Which of the following exhibits the greatest freezing point lowering per mole of solute ?

Options

A. 0.01 m NaCl
B. 0.1 m NaCl
C. 0.01 m `C_2H_5OH`
D. 0.1 m `C_2H_5OH`

Answer

To solve the problem of determining which of the following exhibits the greatest freezing point lowering per mole of solute, we will follow these steps:

### Step 1: Understand the Freezing Point Depression Formula
The freezing point depression (\( \Delta T_f \)) is given by the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \( \Delta T_f \) = change in freezing point,
- \( i \) = van 't Hoff factor (number of particles the solute breaks into),
- \( K_f \) = freezing point depression constant of the solvent,
- \( m \) = molality of the solution.

### Step 2: Identify the Van 't Hoff Factor for Each Solute
1. **NaCl** dissociates into 2 ions: \( Na^+ \) and \( Cl^- \), so \( i = 2 \).
2. **KCl** also dissociates into 2 ions: \( K^+ \) and \( Cl^- \), so \( i = 2 \).
3. **CaCl2** dissociates into 3 ions: \( Ca^{2+} \) and 2 \( Cl^- \), so \( i = 3 \).
4. **MgSO4** dissociates into 2 ions: \( Mg^{2+} \) and \( SO_4^{2-} \), so \( i = 2 \).

### Step 3: Determine the Molality of Each Solution
Assuming we have the following molalities for each solute:
- NaCl: 0.01 m
- KCl: 0.1 m
- CaCl2: 0.1 m
- MgSO4: 0.1 m

### Step 4: Calculate the Freezing Point Depression for Each Solute
Using the formula \( \Delta T_f = i \cdot K_f \cdot m \):
1. **For NaCl**:
\[ \Delta T_f = 2 \cdot K_f \cdot 0.01 \]
2. **For KCl**:
\[ \Delta T_f = 2 \cdot K_f \cdot 0.1 \]
3. **For CaCl2**:
\[ \Delta T_f = 3 \cdot K_f \cdot 0.1 \]
4. **For MgSO4**:
\[ \Delta T_f = 2 \cdot K_f \cdot 0.1 \]

### Step 5: Compare the Values
Now we can compare the values:
- NaCl: \( 2 \cdot K_f \cdot 0.01 = 0.02 K_f \)
- KCl: \( 2 \cdot K_f \cdot 0.1 = 0.2 K_f \)
- CaCl2: \( 3 \cdot K_f \cdot 0.1 = 0.3 K_f \)
- MgSO4: \( 2 \cdot K_f \cdot 0.1 = 0.2 K_f \)

### Conclusion
The greatest freezing point lowering per mole of solute is exhibited by **CaCl2** with a value of \( 0.3 K_f \).