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 problem of determining which solution has the maximum freezing point depression at equimolar concentration, 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:
\[ \Delta T_f = k_f \cdot m \cdot i \]
where:
- \( k_f \) is the cryoscopic constant (a property of the solvent),
- \( m \) is the molality of the solution,
- \( i \) is the Van't Hoff factor (the number of particles the solute dissociates into).

### Step 2: Identify the Importance of Van't Hoff Factor
Since we are given that the concentration (or molality) is equimolar for all solutions, the freezing point depression will depend primarily on the Van't Hoff factor (\( i \)). The higher the \( i \) value, the greater the freezing point depression.

### Step 3: Analyze Each Compound
We will analyze the dissociation of each cobalt complex to determine the \( i \) value.

1. **Cobalt H2O\(_6\)Cl\(_3\)**:
- Dissociates into: 1 Co\(^{3+}\) and 3 Cl\(^{-}\).
- Total ions = 1 + 3 = 4.
- \( i = 4 \).

2. **Cobalt H2O\(_5\)Cl\(_2\)Cl\)**:
- Dissociates into: 1 Co\(^{3+}\) and 2 Cl\(^{-}\).
- Total ions = 1 + 2 = 3.
- \( i = 3 \).

3. **Cobalt H2O\(_4\)Cl\(_2\)**:
- Dissociates into: 1 Co\(^{3+}\) and 2 Cl\(^{-}\).
- Total ions = 1 + 2 = 3.
- \( i = 3 \).

4. **Cobalt H2O\(_3\)Cl\(_3\)**:
- Does not dissociate significantly, remains as a whole compound.
- Total ions = 1.
- \( i = 1 \).

### Step 4: Compare the \( i \) Values
Now we compare the \( i \) values calculated:
- Cobalt H2O\(_6\)Cl\(_3\): \( i = 4 \)
- Cobalt H2O\(_5\)Cl\(_2\)Cl: \( i = 3 \)
- Cobalt H2O\(_4\)Cl\(_2\): \( i = 3 \)
- Cobalt H2O\(_3\)Cl\(_3\): \( i = 1 \)

### Step 5: Conclusion
Since the freezing point depression is directly proportional to the \( i \) value, the solution with the highest \( i \) value will have the maximum freezing point depression. Therefore, the solution with the maximum freezing point depression at equimolar concentration is:

**Cobalt H2O\(_6\)Cl\(_3\)** (Option 1).