Question

The mole fraction of a solute in 2.0 molal aqueous solution is :

• A. 1.87
• B. 0.347
• C. 0.0347
• D. 0.00347

Hint:

2 molal = 2 mol solute in 1000 g water (55.56 mol); x = 2/(2+55.56).

Answer 1

The Correct Option is C

Use the definition of molality and convert to mole fraction. Molality $2.0$ means $n_{solute}=2.0$ mol in $1000$ g water, and $n_{water}=1000/18 \approx 55.6$ mol.
\[x_{solute}=\frac{2.0}{2.0+55.6}\approx\frac{2.0}{57.6}\approx 0.0347\]The value is close to $m\times M_{water}/1000 = 2.0\times18/1000=0.036$, confirming the order of magnitude. Correct option: (C) 0.0347.