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  • Using MO theory predict which of the following species has the shortest bond length ?Option: 1 <img alt="O_{2}^{2+}" src="https://learn.careers360.co

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

Option: 1

O_{2}^{2+}


Option: 2

O_{2}^{+}


Option: 3

O_{2}^{-}


Option: 4

O_{2}^{2-}


Answers (1)

best_answer

\begin{aligned} &\text { 1. } \mathrm{O}_{2}^{2+}\\ &\text { Valence electrons }=6+6-2=10\\ &(\sigma 2 \mathrm{s})^{2}(\sigma ^* 2 \mathrm{s})^{2}(\pi 2 \mathrm{p})^{4}(\sigma 2 \mathrm{p})^{2}\\ &\mathrm{BO}=\frac{1}{2} \times(6-0)=3 \end{aligned}

\begin{array}{l} \text { 2. } \mathrm{O}_{2}^{+} \\ \text {Valence electrons }=6+6-1=11 \\ (\sigma 2 \mathrm{s})^{2}(\sigma ^* 2 \mathrm{s})^{2}(\sigma 2 \mathrm{p})^{2}(\pi 2 \mathrm{p})^{4}\left(\pi^{*} 2 \mathrm{p}\right)^{1} \\ \text { BO }=\frac{1}{2} \times(6-1)=2.5 \end{array}

\begin{aligned} &\text { 3. } \mathrm{O}_{2}^{-}\\ &\text { Valence electrons }=6+6+1=13\\ &(\sigma 2 \mathrm{s})^{2}(\sigma ^* 2 \mathrm{s})^{2}(\sigma 2 \mathrm{p})^{2}(\pi 2 \mathrm{p})^{4}\left(\pi^{*} 2 \mathrm{p}\right)^{3}\\ &\mathrm{BO}=\frac{1}{2} \times(6-3)=1.5 \end{aligned}

\begin{aligned} &\text { 4. } \mathrm{O}_{2}^{2-}\\ &\text { Valence electrons }=6+6+2=14\\ &(\sigma 2 \mathrm{s})^{2}(\sigma ^* 2 \mathrm{s})^{2}(\sigma 2 \mathrm{p})^{2}(\pi 2 \mathrm{p})^{4}\left(\pi^{*} 2 \mathrm{p}\right)^{4}\\ &\mathrm{BO}=\frac{1}{2} \times(6-4)=1 \end{aligned}

\text { Bond length } \propto \frac{1}{\text { bond order }}

\therefore \mathrm{O}_{2}^{2+} \text { has the highest bond order and smallest bond length. }

Hence, the correct option is 1.

Posted by

shivangi.shekhar

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