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Chemical Bonding And Molecular Structure

Question
CBSEENCH11008294

Four diatomic species are listed below. Identify the correct order in which the bond order is increasing in them.

  • NO< O2-<C22- < He2+

  •  O2- <NO< C22- < He2+

  • C22- < He2+ <O2- <NO

  • < He2+  < O2- <NO< C22- 

Solution

D.

< He2+  < O2- <NO< C22- 

Bond space order space space equals space fraction numerator straight N subscript straight b minus straight N subscript straight a over denominator 2 end fraction
left parenthesis where space straight N subscript straight b space equals space number space of space electrons space in space bonding space molecular space orbital
straight N subscript straight a space equals space number space of space electrons space in space anti minus bonding space molecular space orbital right parenthesis
In space NO comma space total space electrons space equals space 7 plus 8 space equals space 15
therefore space configuration space of space NO
equals space straight sigma 1 straight s squared comma space straight sigma asterisk times 1 straight s squared comma space straight sigma 2 straight s squared comma straight sigma asterisk times 2 straight s squared comma straight sigma 2 straight p subscript straight z superscript 2 comma space straight pi 2 straight p subscript straight x superscript 2 almost equal to straight pi 2 straight p subscript straight y superscript 2 space comma space straight pi asterisk times 2 straight p subscript straight x superscript 1
therefore space BO space equals space fraction numerator 8 minus 3 over denominator 2 end fraction space equals space 2.5
space straight O subscript 2 superscript minus space left parenthesis 8 plus 8 plus 1 space equals space 17 right parenthesis
straight sigma 1 straight s squared comma space straight sigma asterisk times 1 straight s squared comma space straight sigma 2 straight s squared comma straight sigma asterisk times 2 straight s squared comma straight sigma 2 straight p subscript straight z superscript 2 comma space straight pi 2 straight p subscript straight x superscript 2 almost equal to straight pi 2 straight p subscript straight y superscript 2 space comma space straight pi asterisk times 2 straight p subscript straight x superscript 2 almost equal to straight pi asterisk times 2 straight p subscript straight y superscript 1
therefore space BO space equals space fraction numerator 8 minus 5 over denominator 2 end fraction space equals space 1.5
In space straight C subscript 2 superscript 2 minus end superscript comma space total space electrons space equals space 12 plus 2 space equals space 14
therefore space comma space configuration space of space straight C subscript 2 superscript 2 minus end superscript
straight sigma 1 straight s squared comma space straight sigma asterisk times 1 straight s squared comma space straight sigma 2 straight s squared comma straight sigma asterisk times 2 straight s squared comma straight sigma 2 straight p subscript straight z superscript 2 comma space straight pi 2 straight p subscript straight x superscript 2 almost equal to straight pi 2 straight p subscript straight y superscript 2
therefore space BO space equals space fraction numerator 8 minus 2 over denominator 2 end fraction space equals space 3
In space He subscript 2 superscript plus space total space electrons space equals space 4 minus 1 space equals space 3
straight sigma 1 straight s squared comma space straight sigma asterisk times 1 straight s to the power of 1
therefore space BO space equals space fraction numerator 2 minus 1 over denominator 2 end fraction space equals space 0.5
Hence space comma space correct space order space space of space bond space order space is space
He subscript 2 superscript plus space less than space straight O subscript 2 superscript minus space less than space NO space less than space straight C subscript 2 superscript 2 minus end superscript