The pH of an aqueous solution containing 1 M benzoic acid $\left(\mathrm{pK}_{\mathrm{a}}=4.20\right)$ and 1 M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 mL of this buffer solution is ____ mL.

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Equilibrium

The pH of an aqueous solution containing 1 M benzoic acid

(pK_{a} = 4.20)

and 1 M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 mL of this buffer solution is ____ mL.

Answer: 100

By the Henderson–Hasselbalch equation,

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

. With pH = 4.5 and

p K_{a} = 4.20

0.3 = lo g \frac{V _{s}}{V _{a}}

, so

\frac{V _{s}}{V _{a}} = 1 0^{0.3} \approx 2

, where

V_{s}

and

V_{a}

are the volumes of the 1 M sodium benzoate and 1 M benzoic acid solutions (equal molarity, so millimoles scale directly with volume). With

V_{s} + V_{a} = 300 mL

and

V_{s} = 2 V_{a}

3 V_{a} = 300

, giving

V_{a} = 100 mL

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Integer answer