Question

In series ethane, ethylene, and acetylene the ${\text{C - H}}$ bond energy is

Answer 1

Bond energy is defined as the amount of energy required to break one mole of the bond. Bond energy is dependent on the bond strength which is related to hybridization and bond length.

Complete step by step answer:
If we discuss the bond length for each of the hydrocarbons given, there is a single bond present in the case of ethane and a double and triple bond is present in ethylene and acetylene respectively. Since the bond length of a single bond is bigger than that of double and triple bond so it is quite easy to break a bond in alkane as compared to alkene and alkyne. So we can say that bond energy for ethane is lesser than ethylene and acetylene.
If we discuss hybridization in the case of ethane there is $s{p^3}$ hybridization and in the case of ethylene and acetylene, there are $s{p^2}$ and $sp$ hybridization respectively. Since the size of p orbital is larger than s orbital and in the case of ethane there is one s orbital and three p orbital and in the case of ethylene there is one s and two p orbitals and in the case of acetylene, there are one s and p orbital so the size of bond in ethane is larger than ethylene and acetylene so we can say lower bond energy is required for ethane.

Note:
Alternatively, we can say that in the case of ethane there is only one sigma bond but in the case of ethylene and acetylene there is one sigma and one pi, and one sigma and two pi bonds respectively. Since pi bond involves sideways overlapping which is always weaker than internuclear overlapping in the sigma bond. But the carbon-carbon double bond is stronger than the carbon-carbon single bond because it contains one stronger sigma bond and one weaker pi bond. Similarly, the carbon-carbon triple bond is still stronger due to one sigma and two pi bonds. So the bond energy will be in order as:
Acetylene> ethylene>ethane.