Q39 / 180 · COMEDK 2025 (10 May Shift 2) · Chemistry

The ionisation constant of the weak acid HF whose concentration is $0.1\text{ M}$ is $3.5 \times 10^{-4}$. The Equilibrium constant value for the reaction $\text{F}^- + \text{H}_2\text{O} \rightleftharpoons \text{HF} + \text{OH}^-$ is _____ and the pH of aqueous solution of the weak acid is _____.

  • A
    $\mathrm{K}_{\mathrm{eq}}=3.58 \times 10^{-11} ~\&~ \mathrm{pH}=4.19$
  • B
    $\mathrm{K}_{\mathrm{eq}}=3.92 \times 10^{-10} ~\&~ \mathrm{pH}=4.07$
  • Correct answer
    C
    $\mathrm{K}_{\mathrm{eq}}=2.86 \times 10^{-11} ~\&~ \mathrm{pH}=2.23$
  • D
    $\mathrm{K}_{\mathrm{eq}}=4.4 \times 10^{-11} ~\&~ \mathrm{pH}=4.25$

Solution

The reaction $F^- + H_2O \rightleftharpoons HF + OH^-$ is hydrolysis of the conjugate base, so $K_{eq} = K_b = \dfrac{K_w}{K_a}$:

$K_{eq} = \dfrac{1.0 \times 10^{-14}}{3.5 \times 10^{-4}} \approx 2.86 \times 10^{-11}$

For pH, using $[H^+] \approx \sqrt{K_a \cdot C}$:

$[H^+] = \sqrt{3.5 \times 10^{-4} \times 0.1} = \sqrt{3.5 \times 10^{-5}} \approx 5.92 \times 10^{-3}$ M

$pH = -\log(5.92 \times 10^{-3}) \approx 2.23$

Hence, the correct answer is option: 'C'.

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