When `AgNO_(3)` solution is added in excess to 1 M solution of `CoCl_(3).XNH_(3)` one mole of `AgCl` is formed? What is the value of 'X' ? (Assume that the co - ordination number is 6)

Options

A. 1
B. 4
C. 3
D. 2

Answer

To solve the problem, we need to analyze the reaction between the silver nitrate solution (AgNO₃) and the cobalt(III) chloride-ammonia complex (CoCl₃·XNH₃). We are given that when AgNO₃ is added in excess to a 1 M solution of CoCl₃·XNH₃, one mole of AgCl is formed. We also know that the coordination number of cobalt (Co) is 6.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- When AgNO₃ is added to CoCl₃·XNH₃, Ag⁺ ions react with Cl⁻ ions to form AgCl, which precipitates out of the solution.
- The formation of 1 mole of AgCl indicates that there is 1 mole of Cl⁻ ions available outside the coordination sphere of the cobalt complex.

2. **Analyzing the Coordination Sphere**:
- The cobalt complex CoCl₃·XNH₃ consists of cobalt coordinated with chloride ions and ammonia ligands.
- The coordination number of cobalt is given as 6. This means that cobalt can coordinate with a total of 6 ligands.

3. **Identifying Chloride Ions**:
- The formula CoCl₃·XNH₃ indicates that there are 3 chloride ions (Cl⁻) in total. However, since 1 Cl⁻ is outside the coordination sphere (as indicated by the formation of AgCl), this means that 2 Cl⁻ ions are coordinated to cobalt.
- Therefore, the number of coordinated Cl⁻ ions is 2.

4. **Determining the Number of Ammonia Ligands**:
- Since the coordination number is 6 and we have established that 2 of those coordination sites are occupied by Cl⁻ ions, we can find the number of ammonia ligands (NH₃) that must be present.
- The equation for the coordination number can be expressed as:
\[ \text{Coordination Number} = \text{Number of Cl} + \text{Number of NH}_3 \]
\[ 6 = 2 + X \]
- Solving for X gives:
\[ X = 6 - 2 = 4 \]

5. **Conclusion**:
- The value of X, which represents the number of ammonia ligands in the complex CoCl₃·XNH₃, is 4.

### Final Answer:
The value of X is 4.