To solve this problem, we need to match each compound in List I with the correct description of its bonding in List II. Let's analyze each compound:$•$Ethane (A):$\\ Ethane \ ({C}_2{H}_6)$is a saturated hydrocarbon with a single bond between the two carbon atoms. Each carbon atom forms three additional single bonds with hydrogen atoms. Therefore, ethane has one $\sigma$-bond between the carbon atoms.$\\$Match: A$\rightarrow$III (One $\sigma$-bond)$•$Ethene (B):$\\ Ethene ({C}_2{H}_4)$ is an unsaturated hydrocarbon with a double bond between the two carbon atoms. A double bond consists of one $\sigma-bond$ and one $\pi-bond. \\$Match: B$\rightarrow$I (One $\sigma$-bond and one $\pi$-bond)$•$Carbon molecule, C$_2$ (C):$\\$ The diatomic carbon molecule $({C}_2)$is known to have a triple bond, which consists of one $\sigma-bond$ and two $\pi-bonds. \\$Match: C$\rightarrow$II (Two $\pi$-bonds)$\newline$Ethyne (D):$\\ Ethyne \ ({C}_2{H}_2)$, also known as acetylene, has a triple bond between the two carbon atoms. A triple bond consists of one $\sigma-bond$ and two $\pi-bonds. \\$Match: D$\rightarrow$IV (One $\sigma$-bond and two $\pi$-bonds)$\newline$Based on the analysis, the correct matching is:$\newline A \rightarrow III - B \rightarrow I - C \rightarrow II - D \rightarrow IV \newline$This corresponds to Option 1.