Question

question 2 (10 points) which of the following species has the shortest carbon - to - carbon bond? a) c2h6 b) c2h2 c) c2h4 d) c6h6 e) all of the c - c bonds are the same length.

Explanation:

Step1: Recall bond - length trends

In hydrocarbons, the bond length decreases as the bond order increases. The bond order of \(C - C\) single bond (\(C_2H_6\)), \(C = C\) double bond (\(C_2H_4\)), \(C\equiv C\) triple bond (\(C_2H_2\)). The bond order of \(C - C\) single bond is \(1\), for \(C = C\) double bond is \(2\), and for \(C\equiv C\) triple bond is \(3\). The higher the bond order, the shorter the bond length.

Step2: Analyze each option

• For \(C_2H_6\) (ethane), it has \(C - C\) single bonds (\(C - C\) bond length \(\approx154\) pm).
• For \(C_2H_2\) (acetylene), it has \(C\equiv C\) triple bonds (\(C\equiv C\) bond length \(\approx120\) pm).
• For \(C_2H_4\) (ethylene), it has \(C = C\) double bonds (\(C = C\) bond length \(\approx134\) pm).
• For \(C_6H_6\) (benzene), it has a delocalized \(\pi\) - system. The \(C - C\) bond length in benzene (\(\approx139\) pm) is between \(C - C\) single and \(C = C\) double bond lengths.

Answer:

B. \(C_2H_2\)