Question

Calculate the mole fraction of solute in solution if vapour pressure of a solution and pure solvent are 27 mm Hg and 30 mm Hg respectively at 298 K.

• A. \(0.9\)
• B. \(0.1\)
• C. \(0.4\)
• D. \(0.6\)

Hint:

Raoult's law: relative lowering of vapour pressure equals the mole fraction of solute.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
For a solution of a nonvolatile solute, the relative lowering of vapour pressure equals the mole fraction of the solute (Raoult's law).

Step 2: Key Formula or Approach:
\[ \frac{p^{\circ} - p}{p^{\circ}} = x_{\text{solute}} \]

Step 3: Detailed Explanation:
Given \(p^{\circ} = 30\) mm Hg and \(p = 27\) mm Hg.
\[ x_{\text{solute}} = \frac{30 - 27}{30} = \frac{3}{30} = 0.1 \]
Check: the mole fraction of the solvent is \(27/30 = 0.9\), so the solute is \(1 - 0.9 = 0.1\). Option (A) 0.9 is the mole fraction of the solvent, which is a common trap. Options (C) and (D) do not match the ratio 3/30.

Final Answer:
The mole fraction of the solute is 0.1, option (B). \[ \boxed{0.1 \text{ (B)}} \]