Question

The mole fraction of urea in an aqueous urea solution containing $900g$ of water is $0.05$. If the density of the solution is $1.2gc{m}^{-3}$, the molarity of urea solution is______
(Given data: Molar masses of urea and water are $60gmo{l}^{-1}$ and $18gmo{l}^{-1}$, respectively.)

• A. 2.98 M
• B. 1.98 M
• C. 1.06 M
• D. 3.98 M

Answer 1

The correct option is A 2.98 M

Let, mole of urea = x
According to the question,
$\frac{x}{x+\frac{900}{18}}=0.05$
$\Rightarrow x=\frac{50}{19}$

We know,
$\text{Mass of solution = mass of solute + mass of solvent}$
$=\frac{50}{19}\times 60+900=\frac{20100}{19}$

Again, density = mass/volume
So,
Volume of solution =$\frac{20100}{19\times 1.2}mL$

=$\frac{20.1}{19\times 1.2}L$

Therefore, Molarity = $\frac{moles}{volume\left(L\right)}$$=\frac{\frac{50}{19}}{\frac{20.1}{19\times 1.2}}$
$=\frac{60}{20.1}$ = 2.98 M