Question

Which from following solutions in water on complete dissociation exhibits minimum freezing point depression?

• A. \(0.2\) m Potassium chloride
• B. \(0.1\) m Sodium chloride
• C. \(0.05\) m Aluminium phosphate
• D. \(0.15\) m Magnesium sulphate

Hint:

Compare i times m for each solution; the smallest value gives the smallest depression.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Freezing point depression is \(\Delta T_f = i K_f m\). With the same solvent (water), the depression depends only on \(i \times m\), the effective molality of particles after complete dissociation.

Step 2: Detailed Explanation:
Find \(i\) from the number of ions each formula unit gives:
KCl gives 2 ions, so \(i \times m = 2 \times 0.2 = 0.40\).
NaCl gives 2 ions, so \(2 \times 0.1 = 0.20\).
\(\text{AlPO}_4\) gives 2 ions (\(\text{Al}^{3+}\) and \(\text{PO}_4^{3-}\)), so \(2 \times 0.05 = 0.10\).
\(\text{MgSO}_4\) gives 2 ions, so \(2 \times 0.15 = 0.30\).

Step 3: Compare:
The smallest effective molality is 0.10 for aluminium phosphate, so its freezing point depression is the least.

Step 4: Why the other options are wrong.
KCl (A), NaCl (B) and MgSO4 (D) have effective molalities of 0.40, 0.20 and 0.30, all higher than 0.10, so each lowers the freezing point more.

Final Answer:
Aluminium phosphate gives the smallest depression, option (C). \[ \boxed{\text{0.05 m aluminium phosphate (C)}} \]