JEE Main · 2019 · Shift-IIeasySOL-106

1 g of a non-volatile non-electrolyte solute is dissolved in 100 g of two different solvents A and B whose…

Solutions · Class 12 · JEE Main Previous Year Question

Question

1 g of a non-volatile non-electrolyte solute is dissolved in 100 g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1:5. The ratio of the elevation in their boiling points, ΔTb(A)ΔTb(B)\frac{\Delta T_b(A)}{\Delta T_b(B)}, is: (assuming they have the same molar mass)

Options
  1. a

    10 : 1

  2. b

    1 : 5

  3. c

    1 : 0.2

  4. d

    5 : 1

Correct Answerb

1 : 5

Detailed Solution

Strategy:\n> The elevation in boiling point (ΔTb\Delta T_b) is proportional to the ebulliosco\pic constant (KbK_b) when the molality (moles of solute per kg of solvent) is constant.\n\nStep 1: Confirm same molality (mm)\n- Mass of solute = 1 g (for both).\n- Molar mass MM = same (for both).\n- Mass of solvent = 100 g (for both).\nSince all mass components are identical, both solutions have the same molality mm.\n\nStep 2: Relate elevation to the constants\nΔTb=Kbm    fracΔTb(A)ΔTb(B)=fracKb,AKb,B\Delta T_b = K_b \cdot m \implies \\frac{\Delta T_b(A)}{\Delta T_b(B)} = \\frac{K_{b,A}}{K_{b,B}}\nGiven the ratio of constants is 1:51 : 5, the ratio of elevations is also 1:51 : 5.\n\ntextAnswer:(2)\boxed{\\text{Answer: (2)}}

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