Question

Vapour pressure of pure water at $298K$ is $23.8mm$ $Hg$. $50g$ of urea is dissolved in $850g$ of water. The vapour pressure of water for this solution and its relative lowering are respectively:

• A. $23.8mm$ $Hg$ and$0.16$
• B. $25.4mm$ $Hg$ and $0.02$
• C. $30.2mm$ $Hg$ and$0.020$
• D. $23.4mm$ $Hg$ and $0.017$

Answer 1

The correct option is D $23.4mm$ $Hg$ and $0.017$

Given, $P_i=23.8mmHg$

$W_1$ (weight of water) = 850 g

$W_2$ (weight of area) = 50 g

Molecular weight of water $M_1=18g/mol$

Molecular weight of area $M_2=60g/mol$

From Raoult's law,

$\frac{P_1^0-P_1}{P_1^0}=\frac{n_2}{n_1+n_2}$

Let 'P' is vapour pressure to be calculated:

$\frac{P_1^0-P_1}{P_1^0}=\frac{\frac{W_2}{M_2}}{\frac{W_1}{M_1}+\frac{W_2}{M_2}}\Rightarrow \frac{23.8-P_1}{23.8}=\frac{\frac{50}{60}}{\frac{850}{18}+\frac{50}{60}}$

$\Rightarrow \frac{23.8-P}{23.8}=\frac{0.83}{47.22+0.83}=0.0173$

$P_1=23.4mm$ of Hg

$\therefore$ Relative lowering is 0.0173 & vapour pressure of solution is 23.4

Option (D) is correct.