Chapter 14, Problem 85AE

Interpretation Introduction

Interpretation: The number of electrons in each of the given molecular orbital for ${\text{N}}_{\text{2}},{\text{N}}_{{}_{\text{2}}}^{+},{\text{N}}_{{}_{\text{2}}}^{-}$ needs to be determined.

	${\text{N}}_{\text{2}}$	${\text{N}}_{{}_{\text{2}}}^{+}$	${\text{N}}_{{}_{\text{2}}}^{-}$
${\text{σ}}_{{}_{\text{2px}}}^{*}$
${\text{π}}_{{}_{\text{2py}}}^{*}$
${\text{σ}}_{\text{2px}}$
${\text{π}}_{\text{2pz}}$
${\text{σ}}_{\text{2s}}$
${\text{σ}}_{{}_{\text{2s}}}^{\text{*}}$

Concept Introduction: Molecular orbital theory explained the bonding, magnetic and spectral properties of molecule. It is based on the formation of molecular orbitals by the combination of atomic orbitals. On the basis of energy and stability these molecular orbitals can be further classified in three types:

• Bonding molecular orbitals (BMO): They have lesser energy than atomic orbital therefore more stable compare to atomic orbital.
• Antibonding molecular orbitals (ABMO): They have higher energy than atomic orbital therefore less stable compare to atomic orbital.
• Non-bonding molecular orbitals (NBMO): They have same energy as atomic orbital.

Molecular orbital diagrams represents the distribution of electrons in different molecular orbitals in increasing order of their energy. Hence lower energy molecular orbitals occupy first then only electron moves in higher energy orbitals.

Answer to Problem 85AE

	${\text{N}}_{\text{2}}$	${\text{N}}_{{}_{\text{2}}}^{+}$	${\text{N}}_{{}_{\text{2}}}^{-}$
${\text{σ}}_{{}_{\text{2p}}}^{*}$	0	0	0
${\text{π}}_{{}_{\text{2p}}}^{*}$	0	0	1
${\text{σ}}_{\text{2p}}$	2	1	2
${\text{π}}_{\text{2p}}$	4	4	4
${\text{σ}}_{\text{2s}}$	2	2	2
${\text{σ}}_{{}_{\text{2s}}}^{\text{*}}$	2	2	2

Explanation of Solution

Given information:

  ${\text{N}}_{\text{2}},{\text{N}}_{{}_{\text{2}}}^{+},{\text{N}}_{{}_{\text{2}}}^{-}$ are related with each other.

The molecular orbital electronic configuration of ${\text{N}}_{\text{2}},{\text{N}}_{{}_{\text{2}}}^{+},{\text{N}}_{{}_{\text{2}}}^{-}$ can be written as:

  ${\text{N}}_{\text{2}}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^{\text{2}}$

  ${\text{N}}_{{}_{\text{2}}}^{+}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^1$

  ${\text{N}}_{{}_{\text{2}}}^{-}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^{\text{2}}{{\text{(π}}_{{}_{\text{2py}}}^{*}\text{)}}^1$

Hence number of electrons in the given molecular orbitals are:

	${\text{N}}_{\text{2}}$	${\text{N}}_{{}_{\text{2}}}^{+}$	${\text{N}}_{{}_{\text{2}}}^{-}$
${\text{σ}}_{{}_{\text{2p}}}^{*}$	0	0	0
${\text{π}}_{{}_{\text{2p}}}^{*}$	0	0	1
${\text{σ}}_{\text{2p}}$	2	1	2
${\text{π}}_{\text{2p}}$	4	4	4
${\text{σ}}_{\text{2s}}$	2	2	2
${\text{σ}}_{{}_{\text{2s}}}^{\text{*}}$	2	2	2

Conclusion

  ${\text{N}}_{\text{2}}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^{\text{2}}$

  ${\text{N}}_{{}_{\text{2}}}^{+}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^1$

  ${\text{N}}_{{}_{\text{2}}}^{-}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^{\text{2}}{{\text{(π}}_{{}_{\text{2py}}}^{*}\text{)}}^1$