Number of `'sigma'` and `'pi'` bonds in solid `SO_(3)` cyclic structure are

Options

A. `12sigma and 6pi`
B. `12sigma and 12pi`
C. `6sigma and 12pi`
D. `6sigma and 6pi`

Answer

To determine the number of sigma (σ) and pi (π) bonds in the cyclic structure of solid \( SO_3 \), we can follow these steps:

### Step 1: Understand the Structure of \( SO_3 \)
Solid \( SO_3 \) has a cyclic structure where each sulfur atom is bonded to three oxygen atoms. In the gaseous state, \( SO_3 \) has a trigonal planar structure with double bonds between sulfur and oxygen. However, in the solid state, these molecules can form a cyclic arrangement.

### Step 2: Identify the Bonds
In the cyclic structure of \( SO_3 \):
- Each sulfur atom forms bonds with two oxygen atoms through single bonds and one oxygen atom through a double bond.
- A double bond consists of one sigma bond and one pi bond.
- A single bond consists of one sigma bond.

### Step 3: Count the Sigma Bonds
1. Each sulfur-oxygen single bond contributes 1 sigma bond.
2. Each sulfur-oxygen double bond contributes 1 sigma bond and 1 pi bond.

In the cyclic structure:
- Each sulfur atom is connected to two oxygen atoms via single bonds and one oxygen atom via a double bond.
- For three sulfur atoms in the cyclic structure:
- **Single Bonds**: 6 single bonds (2 per sulfur × 3 sulfur atoms)
- **Double Bonds**: 3 double bonds (1 per sulfur atom)

Calculating sigma bonds:
- From single bonds: \( 6 \) sigma bonds
- From double bonds: \( 3 \) sigma bonds

Total sigma bonds = \( 6 + 3 = 9 \) sigma bonds.

### Step 4: Count the Pi Bonds
Each double bond contributes 1 pi bond. Therefore, for the three double bonds:
- Total pi bonds = \( 3 \).

### Final Count
- **Total Sigma Bonds**: 9
- **Total Pi Bonds**: 3

### Conclusion
In the cyclic structure of solid \( SO_3 \), there are **9 sigma bonds and 3 pi bonds**.

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