The degree of ionisation of 0.1 M acetic acid (K_a = 1.8x10^-5) in a solution that also contains 0.1 M HCl is yx10^-4. Find y to two decimals (assume [H+]approx0.1 M and [HA]approx0.1 M).

JEE Main levelNumerical answerDifficulty 2 of 3ie033

The degree of ionisation of $0.1 M$ acetic acid ( $K_{a} = 1.8 \times 1 0^{- 5}$ ) in a solution that also contains $0.1 M$ $HCl$ is $y \times 1 0^{- 4}$ . Find $y$ to two decimals (assume $[H X^{+}] \approx 0.1 M$ and $[HA] \approx 0.1 M$ ).

Numerical answer type, tolerance 0.02.

[A X^{-}] = K_{a} [HA] / [H X^{+}] = 1.8 \times 1 0^{- 5} \times 0.1/0.1 = 1.8 \times 1 0^{- 5} M

, so

α = 1.8 \times 1 0^{- 5} /0.1 = 1.8 \times 1 0^{- 4}

and

y = 1.80

. This is about

75

times smaller than in pure acetic acid.