion.