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?
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) 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 +]
[H3O +] = 10 - pH = 10 - 3.53 = 2.95 10 -04 M
We have, pKa1 = - log Ka1
Ka1 = 10 - pKa1 = 10 - 6.37 = 4.26 10 -07
From above values , we can write
4.27 10 -07= (2.95 10 -04 )(2.95 10 -04) / [H2CO3]
[H2CO3] = (2.95 10 -04 )(2.95 10 -04) / 4.26 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 10 -04 ) = 0.204 M
ANSWER : Original concentration of [H2CO3] = 0.204 M
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