Calculate the total number of isomers of square planar complex `[MFCl(SCN)(NO_2)]`

Answer

To calculate the total number of isomers of the square planar complex \([MFCl(SCN)(NO_2)]\), we will follow these steps:

### Step 1: Identify the Ligands
The complex has the following ligands:
- \(F\) (Fluoride)
- \(Cl\) (Chloride)
- \(SCN\) (Thiocyanate)
- \(NO_2\) (Nitro)

### Step 2: Determine the Types of Isomers
In square planar complexes, we can have:
1. **Geometric Isomers**: These arise from different arrangements of the ligands around the metal center.
2. **Linkage Isomers**: These occur when a ligand can attach to the metal in more than one way.

### Step 3: Analyze Geometric Isomers
For the square planar complex with four different ligands, we can arrange the ligands in various ways:
- We can fix one ligand and arrange the others around it.
- The geometric isomers can be derived by placing two ligands opposite each other and arranging the remaining two.

#### Arrangement:
1. Fix \(Cl\) at the top.
2. Place \(F\) at the bottom.
3. The remaining ligands \(SCN\) and \(NO_2\) can be placed on the sides.

This gives us the following arrangements:
- \(Cl\) opposite \(F\) with \(SCN\) and \(NO_2\) on the sides.
- \(SCN\) opposite \(NO_2\) with \(Cl\) and \(F\) on the sides.
- \(F\) opposite \(NO_2\) with \(Cl\) and \(SCN\) on the sides.

Thus, we can have 3 geometric isomers based on the arrangement of the ligands.

### Step 4: Analyze Linkage Isomers
The ligands \(SCN\) and \(NO_2\) can bind to the metal in different ways:
- \(SCN\) can bind through sulfur (S) or nitrogen (N).
- \(NO_2\) can bind through nitrogen (N) or oxygen (O).

This gives us additional isomers based on how these ligands attach:
1. \(SCN\) binds through S and \(NO_2\) binds through N.
2. \(SCN\) binds through S and \(NO_2\) binds through O.
3. \(SCN\) binds through N and \(NO_2\) binds through N.
4. \(SCN\) binds through N and \(NO_2\) binds through O.

### Step 5: Total Isomers Calculation
From the geometric arrangements, we have 3 isomers. Each of these can have 4 linkage isomers based on the binding modes of \(SCN\) and \(NO_2\).

Thus, the total number of isomers can be calculated as:
\[ \text{Total Isomers} = \text{Geometric Isomers} \times \text{Linkage Isomers} = 3 \times 4 = 12 \]

### Final Answer
The total number of isomers of the square planar complex \([MFCl(SCN)(NO_2)]\) is **12**.

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