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:

For molality questions, always take \(1kg\) solvent as the base.

Answer 1

The Correct Option is C

Concept:
Molality means number of moles of solute present in \(1kg\) of solvent. A \(2.0\) molal aqueous solution means: \[ 2.0\;mol\text{ solute in }1kg\text{ water} \] Mole fraction of solute is: \[ X_{\text{solute}}=\frac{n_{\text{solute}}}{n_{\text{solute}}+n_{\text{solvent}}} \]

Step 1: Find moles of solute.
Since the solution is \(2.0\) molal: \[ n_{\text{solute}}=2 \]

Step 2: Find moles of water.
Mass of water: \[ 1kg=1000g \] Molar mass of water: \[ 18g mol^{-1} \] \[ n_{\text{water}}=\frac{1000}{18} \] \[ n_{\text{water}}=55.56 \]

Step 3: Calculate mole fraction of solute.
\[ X_{\text{solute}}=\frac{2}{2+55.56} \] \[ X_{\text{solute}}=\frac{2}{57.56} \] \[ X_{\text{solute}}=0.0347 \] Hence: \[ \boxed{\text{(C) }0.0347} \]