Strategy for the Prediction and Selection of Drug Substance Salt Forms - Pharmaceutical Technology

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Strategy for the Prediction and Selection of Drug Substance Salt Forms
Through consideration of the ionic equilibria of acids and bases, one may readily calculate the formation constant of a salt species solely on the basis of knowledge of the pKA value of the acid and the pKB value of the base.

Pharmaceutical Technology

then Equation 22 becomes:

When converted to the Sørensen scale, Equation 23 becomes:

Equation 25 can be used to make rapid deductions regarding the strength of a particular salt species. Suppose one were contemplating forming a salt between an acid having a pK A value of 4.79 and a base having a pK A value of 9.45. For the base, it would follow that the pK B would equal 4.55, and because pK W = 14.0 at 25 °C, the pK S of the salt would equal -4.66, and that K S would equal approximately 45,710 . A reaction characterized by an equilibrium constant of this magnitude would clearly go to completion, and one would predict that the salt in question would be formed without difficulty.

The ability to calculate K S enables one to estimate the relative position of the equilibrium described by Equation 16. Consider the solution prepared by mixing an acid at an initial concentration of C HA with a base at an initial concentration of C B . For a salt form having a 1:1 stoichiometry, the concentrations of conjugate acid and conjugate base formed in the reaction would necessarily be equal. If the resulting ionic concentrations are represented by X, then the concentration of residual acid would equal (C HAX) and the concentration of residual base would equal (C B X). Equation 24 would then have the form:

Because obtaining the solution of Equation 26 by means of the quadratic equation is trivial, the degree of formation of a salt through the mixing of equimolar amounts of acid and base (i.e., C HA = C B ) can be easily calculated. For example, if log(K S ) = 2, it follows that X = 0.9091, indicating that equation 16 would proceed 90.91% to completion. Similarly, if log(K S ) = 3, then X = 0.9693 and the efficiency of salt formation would be 96.93%. If log(K S ) = 4, the salt would be 99.01% formed, and if log(K S ) = 5, then the salt would be 99.68% formed. It is often stated in the literature that if the ionization constants of the acid and base involved in salt formation differ by 2 or 3 pK units, then the salt would be formed. Use of the log(K S ) quantity serves to place the old empirical rule on a more fundamental basis and facilitates calculation of the actual percentage of salt formation.

Knowledge of the log(K S ) quantity also permits one to deduce the degree of disproportionation that would be anticipated if one were to dissolve a salt in pure water. If the X factor of Equation 26 represents the fraction of salt being formed by the reaction of the acid and base, then it follows that the fraction of salt that would disproportionate would necessarily be given by (1–X), and its percentage as 100 times that quantity.


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