Which of the following solutions has maximum freezing point depression at equimolal concentration ?

Options

A. `[Co(H_2O)_6]Cl_3`
B. `[Co(H_2O)_6Cl]Cl_2.H_2O`
C. `[Co(H_2O)_4Cl]Cl.2H_2O`
D. `[Co(H_2O)_3Cl_3].3H_2O`

Answer

To solve the question of which solution has the maximum freezing point depression at equimolar concentrations, we will follow these steps:

### Step 1: Understand the Formula for Freezing Point Depression
The freezing point depression (\( \Delta T_f \)) 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)
- \( K_f \) = freezing point depression constant (specific to the solvent)
- \( m \) = molality of the solution

Since we are considering equimolar concentrations, the molality (\( m \)) is constant for all solutions.

### Step 2: Identify the Van 't Hoff Factor for Each Compound
We will analyze each compound to determine the van 't Hoff factor (\( i \)), which is the number of particles produced when the compound dissolves.

1. **First Compound**: Cobalt(III) chloride hexahydrate (\( \text{CoCl}_3 \cdot 6\text{H}_2\text{O} \))
- Dissociates into: \( 3 \text{Cl}^- + \text{Co}^{3+} \)
- Total ions = 3 + 1 = **4** (i = 4)

2. **Second Compound**: Cobalt(II) chloride pentahydrate (\( \text{CoCl}_2 \cdot 5\text{H}_2\text{O} \))
- Dissociates into: \( 2 \text{Cl}^- + \text{Co}^{2+} \)
- Total ions = 2 + 1 = **3** (i = 3)

3. **Third Compound**: Cobalt(II) chloride tetrahydrate (\( \text{CoCl}_2 \cdot 4\text{H}_2\text{O} \))
- Dissociates into: \( \text{Cl}^- + \text{Co}^{2+} \)
- Total ions = 1 + 1 = **2** (i = 2)

4. **Fourth Compound**: Cobalt(II) chloride (\( \text{CoCl}_2 \))
- Does not dissociate further in solution.
- Total ions = **1** (i = 1)

### Step 3: Compare the Van 't Hoff Factors
Now we compare the van 't Hoff factors calculated:
- First Compound: \( i = 4 \)
- Second Compound: \( i = 3 \)
- Third Compound: \( i = 2 \)
- Fourth Compound: \( i = 1 \)

### Step 4: Determine the Maximum Freezing Point Depression
Since the freezing point depression is directly proportional to the van 't Hoff factor, the solution with the highest van 't Hoff factor will have the maximum freezing point depression.

Thus, the first compound with \( i = 4 \) will have the maximum freezing point depression.

### Conclusion
The solution with the maximum freezing point depression at equimolar concentrations is the **first compound**.

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