10 mL of 0.1 M HA (K_a = 1.0x10^-5) is diluted to 1.0 L. Using K_a = (calpha^2)/(1-alpha) (do not assume alpha ll 1), the percentage ionisation of HA in the diluted solution is closest to

JEE Advanced levelSingle correct optionDifficulty 3 of 3ie051

$10 mL$ of $0.1 M$ HA ( $K_{a} = 1.0 \times 1 0^{- 5}$ ) is diluted to $1.0 L$ . Using $K_{a} = \frac{c α ^{2}}{1 - α}$ (do not assume $α ≪ 1$ ), the percentage ionisation of HA in the diluted solution is closest to

After dilution

c = 1 0^{- 3} M

c α^{2} + K_{a} α - K_{a} = 0

gives

α = 0.0951

, i.e.

9.5%

. The approximation

K_{a} / c = 0.10

overestimates it.