Question

Using molecular orbital theory, explain why the removal of one electron in O₂ strengthens bonding, while the removal of one electron in N₂ weakens bonding.

Short answer

It depends on bond order. For O₂ bond order increases and so as the bond strength increases and for N₂ bond order decreases and so as the bond strength also decreases.

Step-by-step solution

Writing electronic configuration

According to molecular orbital theory,

The electronic configuration of O₂ is ${\left(\sigma 1s\right)}^2{\left(\sigma 1s^{*} \right)}^2{\left(\sigma 2s\right)}^2{\left(\sigma 2s^{*} \right)}^2{\left(\sigma 2p_z\right)}^2{\left(\pi 2p_x\right)}^2{\left(\pi 2p_y\right)}^2{\left(\pi 2{p_x}^{*}\right)}^1$

The electronic configuration of N₂is

${\left(\sigma 1s\right)}^2{\left(\sigma 1s^{*} \right)}^2{\left(\sigma 2s\right)}^2{\left(\sigma 2s^{*} \right)}^2{\left(\pi 2p_x\right)}^2{\left(\pi 2p_y\right)}^2{\left(\pi 2p_z\right)}^2$

Calculating bond order for O2 and N2

Bond border=(Number of bonding electrons-Number of non-bonding electrons)/2

For O₂ =(10-6)/2=2

For N₂=(10-4)/2=3

Removing electrons and making O2 and N2 charge species.

When you remove an electron from O₂ you remove it from its antibonding orbital resulting in O^2+. Now the electronic configuration of O²⁺ according to Molecular orbital theory is${\left(\sigma 1s\right)}^2{\left(\sigma 1s^{*} \right)}^2{\left(\sigma 2s\right)}^2{\left(\sigma 2s^{*} \right)}^2{\left(\sigma 2p_z\right)}^2{\left(\pi 2p_x\right)}^2{\left(\pi 2p_y\right)}^2$

And for N₂ when you remove one electron it is removed from bonding orbital resulting in N²⁺. Now the electronic configuration according to molecular orbital theory is

${\left(\sigma 1s\right)}^2{\left(\sigma 1s^{*} \right)}^2{\left(\sigma 2s\right)}^2{\left(\sigma 2s^{*} \right)}^2{\left(\pi 2p_x\right)}^2{\left(\pi 2p_y\right)}^2{\left(\sigma 2p_z\right)}^1$

Bond order for O2+ and N2+

Bond border=(Number of bonding electrons-Number of non-bonding electrons)/2

For O²⁺ =(10-5)/2=2.5

For N²⁺=(9-4)/2=2.5

Conclusion

After taking out bond order for both the species you can see that bond order for O₂ increases after taking out one electron whereas for N₂ bond order decreases after taking out one electron. Bond order and bond strength are directly proportional to each other so bond strength for O₂ increases while for N₂ decreases after taking out one electron.