Disproportionation of Pharmaceutical Salts: pH_max and Phase-Solubility/pH Variance

A multiphasic mass action equilibrium model is used to show that the critical pH in the acid-base disproportionation of a solid salt into its corresponding solid free-base form in aqueous suspensions, widely known as "pH_max", is incompletely interpreted. It is shown that the traditional thermodynamic model does not predict the invariance of pH and solubility during the salt-to-free-base conversion process in an alkalimetric titration. Rather, the conversion entails a range of pH and solubility values, depending on the amount of added excess salt above that needed to form a saturated solution. A more precise definition is proposed for pH_max (pH at the maximum solubility of a eutectic mixture), and three new terms are introduced: pH_min (pH at the minimum solubility of the eutectic mixture), pH_δ (disproportionation invariant pH within the eutectic, i.e., the equilibrium pH of a spontaneously disproportionating salt slurry), and pH_γ (Gibbs pH at which disproportionation yields equimolar amounts of excess salt and excess free-base solids within the eutectic). Two test compounds with reported multiple salts and the free-base solubility values were selected to illustrate the expanded concepts, the bases WR-122455 and RPR-127963. Also, dibasic calcium phosphate was selected as an ionizable test excipient. The salts are designated in the study as μ-type, when they are thermodynamically stable with respect to spontaneous disproportionation in pure water (e.g., WR-122455 salts), and δ-type, when they are predicted to spontaneously disproportionate in pure water (e.g., RPR-127963 salts). In an alkalimetric titration, when an acidified suspension of a salt of a basic molecule is titrated with a strong base (e.g., NaOH), the passage across the eutectic domain (bounded by pH_max and pH_min) is often characterized by (a) minimum in ionic strength either at pH_max (μ-type salt) or pH_δ (δ-type salt) and (b) maximum buffer capacity at pH_γ. When the alkalimetric titration is performed with a large excess of added salt, a wide eutectic domain forms: pH_max and pH_δ remain invariant, but pH_min and pH_γ shift substantially in pH. The acid-base mass action model described here can be useful in predicting the stability of salt formulations in mixtures with excipients that can act as pH modifiers.