JEE Main · 2022 · Shift-ImediumSOL-092

Boiling point of a 2% aqueous solution of a nonvolatile solute A is equal to the boiling point of 8% aqueous solution…

Solutions · Class 12 · JEE Main Previous Year Question

Question

Boiling point of a 2% aqueous solution of a nonvolatile solute A is equal to the boiling point of 8% aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is.

Options
  1. a

    MA=4MBM_A = 4M_B

  2. b

    MB=4MAM_B = 4M_A

  3. c

    MA=8MBM_A = 8M_B

  4. d

    MB=8MAM_B = 8M_A

Correct Answerb

MB=4MAM_B = 4M_A

Detailed Solution

Strategy:\n> Solutions with equal boiling points have equal elevations in boiling point (ΔTb\Delta T_b). For non-electrolytes relative to the same solvent, this implies identical molalities.\n\nStep 1: Set molalities equal\nmA=mB    fracwAMAW=fracwBMBWm_A = m_B \implies \\frac{w_A}{M_A \cdot W} = \\frac{w_B}{M_B \cdot W}\nWhere ww is mass of solute and WW is mass of solvent.\n- For solution A: 2 g solute A in 98 g solvent.\n- For solution B: 8 g solute B in 92 g solvent.\n\nStep 2: Substitute and solve for ratio\nAssuming dilute solutions (where 989210098 \approx 92 \approx 100):\nfrac2MA=frac8MB    MB=4MA\\frac{2}{M_A} = \\frac{8}{M_B} \implies M_B = 4 M_A\n\ntextAnswer:(2)\boxed{\\text{Answer: (2)}}

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