JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Solutions

25 mL of an aqueous solution of KCl was found to require 20 mL of

1 M AgNO_{3}

solution when titrated using

K_{2} CrO_{4}

as an indicator. What is the depression in freezing point of KCl solution of the given concentration? ____ (Nearest integer).
(Given :

K_{f} = 2.0 K kg mol^{- 1}

)
Assume
1)

100%

ionization and
2) density of the aqueous solution as

1 g mL^{- 1}

Answer: 3

Solution

The precipitation titration

KCl + AgN O_{3} \to AgCl + KN O_{3}

consumes one mole of silver per mole of chloride, so the

20 mL

1 M

silver nitrate corresponds to

0.020 mol

of potassium chloride in the

25 mL

sample. With a density of

1 g m L^{- 1}

the solvent mass is close to

0.025 kg

, giving a molality of

\frac{0.020}{0.025} = 0.8 mol k g^{- 1}

. As potassium chloride ionises completely the van't Hoff factor is

2

, so

Δ T_{f} = i K_{f} m = 2 \times 2.0 \times 0.8 = 3.2 K

. To the nearest integer the depression in freezing point is 3 K.

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Integer answer