How many isomers are possible for the complex ion `[Cr(NH_(3))_(3)Cl_(3)]` ?

Options

A. 3
B. 2
C. 4
D. 5

Answer

To determine how many isomers are possible for the complex ion \([Cr(NH_3)_3Cl_3]\), we will analyze the geometry and coordination of the complex.

### Step-by-Step Solution:

1. **Identify the Coordination Number and Geometry**:
- The complex ion \([Cr(NH_3)_3Cl_3]\) has chromium (Cr) as the central metal ion, coordinated to three ammonia (NH₃) ligands and three chloride (Cl) ligands.
- The coordination number of chromium in this complex is 6 (3 NH₃ + 3 Cl).
- With a coordination number of 6, the geometry of the complex is octahedral.

2. **Determine Possible Isomers**:
- In octahedral complexes, we can have two types of isomers: **geometric isomers** (cis and trans) and **optical isomers** (chiral).
- For the given complex, we can have:
- **Cis Isomer**: where the three NH₃ ligands are adjacent to each other.
- **Trans Isomer**: where the three NH₃ ligands are opposite each other.

3. **Visualize the Isomers**:
- **Cis Isomer**: In this arrangement, the three NH₃ ligands occupy two adjacent positions while the three Cl ligands occupy the remaining positions.
- **Trans Isomer**: Here, the three NH₃ ligands are positioned opposite each other, with the three Cl ligands also opposite each other.

4. **Check for Optical Isomerism**:
- In this case, the cis isomer can potentially exhibit optical isomerism due to the arrangement of the ligands, but the trans isomer does not have a chiral center and thus does not exhibit optical isomerism.

5. **Count the Isomers**:
- Therefore, we have:
- 1 Cis Isomer
- 1 Trans Isomer
- Total isomers = 2 (Cis and Trans)

### Final Answer:
The total number of isomers possible for the complex ion \([Cr(NH_3)_3Cl_3]\) is **2**.