Consider the following isomerism:
(i) Ionization
(ii) Hydrate
(iii) Coordination
(iv) Geometrical
(v) Optical
Which of the above isomerism are exhibited by `[Cr(NH_(3))_(2)(O)_(2)Cl_(2)]^(-)`?

Options

A. (i) and (v)
B. (ii) and (iii)
C. (iii), (ii) and (i)
D. (iv) and (v)

Answer

To determine which types of isomerism are exhibited by the coordination compound \([Cr(NH_3)_2(O)_2Cl_2]^-\), we will analyze each type of isomerism mentioned in the question.

### Step 1: Identify the Coordination Compound
The given coordination compound is \([Cr(NH_3)_2(O)_2Cl_2]^-\). It contains:
- 2 Ammonia (NH₃) ligands
- 2 Hydroxyl (O) ligands
- 2 Chloride (Cl) ligands

### Step 2: Analyze Each Type of Isomerism
1. **Ionization Isomerism**: This occurs when a ligand can be exchanged with a counter ion. In this case, since there are no counter ions explicitly mentioned, ionization isomerism is not applicable.

2. **Hydrate Isomerism**: This involves the presence of water molecules in the coordination sphere. The given compound does not contain water, so hydrate isomerism is not applicable.

3. **Coordination Isomerism**: This occurs when different ligands are coordinated to the metal in different ways. Since we only have one type of coordination in this compound, coordination isomerism does not apply here.

4. **Geometrical Isomerism**: This occurs when ligands can be arranged differently around the central metal ion. In this case, the compound can exhibit geometrical isomerism due to the presence of two different types of ligands (NH₃ and Cl) and their arrangement can lead to cis and trans forms.

5. **Optical Isomerism**: This occurs when a compound can exist in two non-superimposable mirror images (enantiomers). Since the compound can form geometrical isomers (cis and trans), the cis form can also have a non-superimposable mirror image, allowing it to exhibit optical isomerism.

### Conclusion
Based on the analysis:
- The compound exhibits **Geometrical Isomerism** (option 4).
- The compound exhibits **Optical Isomerism** (option 5).

Thus, the correct answer is that the compound exhibits **Geometrical and Optical Isomerism**.

### Final Answer
The types of isomerism exhibited by \([Cr(NH_3)_2(O)_2Cl_2]^-\) are **Geometrical (iv)** and **Optical (v)**.

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