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

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 $sp$ , $50\%$ S and $50\%$ P character is there.
In $s{p^2}$ , $33.33\%$ S and $66.66\%$ P character is there.
In $s{p^3}$ , $25\%$ S and $75\%$ 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 = $66.66\% + 50\% = 116.66\%$
( $\because$ ${C_2}$ 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 = $50\% + 50\% = 100\%$
( $\because$ ${C_2}$ and ${C_3}$ are $sp$ hybridized respectively.)
For the molecule in option (Ⅲ),
Total p percentage of carbons bonded via single bond = $75\% + 66.66\% = 141.66\%$
( $\because$ ${C_1}$ 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 = $66.66\% + 66.66\% = 133.32\%$
( $\because$ ${C_2}$ 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.