Thermochemical Investigations of Nearly Ideal Binary Solvents VII: Monomer and Dimer Models for Solubility of Benzoic Acid in Simple Binary and Ternary Solvents zyx WILLIAM E. ACREE, Jr., and GARY L. BERTRANDX Received November 10,1980, from the Department zyxwvutsr of Chemistry, University of Missouri-Rolla, Rolla, zyxwv MO zyxw 65401. March 2, 1981. Accepted for publication Abstract Solubilities are reported for benzoic acid at 25.0" in binary mixtures of carbon tetrachloride with cyclohexane, n-hexane, or n- heptane and of cyclohexane with n-hexane or n-heptane and in ternary mixtures of carbon zyxwvutsrq tetrachloride-cyclohexane-n-hexane and carbon tetrachloride-cyclohexane-n -heptane. Solubilities also are reported for benzoic acid in some binary solvents at 30.0" and for rn-toluic acid in binary mixtures of cyclohexane and n-hexane at 25.0". The results are compared to the predictions of equations developed previously for sol- ubility in systems of purely nonspecific interactions, with the benzoic acids considered as either monomeric or dimeric molecules in solution. The dimer model gave more accurate predictions, with a maximum de- viation of 4.4% between observed and predicted solubilities in all systems studied. Solubility maxima were predicted and observed for benzoic and m-toluic acids in cyclohexane-n-hexane and for benzoic acid in cyclo- hexane-n-heptane. The application of these solubility relationships to liquid-liquid partition coefficients is discussed. Keyphrases zyxwvutsrq 0 Binary solvents-thermochemical study of monomer and dimer models for benzoic acid solubility Benzoic acid-thermochemical study, monomer and dimer models for solubility in simple binary and ternary solvents Solubility-benzoic acid in simple binary and ternary solvents, monomer and dimer models 0 Thermochemistry-monomer and dimer models for solubility of benzoic acid in simple binary and ternary solvents The use of mixed solvents for influencing solubility and multiphase partitioning has great potential application in pharmaceutical research. Maximum realization of this potential depends on the development of equations that predict solubilities or partition coefficients in mixed sol- vents from the properties of the individual components. This study continued the testing (1-4) of applications and limitations of the nearly ideal binary solvent (NIBS) model for predicting solution enthalpies (1,2), solubilities (3), and gas-liquid partition coefficients (4) of solutes in binary solvent mixtures relative to their properties in pure sol- vents. BACKGROUND The NIBS model predicts that any partial molar thermodynamic ex- cess property of a solute at infinite dilution in a binary solvent is a volume fraction average (a weighted mole fraction average gives somewhat better predictions for solution enthalpies) of its properties a t infinite dilution in a pure solvent, with a correction for solvent "unmixing" by the presence of the solute. This model gives good predictions for solute properties in systems of nonspecific interactions, but it fails for systems with specific solvent-solvent or solvent-solute interactions. The solubility equations have been successfully applied to solubilities as high as 0.3 mole fraction (3) for solutes that do not self-associate or form solvent-solute com- plexes. Benzoic acid presents an interesting test for these equations because of its very strong self-association in "inert" solvents, even at high dilution. Calculations with reported dimerization constants in cyclohexane (5), carbon tetrachloride (5,6), and benzene (5,7,8) indicate that <4% of the benzoic acid molecules are monomers at saturation at 25". Thus, this approach should give relatively poor predictions of the solubility of benzoic acid in terms of a monomer model, but it has a reasonable chance of success if a dimer model is used. The dimer model may be an oversimplification, however, since Krishnan et al. (8) presented evidence for trimers of benzoic acid in benzene. The reported equilibrium constants for benzoic acid at satu- ration in benzene at 25" led to estimates that 2.5% of the benzoic acid molecules are monomers, 66% are dimers, and the remainder are trimers. To avoid the complications of trimeric forms, the present study was confined to solvents in which benzoic acid is considerably less soluble than in benzene. During this work, the nearly ideal binary solvent model was found to predict maxima for benzoic acid solubility in mixtures of cyclohexane with n-hexane or n-heptane. Such maxima are usually explained with solubility parameter theory (9) in terms of the solubility parameter of the solute lying between the solubility parameters of the solvents. However, all estimates of the solubility parameters of benzoic acid monomers or dimers give values greater than any of the solvents studied, so these measurements provide a test of the more general applicability of the present approach. Similar predictions for maximum solubility of m-toluic acid also were tested. The equations for solubility in binary solvents were expanded to in- clude ternary solvents. Since these equations require excess free energy data (data that are often not available), an approximation was developed from the original nearly ideal binary solvent model for estimating the excess properties of a multicomponent system from the properties of the contributing binary systems. The resultant equations give good predic- tions for the solubility of benzoic acid in two simple ternary solvents. EXPERIMENTAL Benzoic acid (99%)was dried at 60" for several hours, mp 122.5 f 0.5' [lit. (10) mp 122.4"]. rn-Toluic acid (99%)was recrystallized twice from aqueous ethanol and dried at zyxw 80°, mp 109.5 f 0.5" [lit. (10) mp 111-113'1. The recrystallized acid was titrated to a thymol blue end-point with freshly standardized sodium methoxide solution by the method of Fritz and Lisicki (ll), except toluene was substituted for benzene. The purity of the m-toluic acid was calculated to be 100.1 f 0.5%. Cyclohexane (99+%), n-heptane (99+%), and n-hexane (99%) were stored over mo- lecular sieves (Type 4A) and distilled shortly before use. Carbon tetra- chloride (99+%) was purified by the method of Scatchard et al. (121, stored in contact with mercury under an argon atmosphere, and distilled shortly before use. Solvent mixtures were prepared by weight with sufficient accuracy to allow calculation of compositions to 0.0001 mole fraction. Solvents and excess carboxylic acid were placed in brown glass containers and allowed to equilibrate in a constant-temperature bath at 25.00 f 0.01 or 30.00 f 0.01", maintained constant to f0.002", for several days. The attainment of equilibrium was verified by repetitive measurements after several Table I-Solubilities of Benzoic Acid and m-Toluic Acid in Pure Solvents Solute(s) Solvent Temperature 102 x:*t Benzoic acid C-CKHII cc1; m-Toluic acid c-CgH12 n-C6H14 a Reference 15. Reference 16. 25.0' 30.0" 25.0' 30.0" 25.0" 30.0" 25.0" 30.0" 25.0" 25.0' 1.15 1.46 (1.43a) 1.00 1.26 1.14 1.47 4.92 (4.9gb) 5.98 1.27 1.17 0022-35491 8110900-1033$01.00/0 zyxwvutsrqp @ 198 1, American Pharmaceutical Association Journal of Pharmaceutical Sciences I z 1033 Vol. 70, No. 9, September 1981