Of the following 0.2 m aqueous solutions, which one will exhibit largest freezing point depression?

Options

A. Glucose
B. Sucrose
C. Urea
D. NaCI

Answer

To determine which of the given 0.2 m aqueous solutions will exhibit the largest freezing point depression, we can follow these steps:

### Step 1: Understand Freezing Point Depression
Freezing point depression is a colligative property, which means it depends on the number of solute particles in a solution rather than the identity of the solute. The formula for freezing point depression is given by:

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

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

### Step 2: Identify the Solutions
We need to identify the van 't Hoff factor (\(i\)) for each of the solutes in the given solutions. Let's assume we have the following solutes:
1. Glucose (C6H12O6)
2. Sucrose (C12H22O11)
3. Urea (NH2CONH2)
4. Sodium Chloride (NaCl)

### Step 3: Determine the van 't Hoff Factor for Each Solute
- **Glucose**: Does not dissociate in solution, so \(i = 1\).
- **Sucrose**: Also does not dissociate, so \(i = 1\).
- **Urea**: Does not dissociate, so \(i = 1\).
- **Sodium Chloride (NaCl)**: Dissociates into two ions (Na\(^+\) and Cl\(^-\)), so \(i = 2\).

### Step 4: Compare the van 't Hoff Factors
Since the molality (\(m\)) is the same for all solutions (0.2 m), the freezing point depression will depend solely on the van 't Hoff factor (\(i\)):
- Glucose: \(i = 1\)
- Sucrose: \(i = 1\)
- Urea: \(i = 1\)
- Sodium Chloride: \(i = 2\)

### Step 5: Determine the Largest Freezing Point Depression
From the values of \(i\):
- Glucose, Sucrose, and Urea will have the same freezing point depression.
- Sodium Chloride will have the largest freezing point depression because it has the highest \(i\) value.

### Conclusion
The solution that will exhibit the largest freezing point depression is the 0.2 m aqueous solution of Sodium Chloride (NaCl).

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