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:
A \(10%\) w/w aqueous urea solution contains \(10 \text{ g}\) of urea in \(100 \text{ g}\) of solution. We need to calculate the mole fraction of water (\(X_{water}\)).
Step 2: Key Formula or Approach:
Mole fraction of water \(X_{water} = \frac{n_{water}}{n_{water} + n_{urea}}\).
Moles \(n = \frac{mass}{molar mass}\).
Step 3: Detailed Explanation:
1. Mass of urea (\(\text{NH}_2\text{CONH}_2\)) = \(10 \text{ g}\).
2. Mass of water = \(100 \text{ g} - 10 \text{ g} = 90 \text{ g}\).
3. Calculate molar masses:
\(M(urea) = (14 \times 2) + (1 \times 4) + 12 + 16 = 28 + 4 + 12 + 16 = 60 \text{ g/mol}\).
\(M(water) = (1 \times 2) + 16 = 18 \text{ g/mol}\).
4. Calculate moles of each component:
\(n_{urea} = \frac{10}{60} = 0.1667 \text{ mol}\).
\(n_{water} = \frac{90}{18} = 5.0 \text{ mol}\).
5. Calculate mole fraction of water:
\[ X_{water} = \frac{5.0}{5.0 + 0.1667} \]
\[ X_{water} = \frac{5.0}{5.1667} \approx 0.9677 \]
The closest value in the options is \(0.967\).
Step 4: Final Answer:
The mole fraction of water is \(0.967\).