A 0.10 M solution of the sodium salt NaHA of a diprotic acid H2A (with pK_a1 = 1.90) has a measured pH of 4.00 at 298 K. Assuming the amphiprotic formula applies, K_a2 of H2A is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ia033

A 0.10 M solution of the sodium salt $NaHA$ of a diprotic acid $H X_{2} A$ (with $p K_{a 1} = 1.90$ ) has a measured pH of 4.00 at 298 K. Assuming the amphiprotic formula applies, $K_{a 2}$ of $H X_{2} A$ is

For an amphiprotic anion, pH

= \frac{1}{2} (p K_{a 1} + p K_{a 2})

, so

p K_{a 2} = 2 (4.00) - 1.90 = 6.10

and

K_{a 2} = 1 0^{- 6.10} = 7.9 e - 07