Which of the following `0.1 M` aqueous solutions will have the lowest freezing point?

Options

A. Potassium sulphate
B. Sodium chloride
C. Urea
D. Glucose

Explanation

To determine which of the following `0.1 M` aqueous solutions will have the lowest freezing point, we need to calculate the depression in freezing point (ΔTf) for each solution. The depression in freezing point is given by the formula:

\[ \Delta Tf = i \cdot K_f \cdot m \]

Where:
- \( \Delta Tf \) = depression in freezing point
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( K_f \) = freezing point depression constant (a property of the solvent, which is constant for water)
- \( m \) = molality of the solution (for dilute solutions, we can assume molality and molarity are approximately equal)

Since all solutions are `0.1 M`, we can focus on the van 't Hoff factor \( i \) for each solute to determine which solution will have the lowest freezing point.

### Step-by-Step Solution:

1. **Identify the van 't Hoff factor (i) for each solute:**
- **K2SO4 (Potassium sulfate):**
- Dissociates into 2 K⁺ ions and 1 SO₄²⁻ ion.
- \( i = 2 + 1 = 3 \)

- **NaCl (Sodium chloride):**
- Dissociates into 1 Na⁺ ion and 1 Cl⁻ ion.
- \( i = 1 + 1 = 2 \)

- **Urea:**
- A non-electrolyte, does not dissociate.
- \( i = 1 \)

- **Glucose:**
- Also a non-electrolyte, does not dissociate.
- \( i = 1 \)

2. **Calculate ΔTf for each solution:**
- Since \( K_f \) is constant and the same for all solutions, we can compare the values of \( i \) directly to determine the depression in freezing point.
- For K2SO4: \( \Delta Tf \propto 3 \)
- For NaCl: \( \Delta Tf \propto 2 \)
- For Urea: \( \Delta Tf \propto 1 \)
- For Glucose: \( \Delta Tf \propto 1 \)

3. **Determine which solution has the lowest freezing point:**
- The solution with the highest van 't Hoff factor will have the greatest depression in freezing point.
- K2SO4 has the highest \( i \) value of 3, followed by NaCl with 2, and both urea and glucose with 1.

4. **Conclusion:**
- Therefore, the `0.1 M` aqueous solution of K2SO4 will have the lowest freezing point.

### Final Answer:
The `0.1 M` aqueous solution with the lowest freezing point is **K2SO4**.