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

A
$O_{2}$
B
$O_{2}^{2 -}$
C
$O_{2}^{2 +}$
D
$O_{2}^{+}$

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:

$\begin{array}{lll} O_{2}^{2 +} KK (σ 2 s)^{2} (σ * 2 s)^{2} (σ 2 p)^{2} {(π 2 p_{x})}^{2} {(π 2 p_{y})}^{2}; BO = 3 \\ O_{2}^{+} KK (σ 2 s)^{2} (σ * 2 s)^{2} (σ 2 p)^{2} {(π 2 p_{x})}^{2} {(π 2 p_{y})}^{2} {(π^{*} 2 p_{x})}^{1}; BO = 2.5 \\ O_{2}^{-} KK (σ 2 s)^{2} (σ * 2 s)^{2} (σ 2 p)^{2} {(π 2 p_{x})}^{2} {(π 2 p_{y})}^{2} {(π^{*} 2 p_{x})}^{2} {(π^{*} 2 p_{y})}^{1}; BO = 1.5 \\ O_{2}^{2 -} KK (σ 2 s)^{2} (σ * 2 s)^{2} (σ 2 p)^{2} {(π 2 p_{x})}^{2} {(π 2 p_{y})}^{2} {(π^{*} 2 p_{x})}^{2} {(π^{*} 2 p_{y})}^{2}; BO = 1.0 \end{array}$ The bond length is inversely proportional to the bond order. Hence $O_{2}^{2 +}$ is expected to have shortest bond length.

Solution:

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