Calculate the ratio of the molarities of HPO2− 4 and H2PO− 4 ions required to achieve buffering at pH = 7.00. For H3PO4, pKa1 = 2.12, pKa2 = 7.21, and pKa3 = 12.68.

The ratio of molarities required for a buffer of pH = 7.00 is 0.617

Explanation:

For the equilibrium:

H₂PO₄⁻ ⇄ HPO₄²⁻ + H⁺; pka = 7.21

It is possible to use Henderson-Hasselbalch equation:

pH = pka + log₁₀ [A⁻] / [HA]

Where A⁻ is conjugate base (HPO₄²⁻) of weak acid (H₂PO₄⁻).

Replacing:

7.00 = 7.21 log₁₀ [HPO₄²⁻] / [H₂PO₄⁻]

-0.21 =  log₁₀ [HPO₄²⁻] / [H₂PO₄⁻]

0.617 = [HPO₄²⁻] / [H₂PO₄⁻]

That means the ratio of molarities required for a buffer of pH = 7.00 is 0.617

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