Question

In the series, ethane, ethylene and acetylene, the carbon-hydrogen bond length is:
A.Equal in all the three
B.Largest in ethane
C.Smallest in ethylene
D.Largest in ethylene

Answer 1

The ethane molecule contains carbon-carbon single bonds. The ethylene molecule contains carbon-carbon double bonds. And the acetylene molecule contains a carbon-carbon triple bond.

Complete step by step answer:
The distance between the nuclei of the two atoms that are bonded in a molecule is known as bond length.
The structures of ethane, ethylene and acetylene are as follows:

In ethane, each carbon atom forms four bond pairs. Thus, each carbon atom in ethane is $s{p^3}$ hybridised. The $s{p^3}$ hybrid orbital of carbon atom overlaps with the 1s orbital of the hydrogen atom.
Percentage s-character in $s{p^3}$ hybridised orbital $= \dfrac{1}{4} = 0.25 \times 100\% = 25\%$.
Thus, the percentage s-character in ethane is $25\%$.
In ethylene, each carbon atom forms three bond pairs. Thus, each carbon atom in ethylene is $s{p^2}$ hybridised. The $s{p^2}$ hybrid orbital of carbon atom overlaps with the 1s orbital of the hydrogen atom.
Percentage s-character in $s{p^2}$ hybridised orbital $= \dfrac{1}{3} = 0.33 \times 100\% = 33\%$.
Thus, the percentage s-character in ethylene is $33\%$.
In acetylene, each carbon atom forms two bond pairs. Thus, each carbon atom in acetylene is sp hybridised. The sp hybrid orbital of carbon atom overlaps with the 1s orbital of the hydrogen atom.
Percentage s-character in sp hybridised orbital $= \dfrac{1}{2} = 0.5 \times 100\% = 50\%$.
Thus, the percentage s-character in acetylene is $50\%$.
As the percentage s-character increases, the electronegativity increases. As the electronegativity increases, the bond strength increases and the bond length decreases. Thus, more the percentage s-character shorter is the bond length.
The order of percentage s-character is as follows:
Acetylene > Ethylene > Ethane
Thus, the order of bond length is as follows:
Ethane > Ethylene > Acetylene
Thus, in the series, ethane, ethylene and acetylene, the carbon-hydrogen bond length is largest in ethane.
Thus, the correct option is option (A).

Note:
The carbon-hydrogen bond length in ethane is $111{\text{ pm}}$. The carbon-hydrogen bond length in ethylene is $109{\text{ pm}}$. The carbon-hydrogen bond length in acetylene is $105{\text{ pm}}$.