Question

A non-volatile solute (urea) is dissolved in $100g$ of water in order to decrease the vapour pressure of water by $25\%$. Which of the following option(s) is/are correct?
Assume the solution to be non-dilute.

• A. $\text{Mass of urea added is}111.1g$
• B. $\text{Mass of urea added is}88.1g$
• C. $\text{Molality of the solution is}18.52m$
• D. $\text{Molality of the solution is}14.52m$

Answer 1

Answer: (A), (C)

$\text{Molality of the solution is}18.52m$

Using Raoult's law in the following form for non dilute solution:
$\frac{P_A^o-P_s}{P_s}=\frac{w_B\times M_A}{w_A\times M_B}$
$w_A=\text{mass of A (Solvent)}$
$w_B=\text{mass of B (Solute)}$
$M_A=\text{molar mass of A}$
$M_B=\text{molar mass of B}$

If $P_A^o=100mm$, then $P_s=75mm$
$\frac{100-75}{75}=\frac{w_B\times 18}{100\times 60}{w}_B=111.1g\text{Molality}=\frac{w_B\times 1000}{m_B\times w_A}=\frac{111.1\times 1000}{60\times 100}=18.52m$