## S

Figure 6.1a shows a plot of log S versus pH for the weak-acid case (indomethacin, pKa 4.42, log S0 — 5.58, log mol/L [pION]) and Fig. 6.2a shows that of a weak base (miconazole, pKa 6.07, log S0 — 5.85 [pION]). As is evident from the acid curve, for pH < pKa [i.e., 10—pKa+pH < 1 in Eq. (6.4)], the function reduces to the horizontal line log S = log S0. For pH > pKa (i.e., 10—pK"+pH > 1), log S is a straight line as a function of pH, exhibiting a slope of +1. The base shows a slope of — 1. The pH at which the slope is half-integral equals the pKa. Note the mirror relationship between the curve for an acid (Fig. 6.1a) and the curve for a base (Fig. 6.2a).

6.1.2 Diprotic Ampholyte, XH+

In a saturated solution, the three relevant equilibria for the case of a diprotic ampho-lyte are Eqs. (3.3) and (3.4), plus

Note that [XH(s)] by convention is defined as unity. For such a case, effective solubility is

where [HX] is a constant (intrinsic solubility) but [X—] and [XH+] are variables. As before, the next step involves conversions of all variables into expressions containing only constants and pH:

S = S0(1 + 10—pK"2 +pH + 10+pK"1—pH) (6.7)

Figure 6.3a shows the plot of log S versus pH of an ampholyte (ciprofloxacin, pKa values 8.62 and 6.16, log S0 — 3.72 [pION]). In Figs. 6.1b, 6.2b, and 6.3b are the log-log speciation profiles, analogous to those shown in Figs. 4.2b, 4.3b, and 4.4b. Note the discontinuities shown for the solubility speciation curves. These are the transition points between a solution containing some precipitate and a solution where the sample is completely dissolved. These log-log solubility curves are important components of the absorption model described in Section 2.1 and illustrated in Fig. 2.2.

### 6.1.3 Gibbs pKa

Although Figs. 6.1a, 6.2a, and 6.3a properly convey the shapes of solubility-pH curves in saturated solutions of uncharged species, the indefinite ascendency (dotted line) in the plots can be misleading. It is not possible to maintain saturated solutions over 10 orders of magnitude in concentration! At some point long before the solubilities reach such high values, salts will precipitate, limiting further

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