In cyclic structure of `(SO_(3))_(x)` if x is number of `SO_(3)` molecules involved in cycle formation and y is the number of `sp^(3)` hybridised S - atoms What is the sum of `x+y`?

Answer

To solve the problem, we need to determine the values of \( x \) and \( y \) in the cyclic structure of \( (SO_3)_x \) and then find the sum \( x + y \).

### Step-by-Step Solution:

1. **Understanding the Structure of \( SO_3 \)**:
- Sulfur trioxide (\( SO_3 \)) can exist in a cyclic trimeric structure. This means that multiple \( SO_3 \) molecules can combine to form a cyclic arrangement.

2. **Identifying \( x \)**:
- In the cyclic structure of \( SO_3 \), it is known that three \( SO_3 \) molecules combine to form a cyclic trimer. Therefore, we can conclude that:
\[ x = 3 \]

3. **Identifying \( y \)**:
- Each sulfur atom in the cyclic structure is hybridized. In the case of \( SO_3 \), the sulfur atoms undergo \( sp^3 \) hybridization. This is because each sulfur atom forms four sigma bonds (one with each oxygen atom in the cyclic arrangement).
- Since there are three sulfur atoms in the cyclic trimer, we have:
\[ y = 3 \]

4. **Calculating \( x + y \)**:
- Now that we have both \( x \) and \( y \), we can calculate the sum:
\[ x + y = 3 + 3 = 6 \]

### Final Answer:
The sum of \( x + y \) is \( 6 \).

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