Which has the highest freezing point at 1 atm ?

Options

A. 0.1 m NaCl solution
B. 0.1 m ` BaCl_(2)` solution
C. 0.1 m sugar solution
D. 0.1 m `FeCl_(2)` solution

Answer

To determine which solution has the highest freezing point at 1 atm, 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:
- \(\Delta T_f\) = depression in freezing point
- \(i\) = Van't Hoff factor (number of particles the solute dissociates into)
- \(K_f\) = freezing point depression constant (specific to the solvent)
- \(m\) = molality of the solution

### Step 2: Analyze the Given Solutions
We have four solutions with the same molality (0.1 molal):
1. 0.1 molal NaCl
2. 0.1 molal BaCl2
3. 0.1 molal Sugar
4. 0.1 molal FeCl2

### Step 3: Calculate the Van't Hoff Factor (i)
- For **NaCl**: It dissociates into 2 ions (Na⁺ and Cl⁻), so \(i = 2\).
- For **BaCl2**: It dissociates into 3 ions (Ba²⁺ and 2 Cl⁻), so \(i = 3\).
- For **Sugar**: It does not dissociate (non-electrolyte), so \(i = 1\).
- For **FeCl2**: It dissociates into 3 ions (Fe²⁺ and 2 Cl⁻), so \(i = 3\).

### Step 4: Compare the Van't Hoff Factors
Now we list the Van't Hoff factors:
- NaCl: \(i = 2\)
- BaCl2: \(i = 3\)
- Sugar: \(i = 1\)
- FeCl2: \(i = 3\)

### Step 5: Determine the Depression in Freezing Point
Since all solutions have the same molality and the same \(K_f\), the depression in freezing point (\(\Delta T_f\)) will depend solely on the Van't Hoff factor \(i\):
- Higher \(i\) means greater depression in freezing point.
- Lower \(i\) means lesser depression in freezing point.

### Step 6: Identify the Solution with the Highest Freezing Point
From the values of \(i\):
- Sugar has the lowest \(i = 1\), which means it will have the least depression in freezing point.
- Therefore, the solution with the highest freezing point is the one with sugar.

### Conclusion
The solution with the highest freezing point at 1 atm is **0.1 molal Sugar**.

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