How many geometrical isomers and stereoisomers are possible for `[Pt(NO_(2))(NH_(3))(NH_(2)OH)(Py)]^(+) and [Pt(Br)(Cl)(I)(NO_(2))(NH_(3))(Py)]` respectively?

Options

A. 3 and 15
B. 3 and 30
C. 4 and 15
D. 4 and 30

Explanation

To determine the number of geometrical isomers and stereoisomers for the given coordination compounds, we will analyze each compound step by step.

### Step 1: Analyze the first compound `[Pt(NO2)(NH3)(NH2OH)(Py)]^+`

1. **Identify the coordination number and geometry**:
- The central metal ion is platinum (Pt) with a coordination number of 4 (since there are four ligands: NO2, NH3, NH2OH, and Py).
- The geometry for a coordination number of 4 is typically square planar.

2. **Determine possible isomers**:
- For square planar complexes with 4 different ligands, we can have geometrical isomers.
- The possible arrangements can be categorized into cis and trans forms. However, since all ligands are different, we will consider the unique arrangements.
- The possible arrangements (considering A, B, C, D as the ligands) can be:
- A opposite C, B opposite D
- A opposite B, C opposite D
- A opposite D, B opposite C
- Therefore, we can conclude that there are **3 geometrical isomers**.

### Step 2: Analyze the second compound `[Pt(Br)(Cl)(I)(NO2)(NH3)(Py)]`

1. **Identify the coordination number and geometry**:
- The central metal ion is platinum (Pt) with a coordination number of 6 (since there are six ligands: Br, Cl, I, NO2, NH3, and Py).
- The geometry for a coordination number of 6 is octahedral.

2. **Determine possible isomers**:
- For octahedral complexes with 6 different ligands, we can have both geometrical and optical isomers.
- The number of geometrical isomers for octahedral complexes can be calculated using the formula for the number of isomers, which is often found in tables for common coordination compounds.
- In this case, the total number of stereoisomers (including both geometrical and optical) is **30**.
- Out of these, **15** are geometrical isomers, and the other **15** are optical isomers (enantiomers).

### Summary of Isomers:
- For `[Pt(NO2)(NH3)(NH2OH)(Py)]^+`:
- **Geometrical Isomers**: 3
- **Stereoisomers**: 3 (since there are no optical isomers)

- For `[Pt(Br)(Cl)(I)(NO2)(NH3)(Py)]`:
- **Geometrical Isomers**: 15
- **Stereoisomers**: 30 (15 geometrical + 15 optical)

### Final Answer:
- The number of geometrical isomers for `[Pt(NO2)(NH3)(NH2OH)(Py)]^+` is **3**.
- The number of stereoisomers for `[Pt(Br)(Cl)(I)(NO2)(NH3)(Py)]` is **30**.