How many type of isomerism is exhibited by the complex `[Co(NH_(3))_(4)(NO_(2))_(2)]Cl`?

Explanation

To determine how many types of isomerism are exhibited by the complex \([Co(NH_3)_4(NO_2)_2]Cl\), we need to analyze the possible types of isomerism that can occur in coordination complexes.

### Step-by-step Solution:

1. **Identify the Ligands**: The complex contains ammonia (\(NH_3\)) and nitrito (\(NO_2\)) ligands, along with a chloride ion (\(Cl^-\)). The nitrito ligand can coordinate through either the nitrogen atom or the oxygen atom, which is crucial for determining the types of isomerism.

2. **Linkage Isomerism**: Since \(NO_2\) can coordinate through either the nitrogen or the oxygen, we can have two different linkage isomers:
- One where \(NO_2\) coordinates through nitrogen (denoted as \(ONO\)).
- Another where \(NO_2\) coordinates through oxygen (denoted as \(NO_2\)).
Thus, we have linkage isomerism.

3. **Ionization Isomerism**: The complex can also exhibit ionization isomerism. This occurs when the composition of the ions in solution differs. For example:
- One form could be \([Co(NH_3)_4(NO_2)_2]Cl\) where the chloride ion is outside the coordination sphere.
- Another form could be \([Co(NH_3)_4(NO_2)_2]^{2+}\) with \(NO_2^-\) as a counter ion.
This indicates the presence of ionization isomerism.

4. **Geometrical Isomerism**: The complex can also exhibit geometrical isomerism (cis-trans isomerism). In this case, the arrangement of the ligands around the cobalt center can lead to different spatial arrangements:
- Cis isomer: where the two \(NO_2\) groups are adjacent to each other.
- Trans isomer: where the two \(NO_2\) groups are opposite each other.
This indicates the presence of geometrical isomerism.

5. **Optical Isomerism**: In this specific complex, the geometrical isomers do not exhibit optical isomerism because they have a plane of symmetry, making them optically inactive.

### Conclusion:
The complex \([Co(NH_3)_4(NO_2)_2]Cl\) exhibits three types of isomerism:
1. Linkage isomerism
2. Ionization isomerism
3. Geometrical isomerism

### Final Answer:
The complex exhibits **3 types of isomerism**: linkage isomerism, ionization isomerism, and geometrical isomerism.

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