Chapter 9, Problem 54QP

Interpretation Introduction

Interpretation:

The bonding in ${\text{C}}_{\text{2}}{}^{2-}$

is to be explained based on molecular orbital theory, and the bond order of ${\text{C}}_{\text{2}}{}^{2-}$

to be compared with that of ${\text{C}}_{\text{2}}$.

Concept introduction:

Two atomic orbitals undergo a combination process in order to form a bonding and an anti-bonding molecular orbital. Orbitals that lie on the internuclear axis combine to form sigma molecular orbitals, and orbitals parallel to each other combine to form molecular orbitals.

The molecular orbitals formed by the combination of $\text{1s}$

orbitals are a bonding molecular orbital, designated by ${\sigma }_{1s}$, and an antibonding molecular orbital, designated by ${\sigma }^{\ast }{}_{1s}$. The $\text{2s}$

orbital forms corresponding molecular orbitals.

The molecular orbitals formed by the combination of ${\text{2p}}_{\text{x}}$

orbitals area bonding molecular orbital, designated by ${\sigma }_{2{\text{p}}_{\text{x}}}$, and an antibonding molecular orbital, designated by ${\sigma }^{\ast }{}_{2{\text{p}}_{\text{x}}}$.

The molecular orbitals formed by combining ${\text{2p}}_{\text{y}}$ and ${\text{2p}}_{\text{z}}$

orbitals are bonding molecular orbitals, designated by ${\text{π}}_{{\text{2p}}_{\text{y}}}$

and ${\text{π}}_{{\text{2p}}_{\text{z}}}$, and antibonding molecular orbitals, designated by ${\text{π}}^{\ast }{}_{{\text{2p}}_{\text{y}}}$

and ${\text{π}}^{\ast }{}_{{\text{2p}}_{\text{z}}}$.

Electrons are filled in the molecular orbitals in increasing order of energy.

Bond order is determined by subtracting the number of electrons in antibonding orbitals from the number of electrons in bonding orbitals, and dividing by two.

Higher the bond order, more stable is the molecule. Zero bond order indicates the molecule is not stable.