A coordination compound of cobalt has the molecular formula containing five ammonia molecules, one nitro group and two chlorine atoms for one cobalt atom. One mole of this compound produces three ions in an aqueous solution. On reacting this solution with excess of `AgNO_(3)` solution, we get two moles of AgCI precipitates. The ionic formula for this complex would be

Options

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

Explanation

To solve the problem step by step, we will analyze the information provided and deduce the ionic formula for the coordination compound of cobalt.

### Step 1: Identify the components of the coordination compound
The coordination compound of cobalt has:
- 5 ammonia (NH₃) molecules
- 1 nitro (NO₂) group
- 2 chlorine (Cl) atoms
- 1 cobalt (Co) atom

### Step 2: Determine the overall charge of the complex
Ammonia (NH₃) is a neutral ligand, contributing no charge. The nitro group (NO₂) acts as a unidentate ligand and typically has a -1 charge when it coordinates to a metal. Each chloride ion (Cl⁻) has a -1 charge.

Thus, the charges can be summed up as follows:
- Charge from 1 nitro group: -1
- Charge from 2 chloride ions: 2 × (-1) = -2
- Total charge from ligands: -1 - 2 = -3

Let the charge on the cobalt ion be \( x \). The overall charge of the complex can be expressed as:
\[ x - 3 = 0 \]
This implies that \( x = +3 \). Therefore, cobalt is in the +3 oxidation state.

### Step 3: Analyze the dissociation in aqueous solution
The problem states that one mole of this compound produces three ions in an aqueous solution. This means that the dissociation can be represented as:
\[ [Co(NH₃)_5(NO₂)]^{3+} + 2Cl^- \rightarrow 3 \text{ ions} \]

Here, the complex cation \( [Co(NH₃)_5(NO₂)]^{3+} \) contributes 1 ion, and the 2 chloride ions contribute 2 more ions, totaling 3 ions.

### Step 4: Reaction with AgNO₃
When the solution reacts with excess AgNO₃, it forms 2 moles of AgCl precipitate. Since AgCl is formed from the chloride ions, it confirms that there are indeed 2 chloride ions present in the solution.

### Step 5: Write the final ionic formula
Based on the analysis, the ionic formula for the complex can be written as:
\[ [Co(NH₃)_5(NO₂)]Cl_2 \]

### Conclusion
The ionic formula for the coordination compound of cobalt is:
\[ [Co(NH₃)_5(NO₂)]Cl_2 \]