An octahedral complex is prepared by mixing CoCl3 and NH3 in the molar ratio 1 : 4, 0.1 m solution of this complex was found to freeze at 0.372°C. What is the formula of the complex? Given that molal depression constant (Kf) for water = 1.86°C/m.

Answer

To solve the problem, we need to determine the formula of the octahedral complex formed by mixing CoCl3 and NH3 in a 1:4 molar ratio, given the freezing point depression of the solution.

### Step-by-Step Solution:

1. **Understanding Freezing Point Depression**:
The freezing point depression (ΔTf) can be calculated using the formula:
\[ \Delta T_f = K_f \times m \]
where:
- \( K_f \) is the molal depression constant (1.86°C/m for water).
- \( m \) is the molality of the solution.

2. **Calculating Theoretical Freezing Point Depression**:
Given that the molality \( m \) of the solution is 0.1 m, we can substitute the values into the formula:
\[ \Delta T_f = 1.86 \, \text{°C/m} \times 0.1 \, \text{m} = 0.186 \, \text{°C} \]

3. **Finding Observed Freezing Point Depression**:
The problem states that the observed freezing point depression is 0.372°C.

4. **Comparing Theoretical and Observed Values**:
We can see that the observed ΔTf (0.372°C) is greater than the theoretical ΔTf (0.186°C). Specifically, we can calculate the ratio:
\[ \text{Ratio} = \frac{0.372}{0.186} = 2 \]
This indicates that the observed freezing point depression is twice the theoretical value.

5. **Interpreting the Ratio**:
The fact that the observed value is twice the theoretical value suggests that each formula unit of the complex dissociates into two ions in solution.

6. **Determining the Formula of the Complex**:
Given that CoCl3 is mixed with NH3 in a 1:4 ratio, we can deduce the formula of the complex. The complex likely takes the form:
\[ \text{[Co(NH}_3\text{)}_4\text{Cl}_2\text{Cl]} \]
This indicates that one Co ion is coordinated with four NH3 ligands and two Cl ions, leading to the dissociation into two ions in solution.

### Conclusion:
The formula of the octahedral complex is:
\[ \text{[Co(NH}_3\text{)}_4\text{Cl}_2\text{Cl]} \]