Which of the following solutions has the minimum freezing point

Options

A. 1 molal NaCl solution
B. 1 molal KCl solution
C. `1 molal CaCl_(2)` solution
D. 1 molal urea solution

Explanation

To determine which of the given solutions has the minimum freezing point, we can follow these steps:

### Step 1: Understand Freezing Point Depression
The freezing point depression (\( \Delta T_f \)) is related to the concentration of solute particles in a solution. The formula for freezing point depression is given by:

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

Where:
- \( \Delta T_f \) = depression in freezing point
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( K_f \) = freezing point depression constant (specific to the solvent)
- \( m \) = molality of the solution

### Step 2: Identify the van 't Hoff Factor (i)
For each solute, we need to determine the van 't Hoff factor \( i \):
- For NaCl: \( i = 2 \) (dissociates into Na\(^+\) and Cl\(^-\))
- For KCl: \( i = 2 \) (dissociates into K\(^+\) and Cl\(^-\))
- For Cl\(_2\): \( i = 3 \) (dissociates into 2 Cl\(^-\) and 1 Cl\(^+\))
- For Urea: \( i = 1 \) (does not dissociate)

### Step 3: Compare the van 't Hoff Factors
Now we can compare the values of \( i \):
- NaCl: \( i = 2 \)
- KCl: \( i = 2 \)
- Cl\(_2\): \( i = 3 \)
- Urea: \( i = 1 \)

### Step 4: Determine the Freezing Point Depression
Since the freezing point depression is directly proportional to the van 't Hoff factor, the greater the value of \( i \), the greater the depression in freezing point. Therefore:
- Cl\(_2\) has the highest van 't Hoff factor (3), which means it will cause the greatest depression in freezing point.

### Step 5: Conclusion
Thus, the solution with the minimum freezing point is the one containing Cl\(_2\).

**Final Answer: Cl\(_2\) solution has the minimum freezing point.**

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