Dibasic & Tribasic pH Titration Quiz Hints

Dibasic & Tribasic pH Titration

Model reactions: HAH <=> HA^- + H⁺ <=> A^2- + H⁺
Acid dissociation constants:: K_a1 = [HA^-][H⁺]/[HAH]; K_a2 = [A^2-][H⁺]/[HA^-]

The Henderson-Hasselbalch equation is:
pH = pK_a1 + log([HA^-]/[ HAH]), where: pH = the measured pH, (-log[H⁺]);; pK_a1 = -logK_a1;; [HAH] = the concentration of the (dibasic) acid, and; [HA^-] = the concentration of the conjugate base.
(The second dissociation is described by analogous equations.)

The titration of 100 mL of carbonic acid with 1.0 M NaOH is shown below. You are asked to determine
1) the concentration of the acid and
2) the pK_a's.

1a) The first equivalence point is approached as mol NaOH approaches the mol carbonic acid in solution (10 mL NaOH = 10 mmol).
Therefore, the acid concentration, [Acid] = 10 mmol/0.10 L = 0.10 M.
1b) The second equivalence point is approached as mol NaOH approaches 2*mol carbonic acid in solution (20 mL NaOH = 20 mmol).
Therefore, the acid concentration, [Acid] = 20 mmol/2*0.10 L = 0.10 M.
2a) At half the volume of added NaOH required to titrate the acid to the first equivalence point (5.0 mL above), [HAH] = [HA^-], and pH = pK_a1 = 6.4.
2b) At 1.5 times the volume of added NaOH required to titrate the acid to the first equivalence point (15.0 mL above), [HA^-] = [A^-2], and pH = pK_a2 = 10.2.

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