Calculate total number of possible isomers (structrural and stereoisomers) of the compound `[Ir(en)_2(NH_3)(NO_2)]^(2+)`

Explanation

To calculate the total number of possible isomers (structural and stereoisomers) of the compound \([Ir(en)_2(NH_3)(NO_2)]^{2+}\), we will follow these steps:

### Step 1: Identify the Coordination Complex
The compound consists of an iridium (Ir) center with the following ligands:
- Two ethylenediamine (en) ligands
- One ammonia (NH3) ligand
- One nitro (NO2) ligand

### Step 2: Determine the Structure of the Complex
The complex has an octahedral geometry due to the six coordination sites around the iridium ion. The ethylenediamine ligands are bidentate, meaning each can bond through two nitrogen atoms.

### Step 3: Identify Structural Isomers
Structural isomers differ in the connectivity of the ligands. In this case, since we have two identical bidentate ligands (en), there is only **one structural isomer** possible. The arrangement of the ligands does not change the connectivity.

### Step 4: Identify Geometrical Isomers
Geometrical isomers arise from the different spatial arrangements of the ligands. For this complex:
- The two en ligands can be positioned either in a cis or trans arrangement relative to each other.
- The possible arrangements are:
1. **Cis**: Both en ligands adjacent to each other.
2. **Trans**: Both en ligands opposite each other.

Thus, there are **two geometrical isomers**:
1. Cis isomer
2. Trans isomer

### Step 5: Identify Optical Isomers
Optical isomers (enantiomers) are non-superimposable mirror images.
- The cis isomer can have two optical isomers because it has chiral centers.
- The trans isomer does not have optical isomers because it has a plane of symmetry.

Thus, for the geometrical isomers:
- The **cis isomer** has **2 optical isomers**.
- The **trans isomer** has **0 optical isomers**.

### Step 6: Calculate the Total Number of Isomers
Now we can summarize the total:
- **1 Structural Isomer**
- **2 Geometrical Isomers** (Cis and Trans)
- **2 Optical Isomers** from the Cis isomer

Therefore, the total number of possible isomers is:
\[ 1 \text{ (structural)} + 2 \text{ (geometrical)} + 2 \text{ (optical)} = 5 \text{ isomers} \]

### Final Answer
The total number of possible isomers (structural and stereoisomers) of the compound \([Ir(en)_2(NH_3)(NO_2)]^{2+}\) is **5**.

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