Solutions and Colligative Properties - Result Question 3-1
3. At room temperature, a dilute solution of urea is prepared by dissolving $0.60$ g of urea in $360$ g of water. If the vapour pressure of pure water at this temperature is $35$ mm Hg , lowering of vapour pressure will be (Molar mass of urea $=60 \mathrm{~g} \mathrm{~mol}^{-1}$ )
(2019 Main, 10 April I)
(a) $0.027$ mm Hg
(b) $0.031$ mm Hg
(c) $0.017$ mm Hg
(d) $ 0.028$ mm Hg
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Answer:
Correct Answer: 3. (c)
Solution:
Key Idea: For dilute solution, lowering of vapour pressure $(\Delta p)=p^0-p$ and relative lowering of vapour pressure $=\dfrac{\Delta p}{p^0}$ which is a colligative property of solutions.
$ \dfrac{\Delta p}{p^0}=\chi_B \times i \Rightarrow \Delta p=\chi_B \times i \times p^0 $
where, $p^0=$ vapour pressure of pure solvent
$i=$ 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)
$ \begin{aligned} & =\dfrac{n_B}{n_A+n_B}=\dfrac{\dfrac{0.60}{60}}{\dfrac{360}{18}+\dfrac{0.60}{60}}=\dfrac{0.01}{20+0.01} \\ & =\dfrac{0.01}{20.01}=0.0005 \end{aligned} $
$i=$ 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} $ $\mathrm{Hg}$
BETA
