Question

The mole fraction of urea in an aqueous urea solution containing $900g$ of water is $0.05$. If the density of solution is $1.2gc{m}^{-3}$, the molarity of urea solution is

Answer 1

Let moles of urea $=x$

$\therefore \frac{x}{x+\frac{900}{18}}=0.05$

$\Rightarrow x=\frac{50}{19}$

Mass of solution $=\frac{50}{19}\times 60+900=\frac{20100}{19}$

Volume of solution $=\frac{20100}{19\times 1.2}ml$

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

Molarity $=\frac{\frac{50}{19}}{\frac{20.1}{19\times 1.2}}=\frac{50\times 1.2}{20.1}=\frac{60}{20.1}\cong 2.985$