Total number of geometrical isomers for the complex `[Rh Cl (CO) (PPh_(3)) (NH_(3))]` is

Answer

To determine the total number of geometrical isomers for the complex \([RhCl(CO)(PPh_3)(NH_3)]\), we will follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The given complex has a coordination number of 4, which typically leads to a square planar geometry for transition metal complexes.

**Hint:** Remember that square planar complexes can have different arrangements of ligands around the central metal atom.

### Step 2: Identify the Ligands
The ligands in the complex are:
- Chloride ion (Cl)
- Carbon monoxide (CO)
- Triphenylphosphine (PPh₃)
- Ammonia (NH₃)

**Hint:** Count the different types of ligands and their positions to understand how they can be arranged.

### Step 3: Fix One Ligand
To analyze geometrical isomers, we can fix one ligand in a specific position. Let’s fix the chloride ion (Cl) at the top position of the square planar arrangement.

**Hint:** Fixing one ligand helps visualize the possible arrangements of the remaining ligands.

### Step 4: Arrange the Remaining Ligands
With Cl fixed, we can arrange the remaining three ligands (CO, PPh₃, NH₃) in the other three positions. The possible arrangements are:
1. CO in one position, PPh₃ in another, and NH₃ in the last.
2. CO and NH₃ can be exchanged, leading to a different arrangement.
3. PPh₃ and NH₃ can also be exchanged.

**Hint:** Consider how the positions of the remaining ligands can change while keeping the fixed ligand in place.

### Step 5: Identify Distinct Isomers
1. **Isomer 1:** Cl at the top, CO to the right, PPh₃ to the left, NH₃ at the bottom.
2. **Isomer 2:** Cl at the top, NH₃ to the right, PPh₃ to the left, CO at the bottom.
3. **Isomer 3:** Cl at the top, PPh₃ at the right, NH₃ at the left, CO at the bottom.

After considering the arrangements, we find that some configurations may lead to identical arrangements due to symmetry.

**Hint:** Check for symmetry to ensure that you are not counting identical arrangements multiple times.

### Step 6: Count the Distinct Geometrical Isomers
After analyzing the arrangements, we find that there are a total of 3 distinct geometrical isomers for the complex \([RhCl(CO)(PPh_3)(NH_3)]\).

**Final Answer:** The total number of geometrical isomers is **3**.