JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Solutions

Lead storage battery contains

38%

by weight solution of

H_{2} SO_{4}

. The van't Hoff factor is 2.67 at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ____ (Nearest integer).
Given

K_{f} = 1.8 K kg mol^{- 1}

Answer: 243

Solution

Taking

100 g

of the solution, the

38 g

H_{2} SO_{4}

is dissolved in

62 g

of water. The acid amounts to

38/98 = 0.388 mol

, so the molality is

m = \frac{0.388}{62/1000} = 6.25 mol k g^{- 1} .

Allowing for dissociation through the van't Hoff factor, the depression of freezing point is

Δ T_{f} = i K_{f} m = 2.67 \times 1.8 \times 6.25 = 30.0 K .

Subtracting this fall from the normal freezing point of water gives a freezing temperature of

273 - 30 = 243 K .

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Integer answer

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