Question

$500{\text{ g}}$ of urea solution of mole fraction $0.2$ is diluted to $1500{\text{ g}}$. The mole fraction of solute in the diluted solution is:
A.$0.05$
B.$0.23$
C.$0.34$
D.$0.38$

Answer 1

To solve this question, you must recall the formula for calculating the mole fraction of a solution. Mole fraction is a means of calculating the concentration of the solution, alongside many others like molarity, normality, molality, etc. When a solution is diluted, the amount of solute added remains the same.
Formula used: Mole fraction formula: $\chi = \dfrac{{{{\text{n}}_{{\text{solute}}}}}}{{{{\text{n}}_{{\text{solute}}}} + {{\text{n}}_{{\text{solvent}}}}}}$
Where, $\chi$ depicts the mole fraction of the solute in the solution
${n_{solute}}$ depicts the number of moles of solute in the solution
And, ${n_{solvent}}$ depicts the number of moles of solvent present in the solution.

Complete step by step answer:
Mole fraction can be simply termed as the ratio of the number of moles of the solute to the total number of moles of all components present in the solution.
The mass of the solution is given to us as $500{\text{g}}$ initially and the mole fraction of urea is given to be $0.2$. So there are $0.2$ moles of urea and $0.8$ moles of water in the solution which correspond to $12{\text{g}}$ urea and $14.4{\text{g}}$ water respectively. The total mass is given by $26.4{\text{g}}$.
Thus, the mass of urea present in $500{\text{g}}$ of the solution is $m = \dfrac{{12 \times 500}}{{26.4}} = 227.27{\text{g}}$ urea
Or the number of moles of urea ${n_{solvent}} = 3.7878$
When the solution is diluted to $1500{\text{g}}$, only the amount of water changes. The amount of urea present remains the same.
So the mass of water in the solution is now $= 1500 - 227.2 = 127.2{\text{g}}$
The number of moles of water or the solvent in the solution ${n_{solvent}} = \dfrac{{1272.72}}{{18}} = 70.70$ moles
Hence, we can calculate the mole fraction of urea as
$\chi = \dfrac{{3.7878}}{{3.7878 + 70.70}}$
$\therefore \chi = 0.05$

Hence, the correct answer is A.

Note:
The sum of mole fractions of all the components in a solution is always equal to unity. Value of mole fraction is always less than 1.