where Si refers to the solubility of the conjugate base of the acid, which depends on the value of [Na+ ] and is hence a conditional constant. Since pH ^ pKa and [Na+] may be assumed to be constant, Eq. (6.9) reduces to that of a horizontal line in Fig. 6.4: log S = log Si for pH > 8.

3. If the pH is exactly at the special point marking the onset of salt precipitation, the equation describing the solubility-pH relationship may be obtained by recognizing that both terms in Eq. 6.3 become constant, so that

Consider the case of a very concentrated solution of the acid hypothetically titrated from low pH (<pKa) to the point where the solubility product is first reached (high pH). At the start, the saturated solution can only have the uncharged species precipitated. As pH is raised past the pKa, the solubility increases, as more of the free acid ionizes and some of the solid HA dissolves, as indicated by the solid curve in Fig. 6.1a. When the solubility reaches the solubility product, at a particular elevated pH, salt starts to precipitate, but at the same time there may be remaining free acid precipitate. The simultaneous presence of the solid free acid and its solid conjugate base invokes the Gibbs phase rule constraint, forcing the pH and the solubility to constancy, as long as the two interconverting solids are present. In the course of the thought-experiment titration, the alkali titrant is used to convert the remaining free acid solid into the solid salt of the conjugate base. During this process, pH is absolutely constant (a ''perfect'' buffer system). This special pH point has been designated the Gibbs pKa, that is, pKgibbs [472,473]. The equilibrium equation associated with this phenomenon is

HA(s) ^ A—(s)+ H+ Kgibbs = [H[+|jA(s))]s)] = [H+] (6.11)

Note that pKgibbs is the conceptual equivalent of pK°ct andpK™™ [(see.Eq. (5.1)]. We should not be surprised that this is a conditional constant, depending on the value of the background salt.

Figure 6.5 Solubility tetrad equilibria. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]

At this point we bring in the now familiar tetrad diagram, Fig. 6.5, and conclude that sdiff (logSI-N) = log Si - log So = |pKgibbs - pKal (6.12)

Figure 6.4 shows a hypothetical solubility-pH profile with sdiff = 4, as typical as one finds with simple acids in the presence of 0.15 M Na+ or K+ [473]. Compare Eq. (6.12) with Eq. (4.6).

In principle, all the curves in Figs. 6.1a, 6.2a, and 6.3a would be expected to have solubility limits imposed by the salt formation. Under conditions of a constant counterion concentration, the effect would be indicated as a point of discontinuity (pKgibbs), followed by a horizontal line of constant solubility S,.

0 0

Post a comment