Number of possible isomers for the complex `[Co(en)_(2)CI_(2)]`  will be (en = ethylenediamine)

Options

A. 3
B. 4
C. 2
D. 1

Answer

To determine the number of possible isomers for the complex \([Co(en)_{2}Cl_{2}]\), where \(en\) is ethylenediamine, we can follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The complex \([Co(en)_{2}Cl_{2}]\) has a cobalt ion (Co) surrounded by two ethylenediamine (en) ligands and two chloride (Cl) ligands. The coordination number of cobalt in this complex is 6, as it forms six bonds (two from each en and one from each Cl). The geometry of a coordination complex with a coordination number of 6 is typically octahedral.

**Hint:** Remember that the coordination number indicates how many ligands are bonded to the central metal ion.

### Step 2: Determine the Types of Isomers
In coordination compounds, isomers can be classified into two main categories: geometric isomers and optical isomers.

1. **Geometric Isomers:** These arise from different arrangements of ligands around the central metal ion.
2. **Optical Isomers:** These arise when a compound can exist in two non-superimposable mirror images (chiral forms).

**Hint:** Geometric isomers can be identified by the relative positions of the ligands in space.

### Step 3: Analyze Geometric Isomers
For the complex \([Co(en)_{2}Cl_{2}]\):
- The two ethylenediamine ligands can be arranged in two ways relative to the two chloride ligands:
- **Cis Isomer:** Both ethylenediamine ligands are adjacent to each other.
- **Trans Isomer:** The ethylenediamine ligands are opposite each other.

Thus, we have **2 geometric isomers**: cis and trans.

**Hint:** Visualize the octahedral structure to see how ligands can be positioned relative to each other.

### Step 4: Analyze Optical Isomers
Next, we need to check if any of the geometric isomers can exhibit optical isomerism:
- The **cis isomer** does not have a plane of symmetry and can exist in two non-superimposable mirror images (it is chiral).
- The **trans isomer** has a plane of symmetry and does not exhibit optical isomerism (it is achiral).

Thus, the cis isomer contributes **2 optical isomers**, while the trans isomer contributes **0 optical isomers**.

**Hint:** Check for planes of symmetry to determine if a compound is chiral or achiral.

### Step 5: Calculate Total Isomers
Now, we can sum the total number of isomers:
- Geometric isomers: 2 (1 cis + 1 trans)
- Optical isomers: 2 (from the cis isomer)

Total number of possible isomers = 2 (geometric) + 2 (optical) = **4 isomers**.

**Final Answer:** The number of possible isomers for the complex \([Co(en)_{2}Cl_{2}]\) is **4**.