One mole of complex compound `Co(NH_3)_5Cl_3` gives 3 moles of ions on dissolution in water. One mole of same complex reacts with two moles of `AgNO_3` to yield two moles of `AgCl(s)`. The complex is:

Options

A. (a) `[Co(NH_3)_4Cl_2]Cl.NH_3`
B. (b) `[Co(NH_3)_4Cl]Cl_2.NH_3`
C. (c) `[Co(NH_3)_5Cl]Cl_2`
D. (d) `[Co(NH_3)_3Cl_3].2NH_3`

Explanation

To solve the problem, we need to analyze the given complex compound `Co(NH3)5Cl3` based on the information provided.

### Step-by-step Solution:

1. **Understanding the Dissociation of the Complex**:
- The complex `Co(NH3)5Cl3` dissociates in water to produce ions. According to the question, 1 mole of this complex gives 3 moles of ions upon dissolution.
- The dissociation can be represented as:
\[ Co(NH3)_5Cl_3 \rightarrow Co(NH3)_5^{3+} + 3Cl^{-} \]
- Here, the complex ion `Co(NH3)5^{3+}` is a cation and the chloride ions `Cl^{-}` are anions.

2. **Counting the Ions**:
- From the dissociation, we can see that:
- 1 mole of `Co(NH3)5^{3+}` produces 1 mole of cation.
- 3 moles of `Cl^{-}` produce 3 moles of anions.
- Therefore, the total number of moles of ions produced is:
\[ 1 \text{ (cation)} + 3 \text{ (anions)} = 4 \text{ moles of ions} \]
- However, we need to ensure that the total count aligns with the information given in the question, which states that 1 mole of the complex gives 3 moles of ions.

3. **Analyzing the Reaction with AgNO3**:
- The complex reacts with 2 moles of `AgNO3` to yield 2 moles of `AgCl(s)`.
- This indicates that 2 chloride ions are involved in the reaction, which suggests that there are 2 chloride ions outside the coordination sphere of the complex.
- Therefore, the structure of the complex can be inferred as:
\[ Co(NH3)_5Cl^{2+} + 2Cl^{-} \]
- This means that the complex has 5 ammonia ligands and 1 chloride ion coordinated to cobalt.

4. **Final Structure of the Complex**:
- The final structure of the complex can be written as:
\[ [Co(NH3)_5Cl]^{2+} + 2Cl^{-} \]
- This confirms that the complex is indeed `Co(NH3)5Cl2`, which aligns with the information provided.

5. **Conclusion**:
- The complex that satisfies both conditions (dissociating to give 3 moles of ions and reacting with 2 moles of `AgNO3` to yield 2 moles of `AgCl`) is:
\[ [Co(NH3)_5Cl]Cl_2 \]

### Final Answer:
The complex is `Co(NH3)5Cl2`.

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