Question

A solution of carbonic acid had a PH of 3.53. The pKa's for this acid are 6.37 and 10.25. What was the initial concentration of the solution?

Answer 1

pH of H₂CO₃ solution is less than pKa1= 6.37 . Hence, major species at pH = 3.53 will be acidic form i e H₂CO₃.

Consider a reaction, H₂CO₃ (aq) + H₂O (l) $\rightleftharpoons$ H₃O ⁺ (aq) + HCO ₃^- (aq)

For above reaction, Ka1 = [H₃O ⁺] [HCO ₃^-] / [H₂CO₃]

Where, Concentrations of H₂CO₃ , H₃O ⁺ and HCO ₃^- are equilibrium concentrations.

We can calculate equilibrium [H₃O ⁺] from pH.

We have , pH = - log [H₃O ⁺]

$\therefore$ [H₃O ⁺] = 10 ^{- pH} = 10 ^{- 3.53} = 2.95 $\times$ 10 ^-04 M

We have, pKa1 = - log Ka1

$\therefore$ Ka1 = 10 ^{- pKa1} = 10 ^{- 6.37} = 4.26 $\times$ 10 ^-07

From above values , we can write

4.27 $\times$ 10 ^-07= (2.95 $\times$ 10 ^-04 )(2.95 $\times$ 10 ^-04) / [H₂CO₃]

[H₂CO₃] = (2.95 $\times$ 10 ^-04 )(2.95 $\times$ 10 ^-04) / 4.26 $\times$ 10 ^-07 = 0.2038 M

i e Equilibrium [H₂CO₃] = 0.2038 M = Original concentration of [H₂CO₃] - concentration of dissociated [H₂CO₃]

= Original concentration of [H₂CO₃] - [H₃O ⁺]

Original concentration of [H₂CO₃] = Equilibrium [H₂CO₃] + [H₃O ⁺] = 0.2038 + (2.95 $\times$ 10 ^-04 ) = 0.204 M

ANSWER : Original concentration of [H₂CO₃] = 0.204 M