Challenge Problem: It can be shown9 that the buffer capacity iswhere cT is the molar analy...

Challenge Problem: It can be shown9 that the buffer capacity is

where cT is the molar analytical concentration of the buffer.

(a) Show that

ᵦ = 2.303([ OH-] + [ H3O+] + cT⍺0⍺1)

(b) Use the equation in (a) to explain the shape of Figure.

(c) Differentiate the equation presented at the beginning of the problem and show that the buffer capacity is at a maximum when a0 = a1 = 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.

Figure Buffer capacity as a function of the logarithm of the ratio cNaA/cHA. The maximum buffer capacity occurs when the concentration of acid and conjugate base are equal, that is, when a0 5 a1 5 0.5.