Calculate `ppi-dpi` bonds present in `SO_(4)^(2-)", "NO_(3)^(-)` and trimer of `SO_(3)`.

Explanation

To calculate the pπ-dπ bonds present in \( SO_4^{2-} \), \( NO_3^{-} \), and the trimer of \( SO_3 \), we will analyze each species step by step.

### Step 1: Analyze \( SO_4^{2-} \)

1. **Determine the Valence Electrons**:
- Sulfur (S) has 6 valence electrons.
- Each oxygen (O) has 6 valence electrons, and there are 4 oxygens. Thus, total valence electrons from oxygen = \( 4 \times 6 = 24 \).
- The charge of \( SO_4^{2-} \) adds 2 more electrons.
- Total valence electrons = \( 6 + 24 + 2 = 32 \).

2. **Lewis Structure**:
- Sulfur is the central atom bonded to four oxygen atoms.
- There are 4 single bonds (sigma bonds) and 2 double bonds (pi bonds) formed with two of the oxygen atoms.
- The remaining oxygen atoms have single bonds with sulfur.

3. **Identify pπ-dπ Bonds**:
- The double bonds between sulfur and oxygen involve pπ (from oxygen) and dπ (from sulfur) interactions.
- There are 2 pπ-dπ bonds in \( SO_4^{2-} \).

### Step 2: Analyze \( NO_3^{-} \)

1. **Determine the Valence Electrons**:
- Nitrogen (N) has 5 valence electrons.
- Each oxygen has 6 valence electrons, and there are 3 oxygens. Thus, total valence electrons from oxygen = \( 3 \times 6 = 18 \).
- The charge of \( NO_3^{-} \) adds 1 more electron.
- Total valence electrons = \( 5 + 18 + 1 = 24 \).

2. **Lewis Structure**:
- Nitrogen is the central atom bonded to three oxygen atoms.
- There is 1 double bond (1 pπ-dπ bond) and 2 single bonds (sigma bonds) with the remaining oxygen atoms.

3. **Identify pπ-dπ Bonds**:
- The double bond between nitrogen and one oxygen involves pπ (from oxygen) and dπ (from nitrogen) interactions.
- There is 1 pπ-dπ bond in \( NO_3^{-} \).

### Step 3: Analyze the Trimer of \( SO_3 \)

1. **Structure of Trimer**:
- The trimer of \( SO_3 \) consists of three sulfur atoms and forms a cyclic structure with double bonds to oxygen.
- Each sulfur in the trimer forms double bonds with two oxygen atoms.

2. **Identify pπ-dπ Bonds**:
- Each sulfur atom forms 2 pπ-dπ bonds (one with each of the two double-bonded oxygens).
- Since there are 3 sulfur atoms, the total number of pπ-dπ bonds = \( 3 \times 2 = 6 \).

### Final Calculation

- Total pπ-dπ bonds:
- From \( SO_4^{2-} \): 2
- From \( NO_3^{-} \): 1
- From trimer of \( SO_3 \): 6
- Total = \( 2 + 1 + 6 = 9 \).

### Summary of Bonds
- **\( SO_4^{2-} \)**: 2 pπ-dπ bonds
- **\( NO_3^{-} \)**: 1 pπ-dπ bond
- **Trimer of \( SO_3 \)**: 6 pπ-dπ bonds
- **Total pπ-dπ bonds**: 9