Which aqueous solution has minimum freezing point?

Options

A. 0.01 m `NaCl`
B. 0.005 m `MgCl_(2)`
C. 0.005 m `C_(2)H_(5)OH`
D. 0.005 m `MgSO_(4)`

Explanation

To determine which aqueous solution has the minimum freezing point, we can follow these steps:

### Step 1: Understand Freezing Point Depression
The freezing point depression (\( \Delta T_f \)) can be expressed as:
\[ \Delta T_f = i \cdot m \cdot k_f \]
where:
- \( i \) = Van't Hoff factor (number of particles the solute dissociates into)
- \( m \) = molality of the solution
- \( k_f \) = freezing point depression constant (a property of the solvent)

### Step 2: Identify the Solutions and Their Properties
We will analyze the following solutions:
1. NaCl (sodium chloride)
2. MgCl2 (magnesium chloride)
3. C2H5OH (ethanol)
4. MgSO4 (magnesium sulfate)

### Step 3: Calculate \( i \) for Each Solution
- **NaCl**: Dissociates into Na\(^+\) and Cl\(^-\) (2 ions)
\[ i = 2 \]

- **MgCl2**: Dissociates into Mg\(^{2+}\) and 2 Cl\(^-\) (3 ions)
\[ i = 3 \]

- **C2H5OH**: Does not dissociate (1 molecule)
\[ i = 1 \]

- **MgSO4**: Dissociates into Mg\(^{2+}\) and SO4\(^{2-}\) (2 ions)
\[ i = 2 \]

### Step 4: Calculate \( \Delta T_f \) for Each Solution
Assuming the following molalities:
- NaCl: 0.01 m
- MgCl2: 0.005 m
- C2H5OH: 0.005 m
- MgSO4: 0.005 m

Now we calculate \( \Delta T_f \):
1. **For NaCl**:
\[ \Delta T_f = i \cdot m = 2 \cdot 0.01 = 0.02 \]

2. **For MgCl2**:
\[ \Delta T_f = i \cdot m = 3 \cdot 0.005 = 0.015 \]

3. **For C2H5OH**:
\[ \Delta T_f = i \cdot m = 1 \cdot 0.005 = 0.005 \]

4. **For MgSO4**:
\[ \Delta T_f = i \cdot m = 2 \cdot 0.005 = 0.01 \]

### Step 5: Compare \( \Delta T_f \) Values
- NaCl: 0.02
- MgCl2: 0.015
- C2H5OH: 0.005
- MgSO4: 0.01

### Step 6: Determine the Minimum Freezing Point
The freezing point of the solution decreases as \( \Delta T_f \) increases. Therefore, the solution with the highest \( \Delta T_f \) will have the lowest freezing point.

From our calculations, NaCl has the highest \( \Delta T_f \) of 0.02, which means it will have the minimum freezing point.

### Final Answer
The aqueous solution with the minimum freezing point is **NaCl**.

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