Which of the following is a the most preferred and hence of the lower energy for `SO_(3)`?

Options

A.
B.
C.
D.

Explanation

To determine the most preferred and hence the lowest energy structure for \( SO_3 \), we will calculate the formal charges for each of the proposed structures. The structure with the lowest formal charges on individual atoms and an overall formal charge of zero will be the most stable and preferred structure.

### Step-by-Step Solution:

1. **Understanding Formal Charge Calculation**:
The formula for calculating the formal charge (FC) of an atom is:
\[ \text{FC} = \text{Valence Electrons} - \text{Non-bonding Electrons} - \frac{1}{2} \times \text{Bonding Electrons} \]

2. **Analyzing the First Structure**:
- **Oxygen**:
- Valence Electrons = 6
- Non-bonding Electrons = 4
- Bonding Electrons = 4 (2 bonds with sulfur)
- Formal Charge = \( 6 - 4 - \frac{1}{2} \times 4 = 0 \)
- **Sulfur**:
- Valence Electrons = 6
- Non-bonding Electrons = 0
- Bonding Electrons = 12 (6 bonds with oxygen)
- Formal Charge = \( 6 - 0 - \frac{1}{2} \times 12 = 0 \)

This structure has a total formal charge of 0, and each atom has a formal charge of 0.

3. **Analyzing the Second Structure**:
- **Oxygen** (two oxygens with -1 charge):
- Valence Electrons = 6
- Non-bonding Electrons = 6
- Bonding Electrons = 2
- Formal Charge = \( 6 - 6 - \frac{1}{2} \times 2 = -1 \)
- **Sulfur**:
- Valence Electrons = 6
- Non-bonding Electrons = 0
- Bonding Electrons = 8
- Formal Charge = \( 6 - 0 - \frac{1}{2} \times 8 = +2 \)

This structure has an overall charge of 0, but the individual charges are not favorable.

4. **Analyzing the Third Structure**:
- **Oxygen** (one with -1 charge, one with 0):
- Valence Electrons = 6
- Non-bonding Electrons = 2
- Bonding Electrons = 2
- Formal Charge = \( 6 - 2 - \frac{1}{2} \times 2 = -1 \)
- **Sulfur**:
- Valence Electrons = 6
- Non-bonding Electrons = 0
- Bonding Electrons = 6
- Formal Charge = \( 6 - 0 - \frac{1}{2} \times 6 = +1 \)

This structure also has unfavorable charges.

5. **Analyzing the Fourth Structure**:
- **Oxygen** (all with -1 charge):
- Valence Electrons = 6
- Non-bonding Electrons = 6
- Bonding Electrons = 0
- Formal Charge = \( 6 - 6 - 0 = -1 \)
- **Sulfur**:
- Valence Electrons = 6
- Non-bonding Electrons = 0
- Bonding Electrons = 12
- Formal Charge = \( 6 - 0 - \frac{1}{2} \times 12 = +2 \)

This structure also has unfavorable charges.

6. **Conclusion**:
After analyzing all four structures, the first structure (where both sulfur and oxygen have a formal charge of 0) is the most preferred and has the lowest energy. Therefore, the answer is:
\[ \text{The most preferred and lowest energy structure for } SO_3 \text{ is option A.} \]