Question

Citric Acid (C6H8O7) is a triprotic acid (pKa1=3.13; pKa2=4.76; pKa3=6.40), whose acidic forms and weak conjugate bases are often used as buffers. Describe which forms and what concentrations would be used to design a buffer solution that provides a pH of 6 and that does not allow the pH to change more than 0.4 units when 0.005 M of HCl is added.

Answer 1

Citric acid, C₆H₈O₇ is a triprotic acid and can be denoted as H₃A. The acid dissociations are

H₃A (aq) --------> H⁺ (aq) + H₂A^- (aq); pK_a1 = 3.13

H₂A^- (aq) ----------> H⁺ (aq) + HA^2- (aq); pK_a2 = 4.76

HA^2- (aq) ---------> H⁺ (aq) + A^3- (aq); pK_a3 = 6.40

The pH of the desired buffer solution is 6.0 and the pH must not change by more than 0.4 units when HCl is added. It is common knowledge that HCl lowers the pH of the buffer solution; hence, the pH after the addition of HCl will be (6.0 – 0.4) = 5.6.

The acidic and basic forms of citric acid must be so chosen that the pH of the buffer lies within unit of the pK_a of the buffer; therefore, (pK_a1 – 1) < pH < (pK_a1 + 1). Based on the above argument, it seems that the monoprotic salt of citric acid and the tribasic salt will be the best combination for the buffer, i.e, the buffer system will consist of HA^2-/A^3-.

The ratio of the weak acid and the conjugate base can be obtained from the Henderson-Hasslebach equation as

pH = pK_a3 + log [A^3-]/[HA^2-]

====> 5.60 = 6.40 + log [A^3-]/[HA^2-]

====> -0.80 = log [A^3-]/[HA^2-]

====> [A^3-]/[HA^2-] = antilog (-0.80) = 0.1585 ≈ 0.16

====> [A^3-] = 0.16*[HA^2-] (ans)

We need to know the total buffer concentration to find out the individual concentrations.