Question

Calculate the bonding and antibonding electrons in $O_{2}^{2+}$ ion on the basis of molecular orbital theory.

Answer 1

Bond Order:

It is defined as the total number of covalent bonds in the covalent molecule. In other words, it is equal to the half the difference between number of electrons which are involved in bonding and anti-bonding in the molecular orbitals.

We know that,  

$Bond\quad order=\quad \frac { \left( electrons\quad in\quad bonding\quad orbitals \right) \quad -\quad \left( electrons\quad in\quad anti-bonding\quad orbitals \right) }{ 2 }$

To calculate the bond order of ${ O }_{ 2 }^{ + }$

The electronic configuration of ${ O }_{ 2 }^{ + }\quad =\quad KK{ \left[ \sigma \left( 2s \right) \right] }^{ 2 }{ \left[ { \sigma }^{ \ast }\left( 2s \right) \right] }^{ 2 }{ \left[ \sigma \left( { 2p }_{ z } \right) \right] }^{ 2 }{ \left[ \pi \left( { 2p }_{ x } \right) \right] }^{ 2 }{ \left[ \pi \left( { 2p }_{ y } \right) \right] }^{ 2 }{ \left[ { \pi }^{ \ast }\left( 2{ p }_{ x } \right) \right] }^{ 1 }$

Here the number of bonding electrons = 8

The number of anti-bonding electrons = 3

Bond order $= \frac { 8\quad -\quad 3 }{ 2 } \quad =\quad \frac { 5 }{ 2 } \quad =\quad 2.5$

Answer 2

Bond Order:

It is defined as the total number of covalent bonds in the covalent molecule. In other words, it is equal to the half the difference between number of electrons which are involved in bonding and anti-bonding in the molecular orbitals.

We know that,  

Bond\quad order=\quad \frac { \left( electrons\quad in\quad bonding\quad orbitals \right) \quad -\quad \left( electrons\quad in\quad anti-bonding\quad orbitals \right) }{ 2 }Bondorder=2(electronsinbondingorbitals)−(electronsinanti−bondingorbitals)​

To calculate the bond order of { O }_{ 2 }^{ + }O2+​

The electronic configuration of { O }_{ 2 }^{ + }\quad =\quad KK{ \left[ \sigma \left( 2s \right) \right] }^{ 2 }{ \left[ { \sigma }^{ \ast }\left( 2s \right) \right] }^{ 2 }{ \left[ \sigma \left( { 2p }_{ z } \right) \right] }^{ 2 }{ \left[ \pi \left( { 2p }_{ x } \right) \right] }^{ 2 }{ \left[ \pi \left( { 2p }_{ y } \right) \right] }^{ 2 }{ \left[ { \pi }^{ \ast }\left( 2{ p }_{ x } \right) \right] }^{ 1 }O2+​=KK[σ(2s)]2[σ∗(2s)]2[σ(2pz​)]2[π(2px​)]2[π(2py​)]2[π∗(2px​)]1

Here the number of bonding electrons = 8

The number of anti-bonding electrons = 3

Bond order = \frac { 8\quad -\quad 3 }{ 2 } \quad =\quad \frac { 5 }{ 2 } \quad =\quad 2.5=28−3​=25​=2.5