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 a molal solution, always assume 1 kg solvent. In aqueous solutions, 1000 g water corresponds to approximately 55.56 moles of water.

Answer 1

The Correct Option is C

Concept: Molality is defined as the number of moles of solute present in 1 kg of solvent. \[ m=\frac{\text{Moles of solute}}{\text{Mass of solvent in kg}} \] Mole fraction of a component is defined as: \[ X_i=\frac{\text{Moles of component}}{\text{Total moles present}} \] To calculate mole fraction from molality, we first determine the number of moles of solvent and solute separately and then apply the mole fraction formula.

Step 1: Interpreting the given molality. The solution is 2.0 molal. This means: \[ 2.0\text{ moles solute} \] are present in \[ 1000\text{ g water} \]

Step 2: Calculating moles of water. Molar mass of water: \[ =18\text{ g mol}^{-1} \] Therefore, \[ \text{Moles of water} =\frac{1000}{18} =55.56 \]

Step 3: Calculating mole fraction of solute. Total moles present \[ =55.56+2 =57.56 \] Hence, \[ X_{\text{solute}} =\frac{2}{57.56} \] \[ =0.0347 \]

Step 4: Final answer. \[ \boxed{X_{\text{solute}}=0.0347} \] Therefore, the correct answer is \[ \boxed{(C)} \]