Osmotic Pressure

Question

Two solutions of sucrose and urea have the same osmotic pressure at 298 K. If 10 g of sucrose (molar mass 342 g/mol) is dissolved per litre, what mass of urea (molar mass 60 g/mol) per litre would give the same osmotic pressure?

RankGuru · Accepted Answer

Osmotic pressure (π) is given by the van't Hoff equation: π = CRT = (n/V)RT. For two solutions to have the same osmotic pressure at the same temperature, they must have the same molar concentration (C). For sucrose: C = 10/342 = 0.02924 mol/L. For equal osmotic pressure, concentration of urea must also equal 0.02924 mol/L. Therefore, mass of urea per litre = 0.02924 × 60 = 1.754 g ≈ 1.75 g. Option 3.46 g would correspond to double the required concentration. Option 1.46 g results from using an incorrect molar mass for urea. Option 5.12 g is far too high and corresponds to a misapplication of the formula. Equal osmotic pressure implies isotonic solutions, a concept directly from NCERT Chemistry Chapter 2. This concept is also vital in biology — cells in isotonic saline solution maintain equilibrium. Plausibility check: since urea's molar mass (60) is much less than sucrose's (342), far less mass is needed to achieve the same molar concentration — 1.75 g < 10 g, which is correctly lower.

Osmotic Pressure

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