Question

Suppose you perform a titration of a diprotic acid and you determine the following information: pH at first equivalence point: 4.36 pH at second equivalence point: 8.72 pH at first half-equivalence point: 2.61 pH at second half-equivalence point: 6.09 What is pKa2 for this unknown acid?

Answer 1

Explanation:

It is known that in titration of diprotic acid, pH of the half equivalence points represents $pk_{a}'s$ of acid.

Therefore, $pk_{a_{2}}$ = pH of the second half equivalence point = 6.09

Hence, during the titration of a diiprotic acid ($H_{2}A$) with strong base, the following dissociation take place.

     $H_{2}A = H^{+} + HA^{-}$ ( first equivalence point)

    $HA^{-} = H^{+} + A^{2-}$ (second equivalence point)

The $pk_{a_{2}}$ of diprotic acid will be calculated as follows.

           pH = $pka_{2} + log \frac{[A^{2-}]}{[HA^{-}]}$

Now, at half equivalence point,

         $[HA^{-}] = [A^{2-}]$

Therefore,

        pH = $pka_{2} + log 1$

           pH = $pka_{2}$

Thus, we can conclude that $pka_{2}$ for this unknown acid is equal to its pH.