Question

Which among the following statements is false ?

• A. The correct order of osmotic pressure for $0.01 \, \text{M}$ aqueous solution of each compound is $\text{B} \text{a} \text{C} \text{l}_{2} > \text{K} \text{C} \text{l} > \text{C} \text{H}_{3} \text{C} \text{O} \text{O} \text{H} > \text{Sucrose}$ .
• B. The osmotic pressure $\left(\text{\pi }\right)$ of a solution is given by the equation $\left(\right. \text{\pi } = \text{Μ} \text{} \text{R} \text{} \text{T} ⁡ \text{,}$ where M is the molarity of the solution).
• C. Raoult's law states that the vapour pressure of a component over a solution is proportional to its mole fraction.
• D. Two sucrose solutions of the same molality prepared in different solvents will have the same freezing point depression.

Answer 1

Answer: (D)

(i) Osmotic pressure $\text{\pi } = \text{i} \, \, \text{C} \text{R} \text{T}$
$\therefore $ concentration is same so $\text{\pi } \propto \text{i}$ (number of ions)
$\text{i}$ for $BaCl_{2}=3, \, KCl=2,$ $ \, CH_{3}COOH=1\leq i≤2$ and for sucrose $= 1$
So, order of osmotic pressure $\text{B} \text{a} \text{C} \text{l}_{2} > \text{K} \text{C} \text{l} > \text{C} \text{H}_{3} \text{C} \text{O} \text{O} \text{H} > \text{Sucrose}$
Acetic acid does not dissociate completely. Hence, its van't Hoff factor will be in between 1 and 2.
(ii) The extent of depression in freezing point varies with the number of solute particles for a fixed solvent only, and it's a characteristic feature of the nature of solvent also $\Delta T_{f}=k_{f}\times m$
For different solvents, value of $\text{k}_{\text{f}}$ is also different so, for two different solvents the extent of depression may vary even if same number of solute particles be dissolved in them.