JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Solutions

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.

Answer: (B)

Solution

For equal boiling point elevation, the molalities must be equal.

For solution A (2% w/w): 100 g solution contains 2 g A and 98 g water.

m_{A} = \frac{2/ M _{A}}{0.098}

For solution B (8% w/w): 100 g solution contains 8 g B and 92 g water.

m_{B} = \frac{8/ M _{B}}{0.092}

Setting

m_{A} = m_{B}

\frac{2}{0.098 M _{A}} = \frac{8}{0.092 M _{B}}

Solving:

\frac{M _{A}}{M _{B}} = \frac{2 \times 0.092}{8 \times 0.098} = \frac{0.184}{0.784} \approx \frac{1}{4.26} \approx \frac{1}{4}

Therefore,

M_{B} \approx 4 M_{A}

. The answer is (B).

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Single correct option