It can be shown that the buffer capacity is where c T is the molar analytical concentration

Question:

It can be shown that the buffer capacity is

where c_T is the molar analytical concentration of the buffer.
(a) Show that

(b) Use the equation in (a) to explain the shape of Figure 7-10.
(c) Differentiate the equation presented at the beginning of the problem, and show that the buffer capacity is at a maximum when ∝₀ = ∝1 = 0.5.
(d) Describe the conditions under which these relationships apply.
(e) Buffer capacity is sometime called inverse slope. Explain the origin of this term.