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-1 + HA(s),Na A (s) -2 + Na A (s)
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Figure 64 Solubility pH pro le of a weak acid, with salt precipitation taken into account [Avdeef, A, Curr Topics Med Chem, 1, 277 351 (2001) Reproduced with permission from Bentham Science Publishers, Ltd]
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increases Although precipitation of salts is not covered in detail in this chapter, it is nevertheless worthwhile to consider its formation in this limiting sense As the pH change raises the solubility, at some value of pH the solubility product of the salt will be reached, causing the shape of the solubility pH curve to change from that in Fig 61a to that in Fig 64, an example of a weak acid exhibiting salt precipitation As a new rule of thumb [473], in 015 M NaCl (or KCl) solutions titrated with NaOH (or KOH), acids start to precipitate as salts above log S=S0 % 4 and bases above log S=S0 % 3 It is exactly analogous to the diff 3 4 rule; let us call the solubility equivalent the sdiff 3 4 rule [473] Consider the case of the monoprotic acid HA, which forms the sodium salt (in saline solutions) when the solubility product K sp is exceeded In additions to Eqs (31) and (61), one needs to add the following reaction/equation to treat the case: Na A s ! Na A Ksp Na A Na A Na A s 6:8
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Effective solubility is still de ned by Eq (63) However, Eq (63) is now solved under three limiting conditions with reference to a special pH value: 1 If the solution pH is below the conditions leading to salt formation, the solubility pH curve has the shape described by Eq (64) (curve in Fig 61a) 2 If pH is above the characteristic value where salt starts to form (given high enough a sample concentration), Eq (63) is solved differently Under
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this circumstance, [A ] becomes the constant term and [HA] becomes variable H A S A Ka   H A 1 Ka Ksp 1 10 pKa pH Na Si 1 10 pKa pH 6:9
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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 (69) reduces to that of a horizontal line in Fig 64: 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 63 become constant, so that S S0 Si 6:10
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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 rst 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 61a 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 desiggibbs nated the Gibbs pKa , that is, pKa [472,473] The equilibrium equation associated with this phenomenon is HA s ! A s H H A s H HA s
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