Find the value of `(x+5)/(2)` where x = total structural isomers with molecular formula `C_(6)H_(12)` containing cyclo propane ring.

Answer

To solve the problem, we need to find the total number of structural isomers for the molecular formula \( C_6H_{12} \) that contain a cyclopropane ring. Then, we will use this value to calculate \( \frac{x + 5}{2} \), where \( x \) is the number of structural isomers.

### Step-by-Step Solution:

1. **Identify the Structure**:
- The molecular formula \( C_6H_{12} \) indicates that we have a total of 6 carbon atoms and 12 hydrogen atoms. The presence of a cyclopropane ring means that 3 of these carbon atoms will form a cyclic structure.

2. **Calculate Remaining Carbon Atoms**:
- Since 3 carbon atoms are used in the cyclopropane ring, we have \( 6 - 3 = 3 \) carbon atoms left to arrange as structural isomers.

3. **Determine Possible Arrangements**:
- The remaining 3 carbon atoms can be arranged in different ways:
- **Straight Chain (n-propyl)**: This is one isomer.
- **Branched Chains**:
- One branch can be at the first carbon (isobutyl).
- Another arrangement can be a methyl branch on the second carbon (sec-butyl).
- These arrangements yield multiple structural isomers.

4. **Count the Structural Isomers**:
- After analyzing the arrangements, we find that there are a total of 6 structural isomers for \( C_6H_{12} \) containing a cyclopropane ring.

5. **Calculate \( x + 5 \) and then \( \frac{x + 5}{2} \)**:
- Here, \( x = 6 \) (the number of structural isomers).
- Now, calculate \( x + 5 \):
\[ x + 5 = 6 + 5 = 11 \]
- Now, calculate \( \frac{x + 5}{2} \):
\[ \frac{x + 5}{2} = \frac{11}{2} = 5.5 \]

### Final Answer:
The value of \( \frac{x + 5}{2} \) is \( 5.5 \).