Question

What methods and calculations are used in order to obtain the pH of a system with changing dynamics? Please include a mathematical example to accompany each case and solve at pH 3, 7 and 10.

a) Addition of weak base to weak acid

b) Addition of strong base to weak acid

c) Addition of weak base to strong acid

d) Addition of strong base to strong acid

Answer 1

From the titration curve of protonatable group, one can read the so-called pK_a^1/2 which is equal to the pH value where the group is half-protonated. The pK_a^1/2 is equal to the Henderson-Hasselbalch pKa pK_a^HH if the titration curve follows the Henderson-Hasselbalch equation.^[9] Most pKa calculation methods silently assume that all titration curves are Henderson-Hasselbalch shaped, and pKa values in pKa calculation programs are therefore often determined in this way. In the general case of multiple interacting protonatable sites, the pK_a^1/2 value is not thermodynamically meaningful. In contrast, the Henderson-Hasselbalch pKa value can be computed from the protonation free energy via

and is thus in turn related to the protonation free energy of the site via

The protonation free energy can in principle be computed from the protonation probability of the group <x>(pH) which can be read from its titration curve