JEE Main 2026 Apr 5 Shift 2, Chemistry Q23: Colligative Properties

JEE Main2026Apr 5, Shift 2Chemistry

20 g of hemoglobin in a 1 L aqueous solution (A) at 300 K is separated from pure water by a semi-permeable membrane. At equilibrium the height of solution in a tube dipped in solution (A) is found to be 80.0 mm higher than the tube dipped in water.

The molar mass of hemoglobin is _____ kg mol $^{- 1}$ . (Nearest integer)

Given: $g = 10$ ms $^{- 2}$ , $R = 8.3$ kPa·dm $^{3}$ ·K $^{- 1}$ ·mol $^{- 1}$ , density of solution $= 1000$ kg m $^{- 3}$ .

Your answer

Solution

Osmotic pressure from the height column: $π = ρ g h = 1000 \times 10 \times 80 \times 1 0^{- 3} = 800$ Pa.

For dilute solution, $π = C R T$ where $C = \frac{mass}{M \cdot V}$ . With mass $= 20$ g $= 0.02$ kg, $V = 1$ L $= 1 0^{- 3}$ m $^{3}$ :

$800 = \frac{0.02}{M \cdot 1 0 ^{- 3}} \times 8.3 \times 300 = \frac{20 \times 8.3 \times 300}{M}$ (with M in g/mol).

$M = \frac{20 \times 8.3 \times 300}{800} \times 1000 = 62250$ g/mol $\approx 62$ kg/mol.

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JEE Main 2026 Apr 5 Shift 2, Chemistry Q23: Colligative Properties

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