Question

If a non-volatile solute (urea) needs to be dissolved in $100g$ of water in order to decrease the vapour pressure of water by $25\%$, then what will be the molality of solution?

• A. $15.52m$
• B. $18.52m$
• C. $16.52m$
• D. $19.52m$

Answer 1

The correct option is B $18.52m$

Using Raoult's law in the following form,
$\frac{P_0-P_s}{P_s}=\frac{wM}{Wm}$
Where, $P_0=\text{Vapour pressure of pure solvent}$
$P_s=\text{Vapour pressure of solution}$
$M=\text{Molar mass of solvent}$
$W=\text{Mass of solvent}$
$m=\text{Molar mass of solute}$
$w=\text{Mass of solute}$

If $P_0=100mm,\text{then}{P}_s=75mm$
$\therefore \frac{100-75}{75}=\frac{w\times 18}{100\times 60}$
$\Rightarrow w=111.1g$
$\text{Molality}=\frac{w\times 1000}{m\times W}=\frac{111.1\times 1000}{60\times 100}=18.52m$