Question

Which of the following is not correct with respect to bond length of the species?

• A. $ {{C}_{2}}>C_{2}^{2-} $
• B. $ B_{2}^{+}>{{B}_{2}} $
• C. $ Li_{2}^{+}>L{{i}_{2}} $
• D. $ N_{2}^{+}>{{N}_{2}} $
• E. $ {{O}_{2}}>O_{2}^{-} $

Answer 1

Answer: (E)

Greater the bond order, shorter is the bond length.
$ \therefore $ $ Bond\text{ }order\propto \frac{1}{bond\text{ }length} $ (i) Electronic configurations and bond orders of $ {{C}_{2}} $ and $ C_{2}^{2-} $ ions:
EC of $ {{C}_{2}}=KK\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{2},\pi 2p_{y}^{2} $
Bond order $ =\frac{1}{2}(6-2)=2 $
EC of $ C_{2}^{2-}=KK\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{2},\pi 2p_{y}^{2},\sigma 2p_{z}^{2} $
Bond order $ =\frac{1}{2}(8-2)=3 $
$ \therefore $ The order of bond lengths: $ B_{2}^{+} > {{B}_{2}} $
(ii) Electronic configurations and bond orders of
$ B_{2}^{+} $ and $ {{B}_{2}} $ EC of $ {{B}_{2}}=KK\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{1},\pi 2p_{x}^{1},\pi 2p_{1}^{y} $
Bond order $ =\frac{1}{2}(4-2)=1 $
EC of
$ B_{2}^{+}=KK\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{1} $
Bond order $ =\frac{1}{2}(3-2)=\frac{1}{2} $
$ \therefore $ The order of bond lengths: $ B_{2}^{+} > {{B}_{2}} $
(iii) Electronic configurations and bond orders of $ L{{i}_{2}} $ and $ Li_{2}^{+} $ EC of $ L{{i}_{2}}=KK\,\sigma 2{{s}^{2}} $
Bond order $ =\frac{1}{2}(2-0)=1 $ EC of $ Li_{2}^{+}=\,KK\,\sigma 2{{s}^{1}} $
Bond order $ =\frac{1}{2}(1-0)=\frac{1}{2} $
$ \therefore $ The order of bond lengths: $ Li_{2}^{+}>L{{i}_{2}} $ (iv) Electronic configurations and bond orders of
$ {{N}_{2}} $ and $ N_{2}^{+} $ EC of $ {{N}_{2}}=KK\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{2},\pi 2p_{y}^{2},\sigma 2p_{z}^{2} $ Bond order $ =\frac{1}{2}(8-2)\,=3 $
EC of
$ N_{2}^{+}=KK\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{2},\pi 2p_{y}^{2},\sigma 2p_{z}^{1} $
Bond order $ =\frac{1}{2}(7-2)=2.5 $
$ \therefore $ The order of bond lengths $ =N_{2}^{+}>{{N}_{2}} $
(v) Electronic configurations and bond orders of
$ {{O}_{2}} $ and $ O_{2}^{-} $ : EC of $ {{O}_{2}}=KK\,\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\sigma 2p_{z}^{2},\pi 2p_{x}^{2} $
$ \pi 2p_{y}^{2},\overset{*}{\mathop{\pi }}\,2p_{x}^{1},\overset{*}{\mathop{\pi }}\,2p_{y}^{1} $
Bond order $ =\frac{1}{2}\,(8-4)=2 $ EC of $ O_{2}^{-}=KK\sigma 2{{s}^{2}},\overset{*}{\mathop{\sigma }}\,2{{s}^{2}},\pi 2p_{z}^{2},\pi 2p_{x}^{2},\pi 2p_{y}^{2}, $
$ \overset{*}{\mathop{\pi }}\,2p_{x}^{2},\overset{*}{\mathop{\pi }}\,2p_{y}^{1} $
Bond order $ =\frac{1}{2}(8-5)=1.5 $
$ \therefore $ The correct order of bond lengths
$ =O_{2}^{-}>{{O}_{2}} $