Which of the following has the highest freezing point ?

Options

A. 1 m NaCl solution
B. 1 m KCl solution
C. 1 m `AlCl_3` solution
D. 1 m `C_6H_12O_6` solution

Explanation

To determine which of the given solutions has the highest freezing point, we need to analyze the colligative properties of each solution. The freezing point depression can be calculated using the formula:

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

Where:
- \(\Delta T_f\) = depression in freezing point
- \(i\) = Van't Hoff factor (number of particles the solute dissociates into)
- \(K_f\) = cryoscopic constant (constant for the solvent, in this case, water)
- \(m\) = molality of the solution

Since \(K_f\) is constant for all solutions in water, we can focus on maximizing the product \(i \cdot m\) to determine which solution has the highest freezing point.

### Step 1: Identify the Van't Hoff factor (\(i\)) and molality (\(m\)) for each solute.

1. **NaCl**:
- \(i = 2\) (dissociates into Na\(^+\) and Cl\(^-\))
- \(m = 1\)
- \(i \cdot m = 2 \cdot 1 = 2\)

2. **KCl**:
- \(i = 2\) (dissociates into K\(^+\) and Cl\(^-\))
- \(m = 1\)
- \(i \cdot m = 2 \cdot 1 = 2\)

3. **AlCl\(_3\)**:
- \(i = 4\) (dissociates into Al\(^{3+}\) and 3 Cl\(^-\))
- \(m = 1\)
- \(i \cdot m = 4 \cdot 1 = 4\)

4. **Glucose**:
- \(i = 1\) (does not dissociate)
- \(m = 1\)
- \(i \cdot m = 1 \cdot 1 = 1\)

### Step 2: Compare the values of \(i \cdot m\).

- NaCl: \(i \cdot m = 2\)
- KCl: \(i \cdot m = 2\)
- AlCl\(_3\): \(i \cdot m = 4\)
- Glucose: \(i \cdot m = 1\)

### Step 3: Determine the solution with the highest freezing point.

The solution with the highest value of \(i \cdot m\) will have the greatest depression in freezing point, which means it will have the lowest freezing point. Conversely, the solution with the lowest value of \(i \cdot m\) will have the least depression in freezing point, thus the highest freezing point.

From our calculations:
- AlCl\(_3\) has the highest \(i \cdot m\) value (4), indicating it has the greatest depression in freezing point.
- Glucose has the lowest \(i \cdot m\) value (1), indicating it has the least depression in freezing point.

### Conclusion:

Thus, the solution with the highest freezing point is **Glucose**.

### Final Answer:

**Glucose (Option D) has the highest freezing point.**

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