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 solute exhibits the greatest freezing point lowering per mole of solute, we will follow these steps:

### Step 1: Understand the Concept of Freezing Point Depression
The freezing point depression (ΔTf) is the decrease in the freezing point of a solvent when a solute is added. It 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 dissociates into)
- \( K_f \) = cryoscopic constant of the solvent (which is constant for a given solvent)
- \( m \) = molality of the solution

### Step 2: Identify the Given Options
We need to analyze the options provided in the question. Let's assume the options are:
1. 0.01 molal NaCl
2. 0.1 molal NaCl
3. 0.01 molal C2H5OH (ethanol)
4. 0.1 molal C2H5OH (ethanol)

### Step 3: Calculate the van 't Hoff Factor (i)
- For NaCl, which dissociates into Na⁺ and Cl⁻:
- \( i = 2 \) (since it dissociates into 2 particles)
- For C2H5OH (ethanol), which does not dissociate:
- \( i = 1 \)

### Step 4: Calculate ΔTf for Each Option
Now we will calculate ΔTf for each option using the formula:

1. **0.01 molal NaCl:**
\[ \Delta T_f = i \cdot K_f \cdot m = 2 \cdot K_f \cdot 0.01 = 0.02 K_f \]

2. **0.1 molal NaCl:**
\[ \Delta T_f = 2 \cdot K_f \cdot 0.1 = 0.2 K_f \]

3. **0.01 molal C2H5OH:**
\[ \Delta T_f = 1 \cdot K_f \cdot 0.01 = 0.01 K_f \]

4. **0.1 molal C2H5OH:**
\[ \Delta T_f = 1 \cdot K_f \cdot 0.1 = 0.1 K_f \]

### Step 5: Compare the Values of ΔTf
Now we compare the calculated values of ΔTf:
- 0.01 molal NaCl: \( 0.02 K_f \)
- 0.1 molal NaCl: \( 0.2 K_f \)
- 0.01 molal C2H5OH: \( 0.01 K_f \)
- 0.1 molal C2H5OH: \( 0.1 K_f \)

### Step 6: Determine the Greatest Freezing Point Lowering
From the calculations:
- The greatest freezing point lowering is \( 0.2 K_f \) from **0.1 molal NaCl**.

### Conclusion
The solute that exhibits the greatest freezing point lowering per mole of solute is **0.1 molal NaCl**.

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