Question

Number of $\sigma$ and $\pi$ bonds in $C_2$ molecule is/are:
(A) $1\sigma \text{ and 1}\pi$
(B) $1\sigma \text{ and 2}\pi$
(C) $2\pi \text{ only}$
(D) $1\sigma \text{ and 3}\pi$

Answer 1

Hint: Recall the molecular orbital theory (MOT) and write the electronic configuration of $C_2$ molecule according to MOT. You will find that the $C_2$ molecule has two sets of paired orbitals in the degenerate pi-bonding orbitals and bond order comes out to be 2. Thus, $C_2$ molecule will form two bonds and only these 4 electrons in the degenerate pi-bonding orbitals will be involved in bonding.

Complete step by step solution:
Diatomic carbon is a green-greyish inorganic compound. It has a chemical formula $C_2$ and written as $C=C$. It is a component of carbon vapour and is unstable at ambient temperature. Its IUPAC name is ethenediylidene or dicarbon.
Bonding in $C_2$ molecule: Configuration of $C_2$ molecule according to molecular orbital theory (MOT) is: $(\sigma 1s{)}^2({\sigma }^{\ast }1s{)}^2(\sigma 2s{)}^2({\sigma }^{\ast }2s{)}^2(\pi 2p_x{)}^2(\pi 2p_y{)}^2$
The bond order of $C_2$ molecule is:
Bond order= ${\displaystyle \frac{\text{no}\text{. of bonding electrons - no}\text{. of antibonding electrons }}{2}}={\displaystyle \frac{8-4}{2}}=2$
Therefore, the bond order of $C_2$ molecule is two. This means there should exist a double bond between the two carbons in a $C_2$ molecule. But some studies show that a quadruple bond exists in dicarbon. MO theory also shows that the last two paired sets of electrons enter in the degenerate (having same energy) pi-bonding set of orbitals i.e. $\pi 2p_x$ and $\pi 2p_y$. These 4 electrons are in the pi orbitals and thus the two bonds in the $C_2$ molecule will be pi bonds only and no sigma bond. Usually, whenever there is a double bond, one is a sigma bond before a pi-bond. But this is not the case in $C_2$ molecules.
Thus, the number of $\sigma$ and $\pi$ bonds in $C_2$ molecule will be zero and two respectively.

Therefore, the correct option is C.

Note: Usually most people think that $C_2$ molecule, having 8 valence electrons, does not exist. But it does exist at very high temperatures and in the gaseous state. At low temperatures, $C_2$ aggregates to form many allotropic forms of carbon like buckyballs, nanotubes, graphene sheets, graphite, soot and so on. $C_2$ or carbon is diamagnetic in nature because all the electrons are paired.