Question

The length of carbon-carbon single bond of the compounds

is expected to increase in the order
(A) Ⅲ > Ⅱ > Ⅰ > Ⅳ
(B)Ⅰ > Ⅲ > Ⅱ > Ⅳ
(C) Ⅲ > Ⅳ > Ⅰ > Ⅱ
(D)Ⅱ > Ⅳ > Ⅰ > Ⅲ

Answer 1

Hint: The length of the carbon-carbon single bond depends upon the hybridization of the carbon atom. The hybridization of the carbon contains S and P characters. More will be the p percentage, more will be the length of the carbon-carbon single bond.

Complete step by step solution:
For comparing the length of the carbon-carbon single bond, we need to check the hybridization of the carbons bonded via single bonds in each option.
In $sp$ , $50\mathrm{\%}$ S and $50\mathrm{\%}$ P character is there.
In $s{p}^2$ , $33.33\mathrm{\%}$ S and $66.66\mathrm{\%}$ P character is there.
In $s{p}^3$ , $25\mathrm{\%}$ S and $75\mathrm{\%}$ P character is there.
Checking each option separately,
(Ⅰ)
  

 $C_2$ and $C_3$ are $s{p}^2$ and $sp$ hybridized respectively.
(Ⅱ)

Both $C_2$ and $C_3$ are $sp$ hybridized respectively.
(Ⅲ)

 $C_1$ and $C_2$ are $s{p}^3$ and $s{p}^2$ hybridized respectively.
(Ⅳ)

$\because$
Here, both $C_2$ and $C_3$ are $s{p}^2$ hybridized respectively.
Now, we know as the p character increases, the bond length of the carbon-carbon single bond increases.
Combining the percentage p character of the carbon-carbon single bond,
For the molecule in option (Ⅰ),
Total p percentage of carbons bonded via single bond = $66.66\mathrm{\%}+50\mathrm{\%}=116.66\mathrm{\%}$
( $\because$ $C_2$ and $C_3$ are $s{p}^2$ and $sp$ hybridized respectively.)
For the molecule in option (Ⅱ),
Total p percentage of carbons bonded via single bond = $50\mathrm{\%}+50\mathrm{\%}=100\mathrm{\%}$
( $\because$ $C_2$ and $C_3$ are $sp$ hybridized respectively.)
For the molecule in option (Ⅲ),
Total p percentage of carbons bonded via single bond = $75\mathrm{\%}+66.66\mathrm{\%}=141.66\mathrm{\%}$
( $\because$ $C_1$ and $C_2$ are $s{p}^3$ and $s{p}^2$ hybridized respectively.)
For the molecule present in option (Ⅳ),
Total p percentage of carbons bonded via single bond = $66.66\mathrm{\%}+66.66\mathrm{\%}=133.32\mathrm{\%}$
( $\because$ $C_2$ and $C_3$ are $s{p}^2$ hybridized respectively.)
Now, we can easily compare on the basis of combined percentage p character.
The molecule in option (Ⅲ) will have the longest carbon-carbon single bond length followed by (Ⅳ),
(Ⅰ) and (Ⅱ).
Therefore, the correct order will be Ⅲ > Ⅳ > Ⅰ > Ⅱ
So, the correct option will be option C: Ⅲ > Ⅳ > Ⅰ > Ⅱ.

Additional information:
A carbon-carbon bond is a covalent bond between two carbon atoms. Single bond is the most common form: a bond composed of two electrons, one from each of the two atoms. The carbon-carbon single bond is a sigma bond and is formed between one hybridized orbital from each of the carbon atoms.

Note:
The carbon-carbon single bond length is directly proportional to the combined percentage of p of both the carbon atoms bonded via single bond and inversely proportional to the combined percentage of s of both the carbon atoms bonded via single bond.
As the combined percentage of p increases, bond length of carbon-carbon single bond increases.