Salt Solubility and Disproportionation - Uses and Limitations of Equations for pHmax and the In-silico Prediction of pHmax

Abstract

A multiphasic mass action equilibrium model was used to study the phase properties near the critical pH ('pH_max') in an acid-base transformation of a solid drug salt into its corresponding solid free base form in pure water slurries. The goal of this study was to better define the characteristics of disproportionation of pharmaceutical salts, objectively (i) to classify salts as μ-type (microclimate stable) or δ-type (disproportionation prone) based on the relationship between the calculated pH_max and the calculated pH of the saturated salt solution, (ii) to compare the distribution of μ/δ-type salts to predictions from the disproportionation potential equation introduced by Merritt et al.,²⁰ (iii) to determine if the intrinsic solubility of the free base, S₀, can be predicted from the measured μ-type salt solubility as a means of estimating the value of pH_max, (iv) to determine S₀ directly from the measured δ-type salt solubility, and (v) to address some of the limitations of the equations commonly used to calculate pH_max. When the salt solubility is measured for a basic API (pK_a of which is known), but the experimental value of S₀ is unavailable, a potentially useful simple screen for disproportionation is still possible, since pH_max can be estimated from a 'μ-predicted' (objective iii) or 'δ-measured' S₀ (objective iv). Twelve model weak base API were selected in the study. For each API, 2-17 different salt forms with reported salt solubilities in distilled water were sourced from the literature. In all, 73 salt solubility values based on 29 different salt-forming acids comprise the studied set. All the corresponding free base solubility values were available. The pK_a values for all the acids and bases studied are generally well known. For each API salt, an acid-base titration simulation was performed, anchored to the measured salt solubility value, using the general mass action analysis program pDISOL-X. The log S-pH profiles were drawn out by analytic continuity from pH 0 to 13, as described in detail previously.²⁴ Potentially useful in-silico models were developed that correlate pS₀ to linear functions of the salt solubility in water, pS_w, the partition coefficient of the salt-forming acid (log P_OCT^acid) and the melting point (mp) of the drug salt, thereby enabling the derivation of the approximate pH_max value from the predicted pS₀.

Keywords: Disproportionation pH; Eutectic mixture; Gibbs pH; Mass action model; Multiphasic equilibria; Salt disproportionation; Solubility product; Solubility-pH; pH(max); pH(min).