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 coordination number of 6 because it has 3 ammonia (NH3) ligands and 3 chloride (Cl) ligands. This coordination number suggests that the geometry of the complex is octahedral.

**Hint:** Remember that for octahedral complexes, the arrangement of ligands around the central metal ion can lead to different spatial configurations.

### Step 2: Determine the Types of Ligands
In this complex, we have two types of ligands:
- 3 ammonia (NH3) ligands, which are neutral and monodentate.
- 3 chloride (Cl) ligands, which are also monodentate.

**Hint:** Monodentate ligands can occupy only one coordination site on the metal center, which affects how they can be arranged.

### Step 3: Analyze Possible Geometric Isomers
In an octahedral complex with two types of ligands, we can have two main types of geometric isomers:
1. **Facial (fac) Isomer:** In this arrangement, three identical ligands occupy adjacent positions (i.e., they are on one face of the octahedron).
2. **Meridional (mer) Isomer:** In this arrangement, three identical ligands occupy positions that form a plane through the center of the octahedron.

**Hint:** Visualize the octahedral structure to see how the ligands can be arranged to form different isomers.

### Step 4: Count the Geometric Isomers
For the complex \( \text{Cr(NH}_3\text{)}_3\text{Cl}_3 \):
- The **facial isomer** has all three NH3 ligands adjacent to each other.
- The **meridional isomer** has the NH3 ligands arranged such that one NH3 is opposite another NH3, with Cl ligands filling the remaining positions.

Thus, there are **two geometric isomers** for the complex \( \text{Cr(NH}_3\text{)}_3\text{Cl}_3 \).

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

---