Question

State the pH of a solution of a polyprotic weak acid.

Answer 1

Diprotic acid is the one, which is capable of giving 2 protons per molecule in water. Let us take a weak diprotic acid (H₂A) in water whose concentration is c M. In an aqueous solution, following equilbria exist.

If α₁ = degree of ionization of H₂A in presence of HA^– 

Ka₁ = first ionisation constant of H₂A 

α₂ = degree of ionisation of HA^– in presence of H₂A 

Ka₂ = second ionisation constant of H₂A

I step:

II step

Knowing the values of Ka₁ , Ka₂ and c, the values of α₁ and α₂ can be calculated using equations (i) and (ii) After getting the values of α₁ and α₂, [H₃O⁺ ] can be calculated as

Finally, for calculation of pH

If the total [H₃O⁺] < 10^–6 M, the contribution of H₃O⁺ from water should be added. 

If the total [H₃O⁺] > 10^–6 M, then [H₃O⁺] contribution from water can be ignored. Using this [H₃O⁺], pH of the solution can be calculated. 

Approximation : 

For diprotic acids, Ka₂ << Ka₁ and α₂ would be even smaller than α₁. 

Thus, equation (i) can be reduced to 

This is expression similar to the expression for a weak monoprotic acid.

Hence, for a diprotic acid (or a polyprotic acid) the [H₃O⁺] can be calculated from its first equilibrium constant expression alone provided K_a2 << K_a1