The pH-dependence of the degree of hydrogen-bonding between a base and its conjugate acid is considered. When only a small proportion of the total base is complexed, the amount complexed is proportional to (1+coshp)−1 where p=2.303 (pKa–pH), pKa being the dissociation constant of the conjugate acid. This represents sharp pH-dependence. As the proportion complexed increases, the curve broadens, eventually becoming flat-topped, with more than half the base complexed over the range of pH values pKa±logKC, approximately. (K is the complex association constant and C is the formal base concentration, including all forms.) There are similarities to the extent of mono-protonation of a dibasic acid.
