Which of the following isomerism, exhibited by `[CrCl_(2)(OH)_(2)(NH_(3))_(2)]^(-)?`

Options

A. Ionization
B. Linkage
C. Geometrical
D. Hydrate

Explanation

To determine the type of isomerism exhibited by the coordination compound \([CrCl_2(OH)_2(NH_3)_2]^-\), we will analyze the possible isomerisms step by step.

### Step 1: Identify the Coordination Number and Geometry
The central metal ion in this compound is chromium (Cr), which typically has a coordination number of 6 in octahedral complexes. This means that there are six ligands surrounding the chromium ion.

**Hint:** Look for the coordination number based on the number of ligands attached to the central metal ion.

### Step 2: List the Ligands
The ligands present in the compound are:
- 2 Chloride ions (Cl)
- 2 Hydroxide ions (OH)
- 2 Ammonia molecules (NH3)

**Hint:** Identify and categorize the ligands based on their nature (neutral, anionic, etc.).

### Step 3: Determine Possible Isomerisms
We will consider the following types of isomerism:
- **Ionization Isomerism:** This occurs when a ligand can be exchanged with an anion outside the coordination sphere. In this case, there are no anions outside the coordination sphere that can lead to ionization isomerism.

- **Linkage Isomerism:** This occurs when a ligand can coordinate to the metal in more than one way. In this case, there are no ambidentate ligands present.

- **Hydrate Isomerism:** This occurs when water molecules are present in different forms (inside or outside the coordination sphere). There are no water molecules in this compound.

- **Geometrical Isomerism:** This occurs in octahedral complexes when ligands can be arranged differently around the central metal ion. We can have cis and trans forms.

**Hint:** Eliminate isomerism types that do not apply based on the ligands present and their arrangements.

### Step 4: Analyze Geometrical Isomerism
In an octahedral complex with the given ligands:
- **Cis Isomer:** The two Cl ligands can be adjacent to each other, and the two OH or NH3 ligands can also be adjacent, creating different cis configurations.
- **Trans Isomer:** The two Cl ligands can be opposite each other, as can the two OH or NH3 ligands.

**Hint:** Visualize the arrangement of ligands in 3D to differentiate between cis and trans configurations.

### Step 5: Determine Optical Isomerism
The cis isomers can be optically active if they are non-superimposable on their mirror images. In contrast, the trans isomers are usually not optically active because they can be superimposed on their mirror images.

**Hint:** Consider the symmetry of the isomers to determine if they can exist as optical isomers.

### Conclusion
Based on the analysis:
- The compound \([CrCl_2(OH)_2(NH_3)_2]^-\) exhibits **geometrical isomerism** (cis and trans forms) due to the arrangement of the ligands around the central chromium ion.

**Final Answer:** The type of isomerism exhibited by \([CrCl_2(OH)_2(NH_3)_2]^-\) is **geometrical isomerism**.