Which of the following `0.10 m` aqueous solution will have the lowest freezing point?

Options

A. `Al_(2)(SO_(4))_(3)`
B. `C_(5)H_(10)O_(5)`
C. Kl
D. `C_(12)H_(22)O_(11)`

Explanation

To determine which of the following 0.10 m aqueous solutions will have the lowest freezing point, we will use the concept of freezing point depression. The freezing point depression (ΔTf) is given by the formula:

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

Where:
- \( \Delta T_f \) = depression in freezing point
- \( K_f \) = freezing point depression constant (for water, this is a constant)
- \( m \) = molality of the solution (which is given as 0.10 m for all solutions)
- \( i \) = van 't Hoff factor (the number of particles the solute breaks into in solution)

Since \( K_f \) and \( m \) are constant for all solutions, the freezing point depression depends solely on the van 't Hoff factor \( i \). The greater the value of \( i \), the lower the freezing point will be.

Now, let's analyze the van 't Hoff factor \( i \) for each solute:

1. **Aluminum sulfate (Al₂(SO₄)₃)**:
- Dissociates into 2 Al³⁺ ions and 3 SO₄²⁻ ions.
- Total particles = 2 + 3 = 5
- Therefore, \( i = 5 \).

2. **Organic compound (let's assume it does not ionize)**:
- Since it does not dissociate into ions, \( i = 1 \).

3. **Potassium iodide (KI)**:
- Dissociates into K⁺ and I⁻ ions.
- Total particles = 1 + 1 = 2
- Therefore, \( i = 2 \).

4. **Sucrose**:
- A non-electrolyte that does not dissociate in solution.
- Therefore, \( i = 1 \).

Now we can summarize the van 't Hoff factors:
- Aluminum sulfate: \( i = 5 \)
- Organic compound: \( i = 1 \)
- Potassium iodide: \( i = 2 \)
- Sucrose: \( i = 1 \)

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

Thus, the solution with the lowest freezing point is the **0.10 m aqueous solution of Aluminum sulfate (Al₂(SO₄)₃)**.

**Final Answer**: The 0.10 m aqueous solution of Aluminum sulfate (Al₂(SO₄)₃) will have the lowest freezing point.

---