Decreasing order of C-C bond length is (I) `C_2H_4` (II) `C_2H_2` (III) `C_6 H_6` (IV) `C_2H_6`

Options

A. IVgt IIgt I gt II
B. I gt II gt IV gt III
C. II gt I gt IV gt III
D. IV gt I gt III gt II.

Explanation

To determine the decreasing order of C-C bond lengths in the given compounds (C₂H₄, C₂H₂, C₆H₆, and C₂H₆), we need to analyze the type of bonds present in each molecule as well as the nature of those bonds.

### Step-by-Step Solution:

1. **Identify the Types of Bonds**:
- **C₂H₄ (Ethylene)**: Contains a double bond (C=C).
- **C₂H₂ (Acetylene)**: Contains a triple bond (C≡C).
- **C₆H₆ (Benzene)**: Contains alternating double bonds (resonance structure), effectively having C=C bonds.
- **C₂H₆ (Ethane)**: Contains single bonds (C-C).

2. **Understand Bond Lengths**:
- Generally, the bond length decreases with increasing bond order:
- Single bonds (C-C) are longer than double bonds (C=C), which are longer than triple bonds (C≡C).
- Therefore, the order of bond lengths from longest to shortest is:
- Single bond > Double bond > Triple bond.

3. **Analyze Each Compound**:
- **C₂H₆ (Ethane)**: Has single C-C bonds. This will have the longest bond length.
- **C₂H₄ (Ethylene)**: Has a double C=C bond. This will have a shorter bond length than C₂H₆.
- **C₆H₆ (Benzene)**: Has resonance structures with C=C bonds. The bond lengths in benzene are slightly longer than typical C=C bonds due to resonance stabilization, but shorter than C-C single bonds.
- **C₂H₂ (Acetylene)**: Has a triple C≡C bond. This will have the shortest bond length.

4. **Order the Compounds**:
- From the analysis:
- Longest bond length: C₂H₆ (Ethane)
- Next: C₆H₆ (Benzene)
- Next: C₂H₄ (Ethylene)
- Shortest bond length: C₂H₂ (Acetylene)

5. **Final Decreasing Order of C-C Bond Lengths**:
- C₂H₆ > C₆H₆ > C₂H₄ > C₂H₂

### Conclusion:
The decreasing order of C-C bond lengths is:
**C₂H₆ > C₆H₆ > C₂H₄ > C₂H₂**