Question

Phosphoric acid has pK_a values 2.14, 6.86, and 12.4. In human blood, a typical total phosphate concentration is 1.05 mmol L^-1 and the pH is 7.40. Calculate the concentration (in mmol L^-1) of the dominant form of phosphoric acid under these conditions.

Answer 1

H3PO4+H2O⇌H2PO4⁻+H3O⁺, pKa1=2.14
H2PO4⁻+H2O⇌HPO4²⁻+H3O⁺, pKa2=6.86
HPO4²⁻+H2O⇌PO4³⁻+H3O⁺, pKa3=12.4

Because the pH of blood lies between pKa2 and pKa3, the dominant form of the acid will be HPO4²⁻. Because pKa2 and pKa3 vary by more than 4 units, the concentration of PO4³⁻ will be negligible.

So, you know that the total phosphate concentration is 1.05 mmol/L. This means that

[H2PO4⁻]+[HPO4²⁻]=1.05mmol/L (assuming [PO4³⁻] is negligible). (1)

Since you're dealing with a buffer, the Henderson-Hasselbalch equation can be used

[pH]=pKa2+log([HPO4²⁻]/[H2PO4⁻])

7.40=6.86+log([HPO4²⁻]/[H2PO4⁻])⇒[HPO4²⁻]/[H2PO4⁻]=3.47

Plug this value into (1) and you'll get

[HPO4²⁻]/3.47+[HPO4²⁻]=1.05, which will result in

[HPO4²⁻]=0.815 mmol/L

The concentration of H2PO4⁻will be [H2PO4⁻]=0.234 mmol/L.

The dominant form of the phosphoric acid is HPO4²⁻ and its concentration is 0.815 mmol/L.