Chapter 24, Problem 70QP

Interpretation Introduction

Interpretation:

The molecular orbital energy level diagrams are to be drawn for ${\text{O}}_{\text{2}}$, ${\text{O}}_{\text{2}}{}^{-}$, and ${\text{O}}_{\text{2}}{}^{2-}$.

Concept introduction:

In molecular orbital theory, two or more atoms are linked together to make molecular orbitals. It predicts the arrangement of electrons in a molecule.

Molecular orbital theory consists of bonding molecular orbital and antibonding molecular orbital. Electronic structure of a molecule is described by this theory.

The respective energies of the atomic orbitals are shown by the molecular orbital energy level diagram.

Order of increasing energy of molecular orbitals is:

Each orbital can possess maximum two electrons according to Hund’s law.

Answer to Problem 70QP

Solution: The molecular orbital energy level diagram is represented below:

$\underset{\_}{}$

$\underset{\_}{}$

$\underset{\_}{}$

$\underset{\_}{\uparrow }$

$\underset{\_}{\uparrow }$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow }$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

${\pi }_{2{\text{p}}_y},{\pi }_{2{\text{p}}_z}$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

${\pi }_{2{\text{p}}_y},{\pi }_{2{\text{p}}_z}$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

${\pi }_{2{\text{p}}_y},{\pi }_{2{\text{p}}_z}$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{2{\text{p}}_x}$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{2{\text{p}}_x}$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{2{\text{p}}_x}$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{2\text{s}}$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{2\text{s}}$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{2\text{s}}$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{1\text{s}}$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{1\text{s}}$

$\underset{\_}{\uparrow \downarrow }$

${\sigma }_{1\text{s}}$

$\underset{\_}{\uparrow \downarrow }$

${\text{O}}_{\text{2}}$

${\text{O}}_2{}^{-}$

${\text{O}}_2{}^{2-}$

Explanation of Solution

Molecular orbital energy level diagram consists of bonding molecular orbital and antibonding molecular orbital. In the given information, ${\text{O}}_{\text{2}}$ contains $12$

valence electrons, ${\text{O}}_{\text{2}}{}^{-}$ contains $13$

valence electrons, and ${\text{O}}_{\text{2}}{}^{2-}$ contains $14$

valence electrons. Each orbital can possess maximum two electrons according to Hund’s law.

${\text{O}}_{\text{2}}$

has 16 electrons ${\text{O}}_{\text{2}}{}^{-}$

has 17 electrons and ${\text{O}}_{\text{2}}{}^{2-}$

has 18 electrons.

${\text{O}}_{\text{2}}$

has configuration

${\text{O}}_{\text{2}}{}^{-}$

has configuration

${\text{O}}_{\text{2}}{}^{2-}$

has configuration

Conclusion

The molecular energy level diagram is drawn for the ${\text{O}}_{\text{2}}$, ${\text{O}}_{\text{2}}{}^{-}$, and ${\text{O}}_{\text{2}}{}^{2-}$.