The possible number of structural and stereo isomers for the complex `[MBr_(2)Cl_(2)]SO_(4)` is

Options

A. 2
B. 4
C. 5
D. 7

Answer

To solve the problem of finding the possible number of structural and stereo isomers for the complex \([MBr_2Cl_2]SO_4\), we can follow these steps:

### Step 1: Identify the Types of Isomerism
The complex \([MBr_2Cl_2]SO_4\) can exhibit two main types of isomerism: **structural isomerism** and **stereoisomerism**. Structural isomerism includes ionization isomerism and geometrical isomerism.

**Hint:** Consider the different ways ligands can be arranged around the central metal atom.

### Step 2: Determine Ionization Isomers
Ionization isomers occur when the ligands can switch between being part of the coordination sphere and being outside of it. In this case, the sulfate ion (\(SO_4^{2-}\)) can either be inside or outside the coordination sphere.

1. **Possible Ionization Isomers:**
- \([MBr_2Cl_2]SO_4\)
- \([MSO_4Cl_2]Br_2\)
- \([MBr_2SO_4]Cl_2\)

Thus, we have **3 ionization isomers**.

**Hint:** Think about how the sulfate ion can interact with the metal and other ligands.

### Step 3: Determine Geometrical Isomers
Next, we consider geometrical isomerism. The complex can be represented as \(MBr_2Cl_2\) which can show cis-trans isomerism.

1. **Cis Isomer:** Both bromides and both chlorides are adjacent to each other.
- Structure: \(M(Br)(Br)(Cl)(Cl)\)

2. **Trans Isomer:** The bromides are opposite each other and the chlorides are opposite each other.
- Structure: \(M(Br)(Cl)(Br)(Cl)\)

Thus, we have **2 geometrical isomers**.

**Hint:** Visualize the arrangement of the ligands around the central metal atom.

### Step 4: Calculate Total Isomers
Now, we can add the number of ionization isomers and geometrical isomers to find the total number of isomers.

- Total isomers = Ionization isomers + Geometrical isomers
- Total isomers = 3 (ionization) + 2 (geometrical) = 5

### Conclusion
The total number of structural and stereo isomers for the complex \([MBr_2Cl_2]SO_4\) is **5**.

**Final Answer:** The correct answer is option **C: 5**.

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