Using MO theory predict which of the following species has the shortest bond length?

Using MO theory predict which of the following species has the shortest bond length?

1. A

${\mathrm{O}}_{2}$

2. B

${\mathrm{O}}_{2}^{2-}$

3. C

${\mathrm{O}}_{2}^{2+}$

4. D

${\mathrm{O}}_{2}^{+}$

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Solution:

The molecular electronic configuration along with the bond orders [= number of (bonding minus antibonding) electrons divided by two] of the given ions are as follows:

$\begin{array}{l}{\mathrm{O}}_{2}^{2+} \mathrm{KK}\left(\sigma 2\mathrm{s}{\right)}^{2}\left(\sigma \ast 2\mathrm{s}{\right)}^{2}\left(\sigma 2\mathrm{p}{\right)}^{2}{\left(\pi 2{\mathrm{p}}_{x}\right)}^{2}{\left(\pi 2{\mathrm{p}}_{y}\right)}^{2}; \mathrm{BO}=3\\ {\mathrm{O}}_{2}^{+} \mathrm{KK}\left(\sigma 2\mathrm{s}{\right)}^{2}\left(\sigma \ast 2\mathrm{s}{\right)}^{2}\left(\sigma 2\mathrm{p}{\right)}^{2}{\left(\pi 2{\mathrm{p}}_{x}\right)}^{2}{\left(\pi 2{\mathrm{p}}_{y}\right)}^{2}{\left({\pi }^{\ast }2{\mathrm{p}}_{x}\right)}^{1}; \mathrm{BO}=2.5\\ {\mathrm{O}}_{2}^{-} \mathrm{KK}\left(\sigma 2\mathrm{s}{\right)}^{2}\left(\sigma \ast 2\mathrm{s}{\right)}^{2}\left(\sigma 2\mathrm{p}{\right)}^{2}{\left(\pi 2{\mathrm{p}}_{x}\right)}^{2}{\left(\pi 2{\mathrm{p}}_{y}\right)}^{2}{\left({\pi }^{\ast }2{\mathrm{p}}_{x}\right)}^{2}{\left({\pi }^{\ast }2{\mathrm{p}}_{y}\right)}^{1}; \mathrm{BO}=1.5\\ {\mathrm{O}}_{2}^{2-} \mathrm{KK}\left(\sigma 2\mathrm{s}{\right)}^{2}\left(\sigma \ast 2\mathrm{s}{\right)}^{2}\left(\sigma 2\mathrm{p}{\right)}^{2}{\left(\pi 2{\mathrm{p}}_{x}\right)}^{2}{\left(\pi 2{\mathrm{p}}_{y}\right)}^{2}{\left({\pi }^{\ast }2{\mathrm{p}}_{x}\right)}^{2}{\left({\pi }^{\ast }2{\mathrm{p}}_{y}\right)}^{2}; \mathrm{BO}=1.0\end{array}$The bond length is inversely proportional to the bond order. Hence ${\mathrm{O}}_{2}^{2+}$ is expected to have shortest bond length.