JEE Main · 2019 · Shift-ImediumSOL-111

The freezing point of a 4% aqueous solution of X is equal to the freezing point of a 12% aqueous solution of Y. If the…

Solutions · Class 12 · JEE Main Previous Year Question

Question

The freezing point of a 4% aqueous solution of X is equal to the freezing point of a 12% aqueous solution of Y. If the molecular weight of X is A, then the molecular weight of Y will be

Options
  1. a

    2A

  2. b

    A

  3. c

    4A

  4. d

    3A

Correct Answerd

3A

Detailed Solution

Strategy:\n> Equal freezing points imply equal elevations/depressions in the same solvent. For non-electrolytes, this means identical molalities.\n\nStep 1: Set molalities equal\nmX=mYm_X = m_Y.\nLet MX=AM_X = A and MY=BM_Y = B.\nfrac4Afrac1W=frac12Bfrac1W\\frac{4}{A} \cdot \\frac{1}{W} = \\frac{12}{B} \cdot \\frac{1}{W}\n(where WW is mass of solvent, which cancels out)\n\nStep 2: Solve for B\nfrac4A=frac12B    B=frac12A4=3A\\frac{4}{A} = \\frac{12}{B} \implies B = \\frac{12A}{4} = 3A\n\ntextAnswer:(4)\boxed{\\text{Answer: (4)}}

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