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 complex \([Cr(NH_3)_2(OH)_2Cl_2]^-\), we will analyze each type of isomerism mentioned in the question: ionization, hydrate, coordination, geometrical, and optical.

### Step-by-Step Solution:

1. **Ionization Isomerism**:
- Ionization isomerism occurs when two or more compounds have the same formula but differ in the arrangement of ions. In the case of \([Cr(NH_3)_2(OH)_2Cl_2]^-\), there are no ions that can be exchanged with other ions outside the coordination sphere. Therefore, this complex does not exhibit ionization isomerism.
- **Conclusion**: **No ionization isomerism**.

2. **Hydrate Isomerism**:
- Hydrate isomerism occurs when water molecules are part of the coordination sphere or exist outside it. In this complex, there are no water molecules present. Thus, it cannot exhibit hydrate isomerism.
- **Conclusion**: **No hydrate isomerism**.

3. **Coordination Isomerism**:
- Coordination isomerism occurs when the composition of the coordination sphere differs. In this case, the complex is a single coordination entity and does not have separate cationic and anionic coordination spheres. Therefore, it does not exhibit coordination isomerism.
- **Conclusion**: **No coordination isomerism**.

4. **Geometrical Isomerism**:
- Geometrical isomerism (also known as cis-trans isomerism) occurs in octahedral complexes when ligands can be arranged differently around the central metal atom. The complex \([Cr(NH_3)_2(OH)_2Cl_2]^-\) can have different arrangements of the ligands (cis and trans forms). For example, if the two \(NH_3\) ligands are adjacent, it is a cis isomer; if they are opposite each other, it is a trans isomer.
- **Conclusion**: **Exhibits geometrical isomerism**.

5. **Optical Isomerism**:
- Optical isomerism occurs when a compound can exist in two non-superimposable mirror images (enantiomers). The cis form of \([Cr(NH_3)_2(OH)_2Cl_2]^-\) lacks a plane of symmetry, making it optically active. Therefore, it can exhibit optical isomerism.
- **Conclusion**: **Exhibits optical isomerism**.

### Final Summary:
The complex \([Cr(NH_3)_2(OH)_2Cl_2]^-\) exhibits:
- **Geometrical Isomerism** (due to different arrangements of ligands).
- **Optical Isomerism** (due to the absence of a plane of symmetry in the cis form).

Thus, the correct answer is that the complex exhibits **geometrical and optical isomerism**.