How many of the following compounds have `(p pi-dpi)` multiple bonds
(i) `SO_(2)` (ii) `SO_(3)` (iii) `H SO_(4)^(Theta)` (iv) `SO_(4)^(2-)`
(v) `SO_(3)^(3-)` (vi) `H SO_(3)^(Theta)` .

Explanation

To determine how many of the given compounds have (p pi-d pi) multiple bonds, we will analyze each compound step by step.

### Step 1: Analyze SO₂ (Sulfur Dioxide)
- **Structure**: SO₂ has a bent structure with sulfur forming two double bonds with two oxygen atoms.
- **Bonding**: Each double bond consists of one sigma bond and one pi bond. The pi bond is formed by the overlap of p orbitals.
- **Type of Bonds**: In SO₂, there are no d orbitals involved since sulfur does not utilize its d orbitals in this case.
- **Conclusion**: SO₂ has **0 p pi-d pi bonds**.

### Step 2: Analyze SO₃ (Sulfur Trioxide)
- **Structure**: SO₃ has a trigonal planar structure with sulfur forming three double bonds with three oxygen atoms.
- **Bonding**: Each double bond consists of one sigma bond and one pi bond. The pi bonds can involve the d orbitals of sulfur.
- **Type of Bonds**: In SO₃, two of the pi bonds can be classified as p pi-d pi bonds due to the involvement of sulfur’s d orbitals.
- **Conclusion**: SO₃ has **2 p pi-d pi bonds**.

### Step 3: Analyze HSO₄⁻ (Hydrogen Sulfate Ion)
- **Structure**: HSO₄⁻ has a tetrahedral structure with sulfur forming two double bonds and one single bond with oxygen, and one bond with hydrogen.
- **Bonding**: The double bonds consist of one sigma and one pi bond, and the pi bonds can involve the d orbitals of sulfur.
- **Type of Bonds**: In HSO₄⁻, there are two p pi-d pi bonds due to the involvement of sulfur's d orbitals.
- **Conclusion**: HSO₄⁻ has **2 p pi-d pi bonds**.

### Step 4: Analyze SO₄²⁻ (Sulfate Ion)
- **Structure**: SO₄²⁻ has a tetrahedral structure similar to HSO₄⁻ but without the hydrogen.
- **Bonding**: Sulfur forms four sigma bonds and has two double bonds with oxygen.
- **Type of Bonds**: In SO₄²⁻, the two double bonds can also be classified as p pi-d pi bonds.
- **Conclusion**: SO₄²⁻ has **2 p pi-d pi bonds**.

### Step 5: Analyze SO₃³⁻ (Sulfite Ion)
- **Structure**: SO₃³⁻ has a trigonal pyramidal structure with sulfur forming three bonds with oxygen.
- **Bonding**: There are one double bond and two single bonds.
- **Type of Bonds**: The double bond can involve p pi-d pi bonding.
- **Conclusion**: SO₃³⁻ has **1 p pi-d pi bond**.

### Step 6: Analyze HSO₃⁻ (Hydrogen Sulfite Ion)
- **Structure**: HSO₃⁻ has a bent structure with sulfur forming one double bond and two single bonds with oxygen, and one bond with hydrogen.
- **Bonding**: The double bond consists of one sigma and one pi bond.
- **Type of Bonds**: The double bond can involve p pi-d pi bonding.
- **Conclusion**: HSO₃⁻ has **1 p pi-d pi bond**.

### Final Count of Compounds with (p pi-d pi) Bonds
- SO₂: 0
- SO₃: 2
- HSO₄⁻: 2
- SO₄²⁻: 2
- SO₃³⁻: 1
- HSO₃⁻: 1

**Total Compounds with (p pi-d pi) Bonds**: 0 + 2 + 2 + 2 + 1 + 1 = **8**

### Summary
The total number of compounds that have (p pi-d pi) multiple bonds is **8**.