Chemical Bonding and Molecular Structure

Question

What is meant by the term bond order? Calculate the bond order of: $straight N subscript 2 comma space straight O subscript 2 comma space straight O subscript 2 superscript plus space and space straight O subscript 2 superscript minus.$

Solution

Bond order is defined as one-half of the difference between the number of electrons present in the bonding and anti-bonding orbitals of the molecule.
If N_a is equal to the number of electron in an antibonding orbital, then
Nb is equal to the number of electron in a bonding orbital.
1/2(N_b-N_a)

If N_b>N_a, then the molecule is said to stable. However, if N_b

$straight i right parenthesis space Bond space order space of space straight N subscript 2 left square bracket straight sigma 1 straight s squared space right square bracket space left square bracket straight sigma asterisk times left parenthesis 2 straight s right parenthesis right square bracket squared space left square bracket straight sigma left parenthesis 2 straight s right parenthesis right square bracket squared space left square bracket straight sigma asterisk times left parenthesis 2 straight s right parenthesis right square bracket squared space left square bracket straight pi left parenthesis 2 straight p subscript straight y right parenthesis right square bracket squared space left square bracket straight pi 2 straight p subscript straight y right square bracket squared left square bracket straight sigma left parenthesis 2 pz right parenthesis right square bracket squared number space of space bonding space electron space equals 10 Number space of space antibonding space electrons space equals 4 bond space order space of space nitrogen space moleules space equals 1 half left parenthesis 10 minus 4 right parenthesis equals 3 space$
$T h e r e space a r e space 16 space e l e c t r o n s space i n space straight a space d i o x y g e n m o l e c u l e comma space 8 space f r o m space e a c h space o x y g e n space a t o m. T h e space e l e c t r o n i c space c o n f i g u r a t i o n space o f space o x y g e n space m o l e c u l e space c a n space w r i t t e n space a s colon left square bracket straight sigma left parenthesis 1 straight s right parenthesis right square bracket squared left square bracket straight sigma asterisk times left parenthesis 1 straight s right parenthesis right square bracket squared left square bracket straight sigma left parenthesis 2 straight s right parenthesis right square bracket squared left square bracket straight sigma asterisk times left parenthesis 2 straight s right parenthesis right square bracket squared left square bracket straight sigma left parenthesis 1 straight p subscript straight z right parenthesis right square bracket squared left square bracket straight pi left parenthesis 2 straight p subscript straight x right parenthesis right square bracket squared left square bracket straight pi asterisk times left parenthesis 2 straight p subscript straight x right parenthesis right square bracket to the power of 1 left square bracket left parenthesis straight pi asterisk times left parenthesis 2 straight p subscript straight y right parenthesis right square bracket to the power of 1 S i n c e space t h e space 1 straight s space o r b i t a l space o f space e a c h space o x y g e n space a t o m s space i s space n o t space i n v o l v e d space i n space b o n d i n g comma space t h e space n u m b e r space o f space b o n d i n g space e l e c t r o n s equals 8 equals straight N subscript straight b space a n d space t h e space n u m b e r space o f space a n t i minus b o n d i n g space e l o e c t r o n equals 4 equals straight N subscript straight a. equals 1 half left parenthesis straight N subscript straight b minus straight N subscript straight a right parenthesis equals 1 half left parenthesis 8 minus 4 right parenthesis equals 2 H e n c e comma space t h e space b o n d space o r d e r space o f space o x y g e n space m o l e c u l e space i s space 2$

$There space are space 16 space electrons space in space straight a space dioxygen molecule comma space 8 space from space each space oxygen space atom. The space electronic space configuration space of space oxygen space molecule space can space written space as colon left square bracket straight sigma left parenthesis 1 straight s right parenthesis right square bracket squared left square bracket straight sigma asterisk times left parenthesis 1 straight s right parenthesis right square bracket squared left square bracket straight sigma left parenthesis 2 straight s right parenthesis right square bracket squared left square bracket straight sigma asterisk times left parenthesis 2 straight s right parenthesis right square bracket squared left square bracket straight sigma left parenthesis 1 straight p subscript straight z right parenthesis right square bracket squared left square bracket straight pi left parenthesis 2 straight p subscript straight x right parenthesis right square bracket squared left square bracket straight pi asterisk times left parenthesis 2 straight p subscript straight y right parenthesis right square bracket squared space left square bracket left parenthesis straight pi asterisk times left parenthesis 2 straight p subscript straight y right parenthesis right square bracket to the power of 1 Since space the space 1 straight s space orbital space of space each space oxygen space atoms space is space not space involved space in space bonding comma space the space number space of space bonding space electrons equals 8 equals straight N subscript straight b space and space the space number space of space anti minus bonding space eloectron equals 3 equals straight N subscript straight a. equals 1 half left parenthesis straight N subscript straight b minus straight N subscript straight a right parenthesis equals 1 half left parenthesis 8 minus 3 right parenthesis equals 2.5 Hence comma space the space bond space order space of space oxygen space cation space molecule space is space 2.5$

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