Which of these has the least freezing point?

Options

A. 1% sucrose
B. 1% NaCl
C. `1% CaCl_(2)`
D. 1% glucose

Answer

To determine which of the given solutions has the least freezing point, we need to analyze the freezing point depression caused by each solute. The freezing point depression can be calculated using 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 in this case).
- \(m\) is the molality of the solution.

### Step 1: Identify the Van't Hoff factors for each solute.
1. **Sucrose**: A non-electrolyte, does not dissociate. Therefore, \(i = 1\).
2. **Glucose**: Also a non-electrolyte, does not dissociate. Therefore, \(i = 1\).
3. **Sodium Chloride (NaCl)**: Dissociates into 1 sodium ion (Na\(^+\)) and 1 chloride ion (Cl\(^-\)). Therefore, \(i = 2\).
4. **Calcium Chloride (CaCl\(_2\))**: Dissociates into 1 calcium ion (Ca\(^{2+}\)) and 2 chloride ions (Cl\(^-\)). Therefore, \(i = 3\).

### Step 2: Compare the Van't Hoff factors.
- Sucrose: \(i = 1\)
- Glucose: \(i = 1\)
- NaCl: \(i = 2\)
- Calcium Chloride: \(i = 3\)

### Step 3: Determine the depression in freezing point.
Since the molality (\(m\)) and \(K_f\) are constant for all solutions, the depression in freezing point (\(\Delta T_f\)) will depend solely on the Van't Hoff factor (\(i\)):
- For Sucrose: \(\Delta T_f = 1 \cdot K_f \cdot m\)
- For Glucose: \(\Delta T_f = 1 \cdot K_f \cdot m\)
- For NaCl: \(\Delta T_f = 2 \cdot K_f \cdot m\)
- For Calcium Chloride: \(\Delta T_f = 3 \cdot K_f \cdot m\)

### Step 4: Identify which solution has the greatest depression in freezing point.
The solution with the highest Van't Hoff factor will have the greatest depression in freezing point:
- Calcium Chloride has the highest \(i\) value of 3.

### Conclusion:
Since Calcium Chloride has the highest Van't Hoff factor, it will cause the greatest depression in freezing point, leading to the lowest freezing point among the given solutions. Therefore, the solution with the least freezing point is:

**Calcium Chloride (1% CaCl\(_2\))**.