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 will use the concept of freezing point depression, which is a colligative property. 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 breaks into)
- \(K_f\) = freezing point depression constant (specific to the solvent)
- \(m\) = molality of the solution

### Step 1: Identify the van't Hoff factor \(i\) for each solute
1. **1% Glucose**: Glucose is a non-electrolyte, so it does not dissociate in solution. Thus, \(i = 1\).
2. **1% NaCl**: Sodium chloride dissociates into Na\(^+\) and Cl\(^-\) ions. Therefore, \(i = 2\).
3. **1% CaCl\(_2\)**: Calcium chloride dissociates into Ca\(^{2+}\) and 2 Cl\(^-\) ions. Thus, \(i = 3\).
4. **1% Sucrose**: Sucrose is also a non-electrolyte, so \(i = 1\).

### Step 2: Compare the values of \(i\)
- Glucose: \(i = 1\)
- NaCl: \(i = 2\)
- CaCl\(_2\): \(i = 3\)
- Sucrose: \(i = 1\)

### Step 3: Determine the effect on freezing point depression
Since the freezing point depression \(\Delta T_f\) is directly proportional to the van't Hoff factor \(i\), the solution with the highest \(i\) will have the greatest depression in freezing point.

### Step 4: Conclusion
Among the given options, CaCl\(_2\) has the highest van't Hoff factor (\(i = 3\)). Therefore, it will cause the greatest depression in freezing point, leading to the lowest freezing point.

Thus, the solution with the least freezing point is **1% CaCl\(_2\)**.

### Final Answer:
**1% CaCl\(_2\)** has the least freezing point.

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