The depression in freezing point observed for a formic acid solution of concentration $0.5 \mathrm{~mL} \mathrm{~L}^{-1}$ is $0.0405^{\circ} \mathrm{C}$. Density of formic acid is $1.05 \mathrm{~g} \mathrm{~mL}^{-1}$. The Van't Hoff factor of the formic acid solution is nearly : (Given for water $\mathrm{k}_{\mathrm{f}}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ )

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Solutions

The depression in freezing point observed for a formic acid solution of concentration

0.5 mL L^{- 1}

0.040 5^{\circ} C

. Density of formic acid is

1.05 g mL^{- 1}

. The Van't Hoff factor of the formic acid solution is nearly : (Given for water

k_{f} = 1.86 K kg mol^{- 1}

)

(A)0.8
(B)1.1
(C)1.9✓ Correct
(D)2.4

Answer: (C)

Solution

Mass of formic acid in 1 L =

0.5 \times 1.05 = 0.525

g. Molality

m = \frac{0.525/46}{1} = \frac{0.525}{46}

mol/kg. Using

Δ T_{f} = i K_{f} m

, we get

i = \frac{Δ T _{f}}{K _{f} m} = \frac{0.0405 \times 46}{1.86 \times 0.525} \approx 1.9

. This indicates partial dimerization of formic acid.

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Single correct option

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