A 0.1 M solution of a weak monobasic acid has pH 2.85 (10^-2.85 = 1.413x10^-3). Using K_a = [H+]^2/(c - [H+]), find pK_a to two decimals.

JEE Main levelNumerical answerDifficulty 2 of 3ie030

A $0.1 M$ solution of a weak monobasic acid has pH $2.85$ ( $1 0^{- 2.85} = 1.413 \times 1 0^{- 3}$ ). Using $K_{a} = [H X^{+}]^{2} / (c - [H X^{+}])$ , find $p K_{a}$ to two decimals.

Numerical answer type, tolerance 0.02.

[H X^{+}] = 1.413 \times 1 0^{- 3}

, so

K_{a} = (1.413 \times 1 0^{- 3})^{2} / (0.1 - 0.001413) = 2.02 \times 1 0^{- 5}

and

p K_{a} = 4.694 \approx 4.69