The number of geometric isomers of the complex `Cr(NH_3)_3Cl_3` are

Answer

To determine the number of geometric isomers of the complex \( \text{Cr(NH}_3\text{)}_3\text{Cl}_3 \), we can follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The complex \( \text{Cr(NH}_3\text{)}_3\text{Cl}_3 \) has a chromium ion (Cr) coordinated with three ammonia (NH3) ligands and three chloride (Cl) ligands. The coordination number is 6, which typically leads to an octahedral geometry.

**Hint:** The coordination number indicates how many ligands are attached to the central metal ion and helps determine the geometry.

### Step 2: Determine the Type of Isomers
For octahedral complexes of the type \( \text{MA}_3\text{B}_3 \) (where A and B are different ligands), there are two types of geometric isomers:
1. **Facial (fac) Isomer**: where three identical ligands occupy one face of the octahedron.
2. **Meridional (mer) Isomer**: where three identical ligands are arranged in a plane that passes through the center of the octahedron.

**Hint:** Remember that the arrangement of ligands around the central metal ion defines the type of isomer.

### Step 3: Visualize the Isomers
- **Facial Isomer (fac)**: In this isomer, the three ammonia ligands are adjacent to each other on one face of the octahedron, while the three chloride ligands occupy the opposite face.

- **Meridional Isomer (mer)**: In this isomer, the three ammonia ligands are arranged in a plane that divides the octahedron into two equal halves, with one ammonia ligand at the top and two at the bottom, while the three chloride ligands occupy the remaining positions.

**Hint:** Drawing the structures can help visualize the arrangement of ligands and confirm the type of isomer.

### Step 4: Count the Isomers
From the above analysis, we can conclude that there are two distinct geometric isomers for the complex \( \text{Cr(NH}_3\text{)}_3\text{Cl}_3 \):
1. One facial isomer.
2. One meridional isomer.

Thus, the total number of geometric isomers is **2**.

**Final Answer:** The number of geometric isomers of the complex \( \text{Cr(NH}_3\text{)}_3\text{Cl}_3 \) is **2**.