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

Step 1: Define 2.0 molal aqueous solution.
A 2.0 molal (2.0 m) solution contains 2.0 mol of solute dissolved in 1 kg (1000 g) of solvent (water).
Step 2: Calculate moles of solvent (water).
Molar mass of water = 18 g/mol. Mass of water = 1000 g. \[ n_{water} = \frac{1000}{18} = 55.56 \text{ mol} \]
Step 3: Identify moles of solute.
From the molality definition: $n_{solute} = 2.0$ mol.
Step 4: Apply the mole fraction formula.
\[ X_{solute} = \frac{n_{solute}}{n_{solute} + n_{solvent}} = \frac{2.0}{2.0 + 55.56} = \frac{2.0}{57.56} \]
Step 5: Calculate the numerical value.
\[ X_{solute} = \frac{2.0}{57.56} \approx 0.0347 \]
Step 6: Verify and identify the correct option.
Mole fraction must always be between 0 and 1, so option 1 (1.87) is impossible. The calculated value 0.0347 matches option 3. \[ \boxed{X_{solute} = 0.0347} \]