$25.0 mL$ of $0.100 M$ diprotic acid $H X_{2} A$ ( $p K_{a 1} = 4.0$ , $p K_{a 2} = 9.0$ ) is titrated with $0.100 M$ NaOH. Treat the two steps as well separated and use Henderson's equation in buffer regions. Which statements are correct?

AAfter $12.5 mL$ of NaOH the pH is 4.0.
BAt the first equivalence point ( $25.0 mL$ ) the pH is 6.5, the mean of the two $p K_{a}$ values.
CAfter $37.5 mL$ of NaOH the pH is 6.5.
DAt the second equivalence point ( $50.0 mL$ ) the pH is 10.76.

Answer: A, B, D

Region 1:

pH = p K_{a 1} = 4.0

12.5 mL

. First equivalence (

HA X^{-}

amphiprotic):

pH = \frac{1}{2} (4.0 + 9.0) = 6.5

. At

37.5 mL

half of

HA X^{-}

is converted to

A X^{2 -}

, so

pH = p K_{a 2} = 9.0

(not 6.5). At

50 mL

[A X^{2 -}] = 2.5/75 = 0.0333 M

pH = 7 + \frac{1}{2} (9.0 + lo g 0.0333) = 10.76