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

Options

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

Explanation

To determine which 0.1 M aqueous solution has the lowest freezing point, we will use the concept of freezing point depression, which is described by the formula:

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

Where:
- \(\Delta T_f\) is the depression in freezing point,
- \(i\) is the van 't Hoff factor (the number of particles the solute dissociates into),
- \(K_f\) is the freezing point depression constant (which is the same for all solutions at a given temperature),
- \(m\) is the molality of the solution (which is the same in this case as all solutions are 0.1 M).

Since \(K_f\) and \(m\) are constant for all solutions, the freezing point depression (\(\Delta T_f\)) is directly proportional to the van 't Hoff factor (\(i\)). Therefore, to find the solution with the lowest freezing point, we need to identify which solute has the highest \(i\) value.

Let's analyze the given solutes:

1. **Potassium Sulfate (K₂SO₄)**:
- Dissociates into 2 K⁺ ions and 1 SO₄²⁻ ion.
- \(i = 2 + 1 = 3\)

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

3. **Urea**:
- Does not dissociate in solution.
- \(i = 1\)

4. **Glucose**:
- Also does not dissociate in solution.
- \(i = 1\)

Now, we can summarize the van 't Hoff factors for each solute:
- Potassium Sulfate (K₂SO₄): \(i = 3\)
- Sodium Chloride (NaCl): \(i = 2\)
- Urea: \(i = 1\)
- Glucose: \(i = 1\)

Since the freezing point depression is proportional to \(i\), the solution with the highest \(i\) value will have the lowest freezing point.

Thus, the solution with the lowest freezing point is the **0.1 M Potassium Sulfate (K₂SO₄)** solution.