What is meant by the term bond order? Calculate the bond order of `N_(2)`,`O_(2)`,`O_(2)^(o+)` and `O_(2)^(ө)`.

Explanation

Bond order is defined as one half of the difference between the number of electrons present in the bonding and anti-bonding orbitals of a molecule.
If `N_(a)` is equal to the number of electrons in an anti-bonding orbital, then `N_(b)` is equal to the number of electrons in a bonding orbital.
Bond order `=(1)/(2)(N_(b)-N_(a))`
If `N_(b) gt N_(a)`, then the molecule is said be stable. However , if `N_(b) le N_(a)`, then the molecule is considered to be unstable.
Bond order of `N_(2)` can be calculated form its electronic configuration as :
`[sigma(1s)]^(2)[sigma^(**)(1s)]^(2)[sigma(2s)]^(2)[sigma^(**)(2s)]^(2)[pi(2p_(x))]^(2)[pi(2p_(y))]^(2)[sigma(2p_(z))]^(2)`
Number of bonding electron , `N_(b)=10`
Number of anti-bonding electron , `N_(a)=4`
Bond order of nitrogen molecule =`(1)/(2)(10-4)=3`
There are 16 electrons in a dioxygen molecule, 8 from each oxygen atom. The electronic configuration of oxygen molecule can be written as :
`[sigma -(1s)]^(2)[sigma^(**)(1s)]^(2)[sigma(2s)]^(2)[sigma^(**)(2s)]^(2)[sigma(1p_(z))]^(2)[pi(2p_(x))]^(2)[pi(2p_(y))]^(2)[pi^(**)(2p_(x))]^(1)[pi^(**)(2p_(y))]^(1)`
Since the 1s orbital of each oxygen atom is not involved in bonding, the numebr of bonding electrons=8=`N_(b)` and the number of anti-bonding electrons =4=`N_(a)`
Bond order `=(1)/(2)(N_(b)-N_(a))`
`=(1)/(2)(8-4)=2`
Hence, the bond order of oxygen molecule is 2.
Similarly, the electronic configuration of `O_(2)^(+)` can be written as :
`KK[sigma(2s)]^(2)[sigma^(**)(2s)]^(2)[sigma(2p_(z))]^(2)[pi(2p_(x))]^(2)[pi(2p_(y))]^(2)[pi^(**)(2p_(x))]^(1)`
`N_(b)=8`
`N_(a)=3`
Bond order of `O_(2)^(+)=(1)/(2)(8-3)=2.5`
Thus, the bond order of `O_(2)^(+)` is 2.5
The electronic configuration of `O_(2)^(-)` ion will be :
`KK[sigma(2s)]^(2)[sigma^(**)(2s)]^(2)[sigma(2p_(z))]^(2)[pi(2p_(x))]^(2)[pi(2p_(y))]^(2)[pi^(**)(2p_(x))]^(2)[pi^(**)(2p_(y))]^(1)`
`N_(b)=8`
`N_(a)=5`
Bond order of `O_(2)^(-)=(1)/(2)(8-5)=1.5`
Thus, the bond order of `O_(2)^(-)` ion is 1.5.