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Liquids in Liquids

Addition of a...

Question

Addition of a non-volatile solute to a solvent always increases the colligative property such as $π, \frac{Δ P}{P^{\circ}}, Δ T_{b}$ and $Δ T_{f}$ . All these colligative properties are directly proportional to the molality. The increase in colligative properties is due to increase in number of solute particles.
If relative decrease in vapour pressure is 0.4 for a solution containing 1 mole NaCl in 3 moles of $H_{2} O$ , then what is the percentage ionization of NaCl?

A

100%

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B

60%

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C

80%

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D

40%

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Solution

The correct option is A 100%
Let the degree of dissociation be $α$ .
then i = 1 + $α$ (for NaCl)
$\frac{Δ P}{P^{\circ}} = \frac{i n_{N a C l}}{i n_{N a C l} + n_{H_{2} O}}$
$0.4 = \frac{(1 + α) \times 1}{(1 + α) \times 1 + 3}$
$\frac{2}{5} - \frac{(1 + α)}{(4 + α)}$
$8 + 2 α = 5 + 5 α$
$3 α = 3$
$α = 1$
$\Rightarrow 100 %$

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