JEE Main · 2019 · Shift-IeasySOL-105

At room temperature, a dilute solution of urea is prepared by dissolving 0.60 g of urea in 360 g of water. If the…

Solutions · Class 12 · JEE Main Previous Year Question

Question

At room temperature, a dilute solution of urea is prepared by dissolving 0.60 g of urea in 360 g of water. If the vapour pressure of pure water at this temperature is 35 mm Hg, lowering of vapour pressure will be:

(molar mass of urea = 60 g mol⁻¹)

Options
  1. a

    0.028 mm Hg

  2. b

    0.027 mm Hg

  3. c

    0.031 mm Hg

  4. d

    0.017 mm Hg

Correct Answerd

0.017 mm Hg

Detailed Solution

Strategy:\n> Lowering of vapour pressure (ΔP\Delta P) is given by Raoult's Law: ΔP=xtextsoluteP\Delta P = x_{\\text{solute}} \cdot P^\circ. Calculate the mole fraction of urea in the water.\n\nStep 1: Calculate moles of solute and solvent\n- ntexturea=0.60/60=0.01textmoln_{\\text{urea}} = 0.60 / 60 = 0.01\\text{ mol}\n- ntextwater=360/18=20textmoln_{\\text{water}} = 360 / 18 = 20\\text{ mol}\n\nStep 2: Determine the mole fraction (xtextureax_{\\text{urea}})\nxtexturea=fracntextureantexturea+ntextwater=frac0.0120.010.0004997x_{\\text{urea}} = \\frac{n_{\\text{urea}}}{n_{\\text{urea}} + n_{\\text{water}}} = \\frac{0.01}{20.01} \approx 0.0004997\n\nStep 3: Calculate narrowing of vapour pressure\nP=35textmmHgP^\circ = 35\\text{ mm Hg}\nΔP=0.0004997times350.01749textmmHg\Delta P = 0.0004997 \\times 35 \approx 0.01749\\text{ mm Hg}\n\ntextAnswer:(4)\boxed{\\text{Answer: (4)}}

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