1,3,5,7-Octatetraene contains (X)________ `sigma`-bonds and (Y)_______`pi`-bonds. 'X' and 'Y' are

Options

A. 23.4
B. 17,4
C. 18,5
D. 33,2

Explanation

To solve the problem of determining the number of sigma (σ) and pi (π) bonds in 1,3,5,7-octatetraene, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure of 1,3,5,7-Octatetraene**:
- 1,3,5,7-Octatetraene is a hydrocarbon with 8 carbon atoms (C) and 4 double bonds. The structure can be represented as:
```
H2C=CH-CH=CH-CH=CH-CH=CH2
```

2. **Count the Carbon Atoms**:
- There are 8 carbon atoms in total.

3. **Determine the Number of Sigma Bonds**:
- Each carbon atom forms 4 bonds (either with other carbon atoms or hydrogen atoms).
- In a double bond, the first bond is a sigma bond, and the second bond is a pi bond.
- Count the sigma bonds:
- Each of the 7 carbon-carbon (C-C) single bonds contributes 1 sigma bond.
- Each of the 4 double bonds contributes 1 sigma bond.
- Additionally, each carbon atom is bonded to hydrogen atoms. The terminal carbons (C1 and C8) are bonded to 2 hydrogen atoms each, while the internal carbons (C2, C3, C4, C5, C6, C7) are bonded to 1 hydrogen atom each.
- Total hydrogen bonds: 2 (C1) + 1 (C2) + 1 (C3) + 1 (C4) + 1 (C5) + 1 (C6) + 1 (C7) + 2 (C8) = 10 hydrogen atoms.
- Therefore, the total number of sigma bonds is:
- C-C sigma bonds: 7 (from 7 C-C bonds) + 4 (from 4 C=C double bonds) + 10 (from C-H bonds) = 21 sigma bonds.

4. **Determine the Number of Pi Bonds**:
- Each double bond contributes 1 pi bond.
- Since there are 4 double bonds, the total number of pi bonds is:
- 4 pi bonds.

5. **Final Count**:
- The number of sigma bonds (X) = 21.
- The number of pi bonds (Y) = 4.

### Conclusion:
- Therefore, X = 21 and Y = 4.

### Final Answer:
1,3,5,7-Octatetraene contains **(X) 21 sigma bonds** and **(Y) 4 pi bonds**.