Question

$500$ g of urea solution of mole fraction $0.2$ is diluted to $1500$ g. The mole fraction of solute in the diluted solution is:

• A. $0.05$
• B. $0.23$
• C. $0.34$
• D. $0.38$

Answer 1

The correct option is A $0.05$

The molar mass of urea is $60$ g/mol.
$1$ mole of solution will contain $0.2$ mole of urea and $0.8$ mole of water. This corresponds to $12$ g urea and $14.4$ g water. Total mass of the solution will be $26.4$ g.
Thus, $500$ g of solution will contain $\frac{12\times 500}{26.4}=227.27g$ urea which is equal to $3.7878$ moles.
The mass of water in diluted solution $=1500-227.2=1272.72g$. This is equal to $\frac{1272.72}{18}=70.70moles$.
The mole fraction of urea in the diluted solution is $\frac{3.7878}{70.70+3.7878}=0.05$.