Question

Phosphoric acid is a triprotic acid (K_a1=6.9x10^-8, K_a2 = 6.2x10^-8, and K_a3=4.8x10^-13). To find the pH of a buffer composed of H₂PO₄^- (aq) and HPO₄^2-(aq), which pk_a value would you use in the Henderson-Hasselbalch equation? Calculate the pH of a buffer solution obtained by dissolving 22.0 g of KH2PO4 and 32.0 g of Na2HPO4 in water and then diluting to 1.00 L

Answer 1

Answer – Given, H₃PO₄ acid and there are three Ka values

K_a1=6.9x10^-8, K_a2 = 6.2x10^-8, and K_a3=4.8x10^-13

The transformation of H₂PO₄^- (aq) to HPO₄^2-(aq) is the second dissociation, so we need to use the K_a2 = 6.2x10^-8 in the Henderson-Hasselbalch equation.

Mass of KH₂PO₄ = 22.0 g , mass of Na₂HPO₄ = 32.0 g , volume = 1.00 L

First we need to calculate moles of each

Moles of KH₂PO₄ = 22.0 g / 136.08 g.mol^-1

                              = 0.162 moles

Moles of Na₂HPO₄ = 32.0 g /141.96 g.mol^-1

                              = 0.225 moles

[H₂PO₄^-] = 0.162 moles / 1.00 L = 0.162 M

[HPO₄^2-] = 0.225 moles / 1.00 L = 0.225 M

Now we need to calculate the pK_a2

pK_a2 = -log K_a

        = -log 6.2x10^-8

        = 7.21

We know Henderson-Hasselbalch equation

pH = pKa + log [conjugate base] / [acid]

pH = 7.21 + log 0.225 / 0.162

      = 7.35

The pH of a buffer solution obtained by dissolving 22.0 g of KH2PO4 and 32.0 g of Na2HPO4 in water and then diluting to 1.00 L is 7.35