The C–C bond length of the following molecules is in the order

\(C_2H_2 < C_2H_4 < C_6H_6 < C_2H_6\)

The correct answer is option 2. \(C_2H_2 < C_2H_4 < C_6H_6 < C_2H_6\).

To determine the correct order of C–C bond lengths in the given molecules, let's consider the type of bonding and hybridization in each case:

\(C_2H_6\) (Ethane): In ethane, each carbon is \(sp^3\) hybridized, leading to a single bond (sigma bond) between the carbon atoms. The C–C bond length is approximately 1.54 Å.

\(C_2H_4\) (Ethylene): In ethylene, each carbon is \(sp^2\) hybridized, leading to a double bond (one sigma and one pi bond) between the carbon atoms. The C–C bond length is shorter than in ethane, approximately 1.34 Å.

\(C_6H_6\) (Benzene): In benzene, the carbon atoms are also \(sp^2\) hybridized, and the C–C bonds are intermediate between a single and double bond due to resonance. The C–C bond length is approximately 1.39 Å.

\(C_2H_2\) (Acetylene): In acetylene, each carbon is \(sp\) hybridized, leading to a triple bond (one sigma and two pi bonds) between the carbon atoms. The C–C bond length is the shortest, approximately 1.20 Å.

Order of C–C Bond Lengths: Based on the bond types and hybridization, the order from longest to shortest C–C bond length is:

Single bond (\(sp^3\) hybridization) > Resonance bond (\(sp^2\) hybridization in benzene) > Double bond (\(sp^2\) hybridization) > Triple bond (\(sp\) hybridization)

So, the correct order is: \(C_2H_6 > C_6H_6 > C_2H_4 > C_2H_2 \)

This matches option 2 if reversed. Thus the correct answer is option 2: \(C_2H_2 < C_2H_4 < C_6H_6 < C_2H_6\)