The difference in the number of `sigma` and `pi` bond in trimer of `SO_3` i.e. `S_3O_9` is : (consider no co-ordinate bond to be present )

Explanation

To solve the problem of finding the difference in the number of sigma (σ) and pi (π) bonds in the trimer of SO₃, which is S₃O₉, we can follow these steps:

### Step 1: Understand the Structure of S₃O₉
The trimer of SO₃ consists of three sulfur (S) atoms and nine oxygen (O) atoms. Each sulfur atom is bonded to oxygen atoms through double bonds.

### Step 2: Draw the Structure
To visualize the bonding, we can sketch the structure of S₃O₉. Each sulfur atom will be connected to two oxygen atoms through double bonds, and the three sulfur atoms will be connected to each other through single bonds.

### Step 3: Count the Sigma Bonds
1. Each double bond consists of one sigma bond and one pi bond.
2. In the structure of S₃O₉:
- There are 6 double bonds (each S=O bond).
- Each double bond contributes 1 sigma bond.
- Additionally, each S-S bond contributes 1 sigma bond.

Therefore, the total number of sigma bonds can be calculated as follows:
- Sigma bonds from double bonds: 6 (from 6 double bonds)
- Sigma bonds from S-S bonds: 3 (since there are 3 S atoms, they form 3 S-S bonds)

Total sigma bonds = 6 (from double bonds) + 3 (from S-S bonds) = 9 sigma bonds.

### Step 4: Count the Pi Bonds
1. Each double bond contributes one pi bond.
2. Since there are 6 double bonds, the total number of pi bonds is:
Total pi bonds = 6.

### Step 5: Calculate the Difference
Now, we can find the difference between the number of sigma and pi bonds:
Difference = Number of sigma bonds - Number of pi bonds
Difference = 9 (sigma bonds) - 6 (pi bonds) = 3.

### Final Answer
The difference in the number of sigma and pi bonds in S₃O₉ is **3**.

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