Solute pKa, Solvent pH, and Solubility

According to the Henderson-Hasselbach equation, the relationship between pH, pKa, and relative concentrations of an acid and its salt is as follows:

where [A^-] is the molar concentration of the salt (dissociated species) and [HA] is the concentration of the undissociated acid. When the concentrations of salt and acid are equal, the pH of the system equals the pKa of the acid. As the pH decreases, the concentration of the molecular acid increases and that of the salt decreases. This has some interesting implications regarding the aqueous solubility of the acid, since the undissociated form is much less soluble than its salt. Of further interest, therapeutically, is the fact that it is the undissociated acid (HA) that more readily penetrates biological tissues to exert a therapeutic effect. Thus, in formulating the product, some balance must be struck between the more soluble salt form and the biologically active acid and factors other than pKa and pH must be considered (e.g. safety and comfort).

Changes in solubility brought about by alterations of solvent pH can be predicted by the pHp equation. The pHp is the pH below which an acid or above which a base will begin to precipitate.

where,

• S_o = the molar solubility of the undissociated acid or base
• S = the molar concentration of the salt form of the drug initially added

e.g. Calculate the pHp of a 1% sodium phenobarbital solution.

From Merck Index:

• MW phenobarbital = 232.32
• solubility phenobarbital= 1 g/L;
• phenobarbital Ka = 3.9 x 10^-8; pKa = 7.4
• MW phenobarbital sodium = 254.22

S_o = molar solubility of phenobarbital = 1 g/L x 1 mole/232.32 g = 0.0043 moles/L or M

S = 1 g/100 ml x 1000 ml/L x 1 mole/254.22 g = 0.0393 moles/L or M

(i.e. 1% phenobarbital will precipitate at or below a pH of 8.3)