Four solutions of `K_(2)SO_(4)` with the concentrations 0.1m, 0.01m ,0.001 m, and 0.0001 m are available . The maximum value of colligative property corresponds to :

Options

A. (a) 0.0001 msolution
B. (b) 0.001 m solution
C. (c) 0.01 m solution
D. (d) 0.1 m solution

Answer

To solve the problem of determining which solution of K₂SO₄ has the maximum value of colligative property, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Colligative Properties**:
Colligative properties depend on the number of solute particles in a solution, not on the identity of the solute. The main colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

**Hint**: Remember that colligative properties are influenced by the number of solute particles, not their type.

2. **Identify the Given Concentrations**:
The concentrations of the K₂SO₄ solutions provided are:
- 0.1 m (molal)
- 0.01 m (molal)
- 0.001 m (molal)
- 0.0001 m (molal)

**Hint**: List out the concentrations clearly to compare them easily.

3. **Determine the Number of Particles**:
K₂SO₄ dissociates in solution into 3 ions: 2 K⁺ ions and 1 SO₄²⁻ ion. Therefore, each mole of K₂SO₄ produces 3 moles of particles in solution.

**Hint**: Remember to consider the dissociation of the solute when calculating the effective concentration of particles.

4. **Calculate the Effective Concentration of Particles**:
For each concentration, calculate the effective concentration of particles:
- For 0.1 m K₂SO₄:
\[ \text{Effective concentration} = 0.1 \, \text{m} \times 3 = 0.3 \, \text{m} \]
- For 0.01 m K₂SO₄:
\[ \text{Effective concentration} = 0.01 \, \text{m} \times 3 = 0.03 \, \text{m} \]
- For 0.001 m K₂SO₄:
\[ \text{Effective concentration} = 0.001 \, \text{m} \times 3 = 0.003 \, \text{m} \]
- For 0.0001 m K₂SO₄:
\[ \text{Effective concentration} = 0.0001 \, \text{m} \times 3 = 0.0003 \, \text{m} \]

**Hint**: Multiply the molality by the number of ions produced by the dissociation of the solute.

5. **Compare the Effective Concentrations**:
Now, compare the effective concentrations calculated:
- 0.3 m (from 0.1 m solution)
- 0.03 m (from 0.01 m solution)
- 0.003 m (from 0.001 m solution)
- 0.0003 m (from 0.0001 m solution)

The highest effective concentration is 0.3 m from the 0.1 m solution.

**Hint**: Identify which value is the largest to determine which solution has the maximum colligative property.

6. **Conclusion**:
Since the 0.1 m solution has the highest effective concentration of particles, it corresponds to the maximum value of colligative property.

**Final Answer**: The maximum value of colligative property corresponds to the 0.1 m solution of K₂SO₄.