Two research students were instruced intructed to synthesise the complex
`[Co(NH_(3))_(5)(NO_(2))]Br_(2)`
They synthesised the complexes with identical molecular formula molar mass geometry conductane and spin but they differed in colour Based on the above facts answer the following questions
Complexes synthesised can be
(i) `[Cr(NH_(3))_(5)(NO_(2))Br_(2)`,(ii) `[Cr(NH_(3))_(5)(ONO)]Br_(2)`
(iii) `[Cr(NH_(3))_(5)Br_(2)]NO_(2)` (iv) All of these .

Options

A. Both(i) and (ii)
B. Both(i) and(iii)
C. Both(ii)and(iii)
D. All of these

Answer

To solve the question regarding the synthesis of the complex `[Co(NH₃)₅(NO₂)]Br₂`, we need to analyze the given complexes and determine which of them could be synthesized based on the provided characteristics.

### Step-by-Step Solution:

1. **Understanding the Complex**: The complex `[Co(NH₃)₅(NO₂)]Br₂` contains cobalt (Co) as the central metal ion, five ammonia (NH₃) ligands, one nitro (NO₂) ligand, and two bromide (Br) counter ions.

2. **Identifying the Ligands**: The nitro ligand (NO₂) can act as a bidentate ligand, meaning it can bind through either the nitrogen (N) or the oxygen (O) atom. This leads to the possibility of linkage isomerism, where the same ligands are present but attached to the metal ion in different ways.

3. **Analyzing the Options**:
- **(i)** `[Cr(NH₃)₅(NO₂)Br₂]`: This complex has chromium (Cr) instead of cobalt (Co). It has the same formula but a different metal ion.
- **(ii)** `[Cr(NH₃)₅(ONO)]Br₂`: This complex also has chromium and features the nitrito (ONO) ligand, which is a linkage isomer of the nitro (NO₂) ligand.
- **(iii)** `[Cr(NH₃)₅Br₂]NO₂`: This complex has a different arrangement where the nitro group is a counter ion rather than a ligand.
- **(iv)** All of these: This option suggests that all the complexes listed could be synthesized.

4. **Determining the Correct Answer**:
- Since the question specifies that the complexes differ in color but have identical molecular formula, molar mass, geometry, conductance, and spin, it indicates that they are likely linkage isomers.
- The complexes (i) and (ii) fit this description as they both involve the nitro ligand in different binding modes (N vs O).
- The complex (iii) does not fit the criteria as it changes the role of the nitro group from a ligand to a counter ion, which alters the nature of the complex.

5. **Conclusion**: Therefore, the correct answer is that the synthesized complexes can be (i) and (ii), which are linkage isomers of the original complex.

### Final Answer:
The complexes synthesized can be (i) `[Cr(NH₃)₅(NO₂)Br₂]` and (ii) `[Cr(NH₃)₅(ONO)]Br₂`.

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