VerifiedHint: A sigma bond is formed by the head on overlapping of half filled atomic orbitals along the internuclear axis. Formation of sigma bonds involves either s-s overlapping or s-p overlapping or p-p overlapping. On the other hand, a pi bond is formed by the sidewise overlapping of half filled atomic orbitals in a direction perpendicular to the internuclear axis. It involves only p-p sideways overlapping.
Complete step by step answer:
A sigma bond can be formed independently between two atoms but a pi bond can be formed only when a sigma bond has already been formed between two atoms. This means every single bond will contain one sigma bond. Every double bond will also contain one sigma bond. But in a double bond, one pi bond will also be present in addition to the sigma bond. Similarly, in a triple bond, there will be a sigma bond and two pi bonds.
Let us now check the structures of the given compounds and determine the number of sigma and pi bonds present in each of them one by one.
Tetracyanomethane has the formula ${\text{C}}{\left( {{\text{CN}}} \right)_{\text{4}}}$ and has the structure shown below.
Here, the structure is just like methane with all the hydrogen atoms replaced by cyanide groups. The central carbon is attached to 4 cyanide groups by 4 single bonds which mean 4 sigma bonds. Each cyanide group has a triple bond or one sigma and two pi bonds. Since there are 4 cyanide groups, there will be 4 sigma and 8 pi bonds. So, in total, there will be 8 sigma and 8 pi bonds. So, the ratio of sigma to pi bonds will be $\dfrac{8}{8} = 1$ .
Carbon dioxide is a linear molecule and the central carbon is bonded to each of the two oxygen atoms by a double bond. So, overall there are two double bonds which mean 2 sigma and 2 pi bonds. So, the ratio is $\dfrac{2}{2} = 1$ .
In benzene, there are 6 carbon-hydrogen single bonds, 3 carbon-carbon single bonds and 3 carbon-carbon double bonds. Thus, overall there are 12 sigma bonds and 3 pi bonds and so the required ratio is $\dfrac{{12}}{3} = 4$ .
In 1, 3-butadiene, there are 2 double bonds, one carbon-carbon single bond and 6 carbon-hydrogen single bonds. Overall, there are 2 pi bonds and 9 sigma bonds and so the required ratio is \[\dfrac{9}{2} = 4.5\] .
So, the correct order will be A=B<C<D and so the correct option is A.
Note: Sigma bonds are strong bonds as orbitals overlap to a greater extent but pi bonds are weak as the orbitals overlap to less extent. There is free rotation of atoms about the sigma bond but no free rotation about the pi bond. Moreover, the shape of a molecule is decided by the number of sigma bonds and it does not depend upon the pi bonds.
