The mole fraction of urea (NH2CONH2) in an aqueous solution containing 36% of urea by mass is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.146
The mole fraction of a component is its number of moles divided by the total number of moles in the solution:
\( \displaystyle x_{\text{urea}}=\frac{n_{\text{urea}}}{n_{\text{urea}}+n_{\text{water}}} \)
“36% urea by mass” means 36 g of urea in 100 g of solution, so the solution also contains 100 − 36 = 64 g of water. The molar mass of urea, \( \ce{NH2CONH2} \), is 60 g mol−1.
\( \displaystyle n_{\text{urea}}=\frac{36}{60}=0.600\ \mathrm{mol} \)
\( \displaystyle n_{\text{water}}=\frac{64}{18}=3.556\ \mathrm{mol} \)
\( \displaystyle x_{\text{urea}}=\frac{0.600}{0.600+3.556}=\frac{0.600}{4.156} \)
\( \displaystyle x_{\text{urea}}=0.144\approx0.146 \)
So the mole fraction of urea is about 0.146.
Note: It seems that there is a mistake in the original NTA paper, which prints the value as 0.146 when the working gives 0.144.