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0.000 0.005 0.010 0.015 0.020 Titrant Volume (mL 0.5M HCl)

Figure 6.7 Dissolution template titration (DTT) curve of propoxyphene: 0.51 mg of the hydrochloride salt was dissolved in 5.1 mL of 0.15 M KCl solution, with 0.0084 mL of 0.5 M KOH used to raise the pH to 10.5.

compound is anticipated to be (based on the template) the longer the assay time. An entire solubility-pH profile is deduced from the assay.

A graphical analysis follows, based on Bjerrum plots (see Sections 3.3.1 and 4.14). The Bjerrum difference plots are probably the most important graphical tools in the initial stages of solution equilibrium analysis in the pH-metric method. The difference curve is a plot of nH, the average number of bound protons (i.e., the hydrogen ion binding capacity), versus pcH (-log [H+ ]). Such a plot can be obtained by subtracting a titration curve containing no sample ("blank" titration) from a titration curve with sample; hence the term ''difference'' curve. Another way of looking at it is as follows. Since it is known how much strong acid [HCl] and strong base [KOH] have been added to the solution at any point and since, it is known how many dissociable protons n the sample substance brings to the solution, the total hydrogen ion concentration in solution is known, regardless of what equilibrium reactions are taking place (model independence). By measuring the pH, and after converting it into pcH [116], the free hydrogen ion concentration is known. The difference between the total and the free concentrations is equal to the concentration of the bound hydrogen ions. The latter concentration divided by that of the sample substance C gives the average number of bound hydrogen ions per molecule of substance nH

where Kw is the ionization constant of water (1.78 x 10—14 at 25°C, 0.15 M ionic strength).

Figure 6.8 shows the Bjerrum plots for an weak acid (benzoic acid, pKa 3.98, log S0 — 1.55, log mol/L [474]), a weak base (benzydamine, pKa 9.26, log S0 —3.83, log mol/L [472]), and an ampholyte (acyclovir, pKa 2.34 and 9.23, log S0 — 2.16, log mol/L [pION]). These plots reveal the pKa and pKapp values as the pcH values at half-integral nH positions. By simple inspection of the dashed curves in Fig. 6.8, the pKa values of the benzoic acid, benzydamine, and acyclovir are 4.0, 9.3, and (2.3, 9.2), respectively. The pKapp values depend on the concentrations used, as is evident in Fig. 6.8. It would not have been possible to deduce the constants by simple inspection of the titration curves (pH vs. volume of titrant, as in Fig. 6.7). The difference between pKa and pKapp can be used to determine log S0, the intrinsic solubility, or log Ksp, the solubility product of the salt, as will be shown below.

In addition to revealing constants, Bjerrum curves are a valuable diagnostic tool that can indicate the presence of chemical impurities and electrode performance problems [165]. Difference curve analysis often provides the needed ''seed'' values for refinement of equilibrium constants by mass-balance-based nonlinear least squares [118].

As can be seen in Fig. 6.8, the presence of precipitate causes the apparent pKa, pKaapp, to shift to higher values for acids and to lower values for bases, and in opposite but equal directions for ampholytes, just as with octanol (Chapter 4) and liposomes (Chapter 5). The intrinsic solubility can be deduced by inspection of the curves and applying the relationship [472]

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