How many isomers of the complex `Pt(NH_3)_2(SCN)_2` are
possible ?

Explanation

To determine the number of isomers for the complex \( \text{Pt(NH}_3\text{)}_2(\text{SCN})_2 \), we will follow these steps:

### Step 1: Determine the Oxidation State of Platinum
Let the oxidation state of platinum be \( x \).
- The charge from \( \text{NH}_3 \) is \( 0 \) (neutral ligand).
- The charge from \( \text{SCN} \) is \( -1 \) (as it is a monodentate ligand).

The equation can be set up as:
\[ x + 2(0) + 2(-1) = 0 \]
This simplifies to:
\[ x - 2 = 0 \implies x = +2 \]

**Hint:** Remember that the sum of the oxidation states in a neutral complex must equal zero.

### Step 2: Identify the Coordination Number and Geometry
The coordination number of platinum in this complex is \( 4 \) (since there are 2 \( \text{NH}_3 \) and 2 \( \text{SCN} \)). For a coordination number of \( 4 \), platinum typically forms a square planar geometry.

**Hint:** Coordination number helps determine the geometry of the complex.

### Step 3: Consider the Types of Isomerism
In square planar complexes, we can have:
- Geometric isomers (cis and trans)
- Optical isomers (not applicable here due to symmetry)

Since \( \text{SCN} \) is an ambidentate ligand (it can coordinate through either sulfur or nitrogen), we will consider both donor atoms for isomer formation.

**Hint:** Identify the types of isomers based on the ligands and their arrangements.

### Step 4: Draw Possible Geometric Isomers
1. **Cis Isomers:**
- Both \( \text{NH}_3 \) ligands adjacent to each other.
- Both \( \text{SCN} \) ligands adjacent to each other.

2. **Trans Isomers:**
- \( \text{NH}_3 \) ligands opposite each other.
- \( \text{SCN} \) ligands opposite each other.

3. **Consider Ambidentate Nature of \( \text{SCN} \):**
- **Cis with \( \text{N} \) as donor:** \( \text{NH}_3, \text{NH}_3, \text{SCN}_N, \text{SCN}_N \)
- **Cis with \( \text{S} \) as donor:** \( \text{NH}_3, \text{NH}_3, \text{SCN}_S, \text{SCN}_S \)
- **Trans with \( \text{N} \) as donor:** \( \text{NH}_3, \text{NH}_3, \text{SCN}_N, \text{SCN}_N \)
- **Trans with \( \text{S} \) as donor:** \( \text{NH}_3, \text{NH}_3, \text{SCN}_S, \text{SCN}_S \)

4. **Mixed Donor Isomers:**
- One \( \text{SCN} \) donating through \( \text{N} \) and the other through \( \text{S} \) in both cis and trans arrangements.

### Step 5: Count the Isomers
From the arrangements:
- 2 cis isomers (both \( \text{N} \) and both \( \text{S} \))
- 2 trans isomers (both \( \text{N} \) and both \( \text{S} \))
- 2 mixed donor isomers (one \( \text{N} \) and one \( \text{S} \) in both cis and trans)

Thus, the total number of isomers is:
\[ 2 \text{ (cis)} + 2 \text{ (trans)} + 2 \text{ (mixed)} = 6 \]

### Final Answer
The total number of isomers of the complex \( \text{Pt(NH}_3\text{)}_2(\text{SCN})_2 \) is **6**.

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