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 determine the value of 'X' in the complex CoCl3.XNH3, given that when AgNO3 is added, one mole of AgCl is formed. We also know that the coordination number is 6.

### Step-by-Step Solution:

1. **Identify the Complex**:
We start with the complex CoCl3.XNH3. Here, Co is cobalt, Cl is chlorine, and NH3 is ammonia.

2. **Understanding the Reaction**:
When AgNO3 is added to the solution, it reacts with the chloride ions (Cl-) to form AgCl. The problem states that one mole of AgCl is formed, which indicates that there is one mole of Cl- available outside the coordination sphere.

3. **Determine Chlorine Distribution**:
Since we have CoCl3.XNH3, we know there are three chlorine atoms in total. However, since one mole of AgCl is formed, this implies that only one Cl- is outside the coordination sphere. Therefore, the remaining two Cl- must be inside the coordination sphere.

4. **Construct the Coordination Sphere**:
The coordination number is given as 6. This means that the total number of ligands (molecules that donate electron pairs to the metal) must equal 6. We have already established that there are 2 Cl- ions inside the coordination sphere.

5. **Calculate the Number of Ammonia Ligands**:
Let 'X' represent the number of NH3 ligands. The total number of ligands in the coordination sphere can be expressed as:
\[ \text{Total ligands} = \text{Cl- ions inside} + \text{NH3 ligands} = 2 + X \]
Since the coordination number is 6, we set up the equation:
\[ 2 + X = 6 \]

6. **Solve for X**:
Rearranging the equation gives:
\[ X = 6 - 2 = 4 \]

7. **Conclusion**:
Therefore, the value of X is 4. This means there are 4 NH3 ligands in the complex.

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