Among the following molecules, the correct order of `C - C` bond length is

Options

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

Answer

To determine the correct order of C-C bond lengths among the given molecules (C2H6, C2H4, C2H2, and C6H6), we need to analyze the types of bonds present in each molecule. The bond length is inversely related to the bond order; that is, as the bond order increases (single < double < triple), the bond length decreases.

### Step-by-Step Solution:

1. **Identify the Molecules:**
- C2H6 (Ethane): This is an alkane with a single bond between the two carbon atoms.
- C2H4 (Ethene): This is an alkene with a double bond between the two carbon atoms.
- C2H2 (Ethyne): This is an alkyne with a triple bond between the two carbon atoms.
- C6H6 (Benzene): This is a cyclic compound with resonance structures, effectively having bonds that are between single and double bonds.

2. **Determine Bond Types:**
- C2H6 has a single bond (C-C).
- C2H4 has a double bond (C=C).
- C2H2 has a triple bond (C≡C).
- C6H6 has bonds that are considered to be of bond order 1.5 due to resonance.

3. **Rank the Bond Orders:**
- Triple bond (C≡C) in C2H2 has the highest bond order (3).
- Double bond (C=C) in C2H4 has a bond order of 2.
- Benzene (C6H6) has a bond order of 1.5 due to resonance.
- Single bond (C-C) in C2H6 has the lowest bond order (1).

4. **Determine the Bond Length Order:**
- The bond length is inversely proportional to the bond order. Therefore, the order of bond lengths from longest to shortest is:
- C2H6 (longest, single bond)
- C6H6 (next longest, resonance bond)
- C2H4 (shorter, double bond)
- C2H2 (shortest, triple bond)

5. **Final Order of C-C Bond Lengths:**
- The correct order of C-C bond lengths from longest to shortest is:
- C2H6 > C6H6 > C2H4 > C2H2

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