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Question: The number of antibonding electron pairs in \( {\text{O}}_2^{2 - } \) molecular ion on the basis of ...

The number of antibonding electron pairs in O22−{\text{O}}_2^{2 - } molecular ion on the basis of molecular orbital theory is:
(A) 22
(B) 33
(C) 44
(D) 55

Explanation

Solution

On the basis of molecular orbital theory, the molecular orbital configuration is different for upto 1414 electrons and that for more than 1414 electrons. Once we know the correct energy order for more than 1414 electrons, we can put two electrons in each orbital and then count the number of antibonding electron pairs.

Complete step by step solution:
The number of electrons in O{\text{O}} atom =8= 8 .
Therefore, the number of electrons in O2{{\text{O}}_2} molecule =2×8=16= 2 \times 8 = 16 .
Also, the number of electrons in O22−{\text{O}}_2^{2 - } molecular ion =16+2=18= 16 + 2 = 18 .
The bonding molecular orbitals are lower in energy than their corresponding anti-bonding molecular orbitals. The energy of various molecular orbitals for O2{{\text{O}}_2} molecule follows the following increasing order:
σ1s\sigma 1s < σ∗1s\sigma *1s < σ2s\sigma 2s < σ∗2s\sigma *2s < σ2pz\sigma 2{p_z} < π2px\pi 2{p_x} = π2py\pi 2{p_y} < π∗2px\pi *2{p_x} = π∗2py\pi *2{p_y} < σ∗2pz\sigma *2{p_z} .
Here, ∗* represents anti-bonding orbitals.
Now, filling all the 1818 electrons in this order, we can get the molecular orbital configuration as:
(σ1s)2(σ∗1s)2(σ2s)2(σ∗2s)2(σ2pz)2(π2px)2(π2py)2(π∗2px)2(π∗2py)2{(\sigma 1s)^2}{(\sigma *1s)^2}{(\sigma 2s)^2}{(\sigma *2s)^2}{(\sigma 2{p_z})^2}{(\pi 2{p_x})^2}{(\pi 2{p_y})^2}{(\pi *2{p_x})^2}{(\pi *2{p_y})^2}
The number of antibonding electron pairs =4= 4
Hence, the correct option is (C).

Additional Information
The energy of various molecular orbitals for molecules/ ion having less than or equal to 1414 electrons follows the following increasing order:
σ1s\sigma 1s < σ∗1s\sigma *1s < σ2s\sigma 2s < σ∗2s\sigma *2s < π2px\pi 2{p_x} = π2py\pi 2{p_y} < σ2pz\sigma 2{p_z} < π∗2px\pi *2{p_x} = π∗2py\pi *2{p_y} < σ∗2pz\sigma *2{p_z} .
Note the difference of energy order of σ2pz\sigma 2{p_z} orbital.

Note:
If we remember that there are six electrons in antibonding orbitals in an O2{{\text{O}}_2} molecule, we can calculate that there will be eight electrons in antibonding orbitals of O22−{\text{O}}_2^{2 - } molecule ion. This is another short method to know the number of antibonding electron pairs.