Abstract

It is tempting to “assign” the macroscopic ionization constants (apparent pKa ‘s obtained from titration experiments) of molecules to specific ionizable groups; however, this is strictly appropriate only in the case of monoprotic molecules. An extreme example at the other end of the spectrum is mellitic (benzene hexacarboxylic) acid [1] where the six measured apparent pKa ’s range from 1.4 to 7.0 – a span of 5.6 orders of magnitude. Assigning each apparent pKa to a specific group is clearly absurd in this case, since the six carboxylic acid groups are completely equivalent. This potentially confusing situation is clarified by considering microscopic ionization equilibria, yielding a precise thermodynamic picture, replacing the inaccurate and misleading “one group = one pKa ” paradigm. We have explored microequilibria theory in detail and have developed novel concepts: the pH-dependent Average Single Proton Acidity (ASPA), and the pH-dependent Average Site Protonation profiles (ASP). The ionization midpoint of the latter – the pK50 – is pH-independent and closely related to concepts from the physical chemistry of proteins. We show that the pK50 , unlike macroscopic pKa , is a transferable property of an individual ionizable group, illustrating its inherent acidity in the absence of intergroup interactions. For example, we calculate a chemically realistic pK50 = 3.92 for each carboxyl group in the mellitic acid. In the case of monoprotic molecules as well as molecules with well-separated ionization patterns, the pK50’s correspond to macroscopic pKa ‘s exactly and approximately, respectively. An added bonus is a direct determination of individual site occupancies from the calculated AAPP at any pH of interest, which eliminates the need to deduce these quantities from pKa.

Robert Fraczkiewicz, Marvin Waldman, Robert D. Clark