Arrange the following molecules in the correct order of decreasing C-C bond length:
`C_(2)H_(6), C_(2)H_(4), C_(2)H_(2), C_(6)H_(6)`

Options

A. `C_(2)H_(6) gt C_(6)H_(6) gt C_(2)H_(4) gt C_(2)H_(2)`
B. `C_(2)H_(6) gt C_(2)H_(4) gt C_(6)H_(6) gt C_(2)H_(2)`
C. `C_(2)H_(4) gt C_(2)H_(2) gt C_(2)H_(6) gt C_(6)H_(6)`
D. `C_(2)H_(2) gt C_(6)H_(6) gt C_(2)H_(4) gt C_(2)H_(6)`

Explanation

To arrange the given molecules in the correct order of decreasing C-C bond length, we need to analyze the bond types present in each molecule. The bond length is inversely related to the bond order; that is, the higher the bond order, the shorter the bond length.

### Step-by-Step Solution:

1. **Identify the molecules and their structures**:
- **C₂H₆ (Ethane)**: Contains single C-C bonds. Each C-C bond has a bond order of 1.
- **C₂H₄ (Ethene)**: Contains a double C=C bond. The bond order for C-C in this case is also 1 (since we only consider the C-C bond).
- **C₂H₂ (Ethyne)**: Contains a triple C≡C bond. The bond order for C-C here is 3.
- **C₆H₆ (Benzene)**: Contains alternating single and double bonds due to resonance. The effective bond order for C-C in benzene is 1.5.

2. **Determine the bond order for each molecule**:
- Ethane (C₂H₆): Bond order = 1
- Ethene (C₂H₄): Bond order = 1
- Ethyne (C₂H₂): Bond order = 3
- Benzene (C₆H₆): Bond order = 1.5

3. **Rank the bond lengths based on bond order**:
- The bond with the lowest bond order will have the longest bond length.
- Therefore, the order of bond lengths from longest to shortest is:
- Ethane (C₂H₆) and Ethene (C₂H₄) have the longest bond lengths (bond order = 1).
- Benzene (C₆H₆) comes next (bond order = 1.5).
- Ethyne (C₂H₂) has the shortest bond length (bond order = 3).

4. **Final Arrangement**:
- C₂H₆ (Ethane) = longest bond length
- C₂H₄ (Ethene) = same as Ethane
- C₆H₆ (Benzene) = shorter than Ethane and Ethene
- C₂H₂ (Ethyne) = shortest bond length

Thus, the correct order of decreasing C-C bond length is:
**C₂H₆ = C₂H₄ > C₆H₆ > C₂H₂**