Number of S-O-S bridges, no. of `sigma` and `pi` bonds in cyclic trimer of `SO_3`

Options

A. `3, 12 sigma, 6 pi`
B. `3,18 sigma, 6 pi`
C. `2, 12 sigma, 4 pi`
D. `4, 12 sigma, 3 pi`

Explanation

To solve the problem regarding the cyclic trimer of \( SO_3 \), we need to determine the number of S-O-S bridges, the number of sigma bonds, and the number of pi bonds. Let's break this down step by step.

### Step 1: Identify the Structure of Cyclic Trimer of \( SO_3 \)

The cyclic trimer of \( SO_3 \) can be represented as \( S_3O_9 \). In this structure, three sulfur atoms are bonded to nine oxygen atoms. Each sulfur atom forms bonds with oxygen atoms, creating a cyclic arrangement.

**Hint:** Visualize the cyclic structure of \( SO_3 \) to understand how the sulfur and oxygen atoms are connected.

### Step 2: Count the S-O-S Bridges

In the cyclic trimer \( S_3O_9 \), each sulfur atom is connected to two oxygen atoms and is also connected to the other sulfur atoms. The connections between sulfur atoms through oxygen atoms are referred to as S-O-S bridges.

In this structure, there are three S-O-S bridges formed between the sulfur atoms.

**Hint:** Look for the connections between sulfur atoms that are mediated by oxygen atoms to count the S-O-S bridges.

### Step 3: Count the Sigma Bonds

Each sulfur atom in \( SO_3 \) forms double bonds with oxygen atoms. In a double bond, there is one sigma bond and one pi bond.

In the cyclic trimer \( S_3O_9 \):
- Each sulfur atom forms double bonds with three oxygen atoms.
- Therefore, there are a total of 6 double bonds (2 for each sulfur atom).

Since each double bond consists of one sigma bond:
- Total sigma bonds = Number of double bonds = 6.

Additionally, there are sigma bonds formed between sulfur and oxygen in the S-O-S bridges:
- Each S-O-S bridge contributes one sigma bond.

Thus, the total number of sigma bonds is:
- Total sigma bonds = 6 (from double bonds) + 6 (from S-O-S bridges) = 12.

**Hint:** Remember that each double bond contributes one sigma bond and that S-O-S bridges also contribute to the sigma bond count.

### Step 4: Count the Pi Bonds

In the cyclic trimer \( S_3O_9 \), each double bond contributes one pi bond. Since there are 6 double bonds:
- Total pi bonds = 6.

**Hint:** Recall that pi bonds are formed in double bonds, and each double bond contributes exactly one pi bond.

### Final Summary

- Number of S-O-S bridges: **3**
- Number of sigma bonds: **12**
- Number of pi bonds: **6**

Thus, the final answer is:
- **3 S-O-S bridges, 12 sigma bonds, and 6 pi bonds.**