First slide

Molecular Orbital Theory

Question

Which of the following species has its bond order lesser than that of O₂ and is paramagnetic with one unpaired electron in pi anti bonding molecular orbital

Moderate

A

$O_{2}$
B

$O_{2}^{+}$
C

$O_{2}^{-}$
D

$O_{2}^{- 2}$

Solution

$O_{2}^{- 2} - {KK}^{'} {(σ_{2 s})}^{2} {(σ_{2 s}^{})}^{2} {({σ_{2 p}}_{z})}^{2} {(π_{2 p_{x}})}^{2} {(π_{2 p_{y}})}^{2} {(π_{2 p_{x}}^{})}^{2} {(π_{2 p_{y}}^{})}^{2}$
$O_{2}^{-} - {KK}^{'} {(σ_{2 s})}^{2} {(σ \overset{}{_{2 s}})}^{2} {({σ_{2 p}}_{z})}^{2} {(π_{2 p_{y}})}^{2} {(π_{2 p_{y}})}^{2} {(π_{2 p_{x}}^{})}^{2} {(π_{2 p_{y}}^{})}^{1}$
$O_{2}^{} - {KK}^{'} {(σ_{2 s})}^{2} {(σ_{2 s}^{})}^{2} {({σ_{2 p}}_{z})}^{2} {(π_{2 p_{x}})}^{2} {(π_{2 p_{y}})}^{2} {(π_{2 p_{x}}^{})}^{1} {(π_{2 p_{y}}^{})}^{1}$
$O_{2}^{+} - {KK}^{'} {(σ_{2 s})}^{2} {(σ_{2 s}^{})}^{2} {(σ_{2 p_{z}})}^{2} {(π_{2 p_{x}})}^{2} {(π_{2 p_{y}})}^{2} {(π_{2 p_{x}}^{})}^{1} {(π_{2 p_{y}}^{})}^{0}$
Bond order in
$O_{2}^{- 2} = \frac{10 - 8}{2} = 1; O_{2}^{-} = \frac{10 - 7}{2} = 1.5; O_{2} = \frac{10 - 6}{2} = 2; O_{2}^{+} = \frac{10 - 5}{2} = 2.5;$
O $—$ O bond length in
$O_{2}^{- 2} > O_{2}^{-} > O_{2} > O_{2}^{+}$

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