Solutions and Colligative Properties 2 Question 3
3. At room temperature, a dilute solution of urea is prepared by dissolving $0.60 \mathrm{~g}$ of urea in $360 \mathrm{~g}$ of water. If the vapour pressure of pure water at this temperature is $35 \mathrm{~mm} \mathrm{Hg}$, lowering of vapour pressure will be (Molar mass of urea $=60 \mathrm{~g} \mathrm{~mol}^{-1}$ )
(2019 Main, 10 April I) same temperature by the mixing $60 \mathrm{~g}$ of ethanol with $40 \mathrm{~g}$ of methanol. Calculate the total vapour pressure of the solution and the mole fraction of methanol in the vapour. $(1986,4 \mathrm{M})$
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Solution:
Key Idea For dilute solution, lowering of vapour pressure $(\Delta p)=p^{0}-p$ and relative lowering of vapour pressure $=\frac{\Delta p}{p^{0}}$ which is a colligative property of solutions.
$$ \frac{\Delta p}{p^{0}}=\chi_{B} \times i \Rightarrow \quad \Delta p=\chi_{B} \times i \times p^{0} $$
where, $p^{0}=$ vapour pressure of pure solvent
$$ i=\text { van’t Hoff factor } $$
$\chi_{B}=$ mole fraction of solute
Given,
$p^{\circ}=$ vapour pressure of pure water of $25^{\circ} \mathrm{C}$
$=35 \mathrm{~mm} \mathrm{Hg}$
$\chi_{B}=$ mole fraction of solute (urea)
$=\frac{n_{B}}{n_{A}+n_{B}}=\frac{\frac{0.60}{60}}{\frac{360}{18}+\frac{0.60}{60}}=\frac{0.01}{20+0.01}$
$=\frac{0.01}{20.01}=0.0005$
$i=$ van’t Hoff factor $=1$ (for urea)
Now, according to Raoult’s law
$$ \Delta p=\chi_{B} \times i \times p^{\circ} $$
On substituting the above given values, we get $\Delta p=0.0005 \times 1 \times 35=0.0175 \mathrm{~mm} \mathrm{Hg}$
