When one mole of `CoCl_(3).5NH_(3)` was treated with excess of silver nitrate solution, 2 mol of `AgCl` was precipitated. The formula of the compound is:
(a) `[Co(NH_(3))_(5)Cl_(2)]Cl`
(b) `[Co(NH_(3))_(5)Cl]Cl_(2)`
(c) `[Co(NH_(3))_(4)Cl_(2)](NH_(3))Cl`
(d) `[Co(NH_(3))_(3)Cl_(3)](NH_(3))_(2)`

Options

A. `[Co(NH_(3))_(5)Cl_(2)]Cl`
B. `[Co(NH_(3))_(5)Cl]Cl_(2)`
C. `[Co(NH_(3))_(4)Cl_(2)](NH_(3))Cl`
D. `[Co(NH_(3))_(3)Cl_(3)](NH_(3))_(2)`

Answer

To solve the problem, we need to analyze the information provided and determine the correct formula of the compound based on the precipitation of silver chloride (AgCl) when treated with silver nitrate.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- We start with one mole of `CoCl3·5NH3` (cobalt trichloride pentamine).
- When treated with excess silver nitrate, we observe that 2 moles of AgCl are precipitated.

2. **Analyzing the Precipitation**:
- The formation of AgCl indicates that chloride ions (Cl⁻) are present in the solution.
- Since 2 moles of AgCl are formed, this means there are 2 moles of Cl⁻ ions that have reacted with silver ions (Ag⁺).

3. **Determining the Source of Chloride Ions**:
- In coordination compounds, chloride ions can be either part of the coordination sphere (bonded to the metal) or outside the coordination sphere (free ions).
- The chloride ions that precipitate as AgCl must come from the ions that are not part of the coordination sphere.

4. **Identifying the Coordination Compound**:
- The formula `CoCl3·5NH3` suggests that there are 3 chloride ions associated with cobalt.
- If 2 of these chloride ions are free (outside the coordination sphere), it implies that 1 chloride ion is part of the coordination sphere.

5. **Formulating the Compound**:
- Since we have 5 ammonia (NH3) ligands and 1 chloride ion in the coordination sphere, the remaining 2 chloride ions must be outside.
- This leads us to the formula: `[Co(NH3)5Cl]Cl2`, where 1 Cl is coordinated to Co and 2 Cl are free.

6. **Conclusion**:
- Therefore, the correct formula of the compound is `[Co(NH3)5Cl]Cl2`, which corresponds to option (b).

### Final Answer:
(b) `[Co(NH3)5Cl]Cl2`