In coordination chemistry there are a variety of methods applied to find out the structure of complexes.One method involves treating the complex with known reagents and from the nature of reaction, the formula of the complex can be predicted.An isomer of the complex `Co(en)_2(H_2O)Cl_2Br`,on reaction with concentrated `H_2SO_4` (dehydrating agent) it suffers loss in weight and on reaction with `AgNO_3` solution it gives a white precipitate which is soluble in `NH_3`(aq).
The correct formula of the complex is :

Options

A. `[CoClBr(en)_2] H_2O`
B. `[CoCl(en)_2 (H_2O)]BrCl`
C. `[Co Br(en)_2 (H_2O)]Cl_2`
D. `[CoBrCl(en)_2]Cl. H_2O`

Explanation

To solve the problem, we need to analyze the reactions of the complex `Co(en)₂(H₂O)Cl₂Br` with the given reagents and determine the correct formula of the complex based on the observations.

### Step-by-Step Solution:

1. **Identify the Complex**: The given complex is `Co(en)₂(H₂O)Cl₂Br`. Here, `Co` is cobalt, `en` is ethylenediamine (a bidentate ligand), `H₂O` is water, `Cl` is chloride, and `Br` is bromide.

2. **Reaction with Concentrated H₂SO₄**:
- When the complex is treated with concentrated sulfuric acid (H₂SO₄), which is a dehydrating agent, it suffers a loss in weight.
- This indicates that water (H₂O) is lost from the complex. Therefore, we can conclude that the water molecule is not part of the coordination sphere and is present outside it.

3. **Reaction with AgNO₃**:
- The complex reacts with silver nitrate (AgNO₃) to produce a white precipitate that is soluble in aqueous ammonia (NH₃).
- The formation of a white precipitate indicates the presence of chloride ions (Cl⁻) in the complex, as AgCl is a white precipitate.
- Since the precipitate is soluble in NH₃, it confirms that the chloride ion is also outside the coordination sphere. If it were inside, it would not form a precipitate with AgNO₃.

4. **Determine the Remaining Ligands**:
- Since both water and chloride ions are outside the coordination sphere, we are left with the ligands `en` and `Br`.
- The complex must have one bromide ion (Br) inside the coordination sphere because if it were outside, it would also react with AgNO₃, potentially forming a precipitate.

5. **Construct the Correct Formula**:
- From the analysis, we conclude that the complex has two ethylenediamine ligands (en), one bromide ion (Br), and one chloride ion (Cl) inside the coordination sphere.
- Therefore, the correct formula of the complex is `Co(en)₂BrCl`.

### Conclusion:
The correct formula of the complex is **`Co(en)₂BrCl`**.

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