pH-metric log P. II: Refinement of partition coefficients and ionization constants of multiprotic substances

A generalized, weighted, nonlinear least squares procedure is developed, based on pH titration data, for the refinement of octanol-water partition coefficients (log P) and ionization constants (pKa) of multiprotic substances. Ion-pair partition reactions, self-association reactions forming oligomers, and formations of mixed-substance complexes can be treated with this procedure. The procedure allows for CO2 corrections in instances where the base titrant may have CO2 as an impurity. Optionally, the substance purity and the titrant strength may be treated as adjustable parameters. The partial differentiation in the Gauss-Newton refinement procedure is based on newly derived analytical expressions. The new procedure was experimentally demonstrated with benzoic acid, 1-benzylimidazole, (+/-)-propranolol, and mellitic acid (benzenehexacarboxylic acid, AH6). Ionic strength (l) was adjusted with KNO3. Benzoic acid (20 degrees C; l 0.1 M): pKa = 3.99 +/- 0.02, log P = 1.96 +/- 0.02, log P (anion) = -1.2; 1-benzylimidazole (25 degrees C; l 0.1 M): pKa = 6.70 +/- 0.03, log P = 1.60 +/- 0.04; propranolol (25 degrees C; l 0.1 M): pKa = 9.53 +/- 0.06, log P = 3.35 +/- 0.03, log P (cation) = 0.62 +/- 0.08; mellitic acid (26 degrees C; l 0.2 M): pKas 1.10 +/- 0.46, 1.69 +/- 0.03, 2.75 +/- 0.02, 4.00 +/- 0.02, 5.05 +/- 0.01, and 6.04 +/- 0.02; in the presence of 0.01 M n-Bu4NBr, log P (AH6) = 1.5, log P (AH5-) = 1.1, log P (AH4(2-)) = 0.8, log P (AH3(3-)) = 0.3, log P (AH2(4-)) = -0.1, and log P (AH5-) = -0.5 (all +/- 0.1).(ABSTRACT TRUNCATED AT 250 WORDS)