How many isomers are possible in `[Cr(en)_(2)Br_(2)]` ?

Options

A. 2
B. 3
C. 6
D. 1

Answer

To determine the number of isomers possible for the coordination compound \([Cr(en)_{2}Br_{2}]\), we will follow these steps:

### Step 1: Identify the Coordination Number
The coordination number of chromium in this complex is 6. This is because there are two bidentate ethylenediamine (en) ligands, which contribute 4 coordination sites (2 sites per en), and 2 monodentate bromine (Br) ligands contribute 2 coordination sites.

**Hint:** The coordination number is determined by counting the number of donor atoms from the ligands attached to the central metal atom.

### Step 2: Determine the Types of Isomers
In coordination chemistry, isomers can be classified into two main types: geometric isomers and optical isomers.

- **Geometric Isomers:** These arise from different arrangements of ligands around the central metal atom. For this complex, we can have cis and trans isomers due to the presence of two identical ligands (Br).
- **Optical Isomers:** These are non-superimposable mirror images of each other.

**Hint:** Consider the arrangement of ligands in space to identify geometric isomers.

### Step 3: Draw the Geometric Isomers
1. **Cis Isomer:** In the cis configuration, the two bromine ligands are adjacent to each other, and the two ethylenediamine ligands are also adjacent.
2. **Trans Isomer:** In the trans configuration, the two bromine ligands are opposite each other, and the two ethylenediamine ligands are also opposite.

**Hint:** Visualizing or sketching the structures can help in identifying the spatial arrangement of ligands.

### Step 4: Analyze Optical Activity
- The **cis isomer** can exist in two forms: one isomer and its non-superimposable mirror image, making it optically active.
- The **trans isomer**, however, has a mirror image that is superimposable on itself, making it optically inactive.

**Hint:** Optical activity depends on whether the mirror images of the isomer can be superimposed or not.

### Step 5: Count the Total Isomers
From the analysis:
- **Cis Isomer:** 2 (one isomer + its non-superimposable mirror image)
- **Trans Isomer:** 1 (optically inactive)

Adding these together gives a total of \(2 + 1 = 3\) isomers.

### Conclusion
The total number of isomers possible in \([Cr(en)_{2}Br_{2}]\) is **3**.

**Final Answer:** The correct option is **B: 3 isomers**.