The question is attached.
Starting with equation (8.5) show that the maximum buffer capacity occur at pH=pKa.
The units of buffer capacity are mol L^-1. As a consequence of the definitions, buffer capacity is always a positive quantity. For a monoprotic acid the buffer capacity (as a function of pH) is given by: (see attachment).
The buffer capacity depends n both the pH of the buffer and the concentrations of the components of the buffer.© BrainMass Inc. brainmass.com October 9, 2019, 8:27 pm ad1c9bdddf
It shows that the maximum buffer capacity occur at pH=pKa.