JEE Main · 2019 · Shift-IImediumSOL-107

A solution is prepared by dissolving 0.6 g of urea (molar mass = 60 g mol⁻¹) and 1.8 g of glucose (molar mass = 180 g…

Solutions · Class 12 · JEE Main Previous Year Question

Question

A solution is prepared by dissolving 0.6 g of urea (molar mass = 60 g mol⁻¹) and 1.8 g of glucose (molar mass = 180 g mol⁻¹) in 100 mL of water at 27°C. The osmotic pressure of the solution is:

(R=0.08206 L atm K1 mol1R = 0.08206\ \mathrm{L\ atm\ K^{-1}\ mol^{-1}})

Options
  1. a

    8.2 atm

  2. b

    2.46 atm

  3. c

    4.92 atm

  4. d

    1.64 atm

Correct Answerc

4.92 atm

Detailed Solution

Strategy:\n> For a mixture of non-volatile, non-electrolytic solutes, the total osmotic pressure is the sum of the partial pressures, which corresponds to the total molarity of particles (Ctexttotal=C1+C2C_{\\text{total}} = C_1 + C_2).\n\nStep 1: Calculate moles for each component\n- ntexturea=0.6/60=0.01textmoln_{\\text{urea}} = 0.6 / 60 = 0.01\\text{ mol}\n- ntextglucose=1.8/180=0.01textmoln_{\\text{glucose}} = 1.8 / 180 = 0.01\\text{ mol}\n- ntexttotal=0.02textmoln_{\\text{total}} = 0.02\\text{ mol}\n\nStep 2: Calculate total molarity (CC)\nVolume = 100 mL = 0.1 L.\nC=frac0.02textmol0.1textL=0.2textMC = \\frac{0.02\\text{ mol}}{0.1\\text{ L}} = 0.2\\text{ M}\n\nStep 3: Solve for Osmotic Pressure (π\pi)\n- T=27+273=300textKT = 27 + 273 = 300\\text{ K}\n- R=0.08206R = 0.08206\nπ=CRT=0.2times0.08206times300=60times0.08206=4.9236textatm\pi = CRT = 0.2 \\times 0.08206 \\times 300 = 60 \\times 0.08206 = 4.9236\\text{ atm}\n\ntextAnswer:(3)\boxed{\\text{Answer: (3)}}

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