where C is the sample concentration. To simplify Eq. (6.15), Fig. 6.9 shows characteristic Bjerrum plots taken at 2M concentration of an acid (ketoprofen, log S0 — 3.33 [473]), a base (propranolol, log S0 — 3.62 [473]), and an ampholyte (enalapril maleate, log S0 — 1.36 [474]). In Fig. 6.9, all examples are illustrated with C = 2 M, so that the difference between true pKa and the apparent pKa is directly read off as the log S0 value.

In an ideally designed experiment, only a single titration is needed to determine the solubility constant and the aqueous pKa. This is possible when the amount of sample, such as a weak base, added to solution is such that from the start of an alkalimetric titration (pH ^ pKa) to the midbuffer region (pH = pKa) the compound stays in solution, but from that point to the end of titration (pH ^ pKa), precipitation occurs. (The idea is similar to that described by Seiler [250] for log P determinations by titration.) After each titrant addition, pH is measured. The curve represented by unfilled circles in Fig. 6.8b is an example of such a titration of a weak base whose pKa is 9.3, with precipitation occurring above pH 9.3, with onset indicated by the ''kink'' in the curve at that pH. In practice, it is difficult to know a pr/or/ how much compound to use in order to effect such a special condition. So, two or more titrations may be required, covering a probable range of concentrations, nH

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