Question

What is the mole fraction of water in \(10%\) by weight (w/w) of aqueous urea solution? [Given: Molar mass of H, O, C and N are 1, 16, 12 and \(14 \text{ g mol}^{-1}\) respectively.]

• A. 0.825
• B. 0.032
• C. 0.867
• D. 0.967

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The topic is Solutions and Concentration Terms.
We are given the weight percentage (w/w) of a urea solution and asked to find the mole fraction of the solvent, water.
Step 2: Key Formula or Approach:
The mole fraction of a component is the ratio of its moles to the total moles in the mixture.
\[ X_{water} = \frac{\text{moles of water}}{\text{moles of water} + \text{moles of urea}} \]
The easiest way to solve this is to assume a \(100 \text{ g}\) sample of the solution.
Step 3: Detailed Explanation:
1. Determine Masses from Percentage:
Assume we have \(100 \text{ g}\) of the solution.
A \(10%\) (w/w) solution means:
Mass of urea (solute) = \(10 \text{ g}\).
Mass of water (solvent) = \(100 \text{ g} - 10 \text{ g} = 90 \text{ g}\).
2. Calculate Molar Masses:
Molar mass of urea (\(\text{CH}_4\text{N}_2\text{O}\)) = \(12 + (4 \times 1) + (2 \times 14) + 16 = 60 \text{ g/mol}\).
Molar mass of water (\(\text{H}_2\text{O}\)) = \((2 \times 1) + 16 = 18 \text{ g/mol}\).
3. Calculate Moles of Each Component:
Moles of urea (\(n_{urea}\)) = \(\frac{10 \text{ g}}{60 \text{ g/mol}} \approx 0.167 \text{ mol}\).
Moles of water (\(n_{water}\)) = \(\frac{90 \text{ g}}{18 \text{ g/mol}} = 5.0 \text{ mol}\).
4. Calculate Mole Fraction of Water:
\[ X_{water} = \frac{n_{water}}{n_{water} + n_{urea}} = \frac{5.0}{5.0 + 0.167} = \frac{5.0}{5.167} \approx 0.9677 \]
This value matches option (D).
Step 4: Final Answer:
The mole fraction of water is \(0.967\).