Find the pH of 0.1 M of a weak monobasic acid with K_a = 2.0x10^-4. Do not neglect the ionised amount (solve the quadratic). Give two decimals.

JEE Advanced levelNumerical answerDifficulty 3 of 3ie046

Find the pH of $0.1 M$ of a weak monobasic acid with $K_{a} = 2.0 \times 1 0^{- 4}$ . Do not neglect the ionised amount (solve the quadratic). Give two decimals.

Numerical answer type, tolerance 0.01.

x^{2} / (0.1 - x) = 2.0 \times 1 0^{- 4}

gives

x^{2} + 2.0 \times 1 0^{- 4} x - 2.0 \times 1 0^{- 5} = 0

, so

x = 4.37 \times 1 0^{- 3} M

and

pH = 2.359 \approx 2.36

. (The approximation

K_{a} c

would give

2.35