Molal depression constant for a solvent is `4.0 kg mol^(-1)`. The depression in the freezing point of the solvent for `0.03 mol kg^(-1)` solution of `K_(2)SO_(4)` is : (Assume complete dissociation of the electrolyte)

Options

A. 0.18 K
B. 0.24 K
C. 0.12 K
D. 0.36 K

Answer

To solve the problem, we need to calculate the depression in freezing point (ΔTf) for a 0.03 mol/kg solution of K₂SO₄, given that the molal depression constant (Kf) for the solvent is 4.0 kg mol⁻¹.

### Step-by-Step Solution:

1. **Identify the given values:**
- Molar depression constant (Kf) = 4.0 kg mol⁻¹
- Molality (m) = 0.03 mol/kg

2. **Determine the dissociation of K₂SO₄:**
K₂SO₄ dissociates completely in solution to produce:
- 2 K⁺ ions
- 1 SO₄²⁻ ion

Therefore, for every 1 mole of K₂SO₄, we get a total of 3 moles of ions (2 from K⁺ and 1 from SO₄²⁻).

3. **Calculate the Van't Hoff factor (i):**
The Van't Hoff factor (i) is the total number of particles in solution after dissociation. For K₂SO₄:
\[ i = 2 + 1 = 3 \]

4. **Use the formula for depression in freezing point:**
The formula for depression in freezing point is given by:
\[ \Delta Tf = Kf \cdot m \cdot i \]
Where:
- ΔTf = depression in freezing point
- Kf = molal depression constant
- m = molality of the solution
- i = Van't Hoff factor

5. **Substitute the values into the formula:**
\[ \Delta Tf = 4.0 \, \text{kg mol}^{-1} \cdot 0.03 \, \text{mol kg}^{-1} \cdot 3 \]

6. **Calculate ΔTf:**
\[ \Delta Tf = 4.0 \cdot 0.03 \cdot 3 = 0.36 \, \text{K} \]

### Final Answer:
The depression in the freezing point of the solvent for a 0.03 mol/kg solution of K₂SO₄ is **0.36 K**.