Compare the relative stability of the following species and indicate their magnetic properties;

$O _{2}, O _{2}^{+}, O _{2}^{-}$ (superoxide), $O _{2}^{2-}$ (peroxide)

There are $16$ electrons in a molecule of dioxygen, $8$ from each oxygen atom. The electronic configuration of oxygen molecule can be written as:

${[\sigma  - (1s)]^2}{\left[ {{\sigma ^*}(1s)} \right]^2}{[\sigma (2s)]^2}{\left[ {{\sigma ^*}(2s)} \right]^2}{\left[ {\sigma \left( {1{p_z}} \right)} \right]^2}

{\left[ {\pi \left( {2{p_x}} \right)} \right]^2}{\left[ {\pi \left( {2{p_y}} \right)} \right]^2}{\left[ {{\pi ^*}\left( {2{p_x}} \right)}\right]^1}{\left[ {{\pi ^*}\left( {2{p_y}} \right)} \right]^1}$

Since the $1 s$ orbital of each oxygen atom is not involved in boding, the number of bonding electrons $=8=N_{ b }$ and the number of anti-bonding orbitals $=4=N_{ a }$

Bond order $=\frac{1}{2}\left(N_{ b }-N_{ a }\right)$

$=\frac{1}{2}(8-4)$

$=2$

Similarly, the electronic configuration of $O _{2}^{+}$ can be written as:

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

$N_{b}=8$

$N_{a}=3$

Bond order $O _{2}^{+}=\frac{1}{2}(8-3)$

$=2.5$

Electronic configuration of $O _{2}^{-}$ ion will be:

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

{\left[ {{\pi ^*}\left( {2{p_y}} \right)} \right]^1}$ 

$N_{b}=8$

$N_{a}=5$

Bond order $O _{2}^{-}=\frac{1}{2}(8-5)$

$=1.5$

Electronic configuration of $O _{2}^{2-}$ ion will be:

$KK{[\sigma (2s)]^2}{\left[ {{\sigma ^*}(2s)} \right]^2}{\left[ {\sigma \left( {2{p_z}} \right)} \right]^2}{\left[ {\pi \left( {2{p_x}} \right)} \right]^2}

{\left[ {\pi \left( {2{p_y}} \right)} \right]^2}{\left[ {{\pi ^*}\left( {2{p_x}} \right)} \right]^2}{\left[ {{\pi ^*}\left( {2{p_y}} \right)} \right]^2}$

$N_{ b }=8$

$N_{ a }=6$

Bond order of $O _{2}^{2-}=\frac{1}{2}(8-6)$ $=1$

Bond dissociation energy is directly proportional to bond order. Thus, the higher the bond order, the greater will be the stability. On this basis, the order of stability is

$O_2^ + \, > \,{O_2}\, > \,O_2^ - \, > \,O_2^{2 - }$