The dissociation constant of acetic is $\mathrm{x} \times 10^{-5}$. When 25 mL of $0.2 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa}$ solution is mixed with 25 mL of $0.02 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}$ solution, the pH of the resultant solution is found to be equal to 5. The value of $x$ is ______.

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Equilibrium

The dissociation constant of acetic is

x \times 1 0^{- 5}

. When 25 mL of

0.2 M CH_{3} COONa

solution is mixed with 25 mL of

0.02 M CH_{3} COOH

solution, the pH of the resultant solution is found to be equal to 5. The value of

x

is ______.

Answer: 10

Mixing the acetate salt with acetic acid makes an acidic buffer. In the combined

50 mL

the acetate concentration is

\frac{0.2 \times 25}{50} = 0.1 M

and the acid concentration is

\frac{0.02 \times 25}{50} = 0.01 M

. The Henderson–Hasselbalch relation

pH = p K_{a} + lo g \frac{[ salt ]}{[ acid ]}

gives

5 = p K_{a} + lo g \frac{0.1}{0.01} = p K_{a} + 1

, so

p K_{a} = 4

. Hence

K_{a} = 1 0^{- 4} = 10 \times 1 0^{- 5}

, and the value of

x

10

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Integer answer