Question

What is meant by the term bond order? Calculate the bond order of: \(N_2\), \(O_2\), \(O_2^+\) and \(O_2^-\) .

Answer 1

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, thenNb is equal to the number of electrons in a bonding orbital. 
Bond order = \(\frac{1}{2}(N_b-N_a)\)
If \(Nb > Na\) , then the molecule is said be stable. However, if \(Nb \leq  Na\), then the molecule is considered to be unstable.
Bond order of \(N_2\) can be calculated from 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 electrons, \(N_b\) = \(10\) 
Number of anti-bonding electrons, \(N_a\) = \(4\) 
Bond order of nitrogen molecule =\(\frac{1}{2}(10-4)\)
\(=3\)
There are \(16\) electrons in a dioxygen molecule, \(8\) from each oxygen atom. The electronic configuration of oxygen molecule can be written as:

\([\sigma-(1s)]^2[\sigma^*(1s)]^2[\sigma(2s)]^2[\sigma^*(2s)]^2[\sigma(1p_z)]^2[\pi(2p_x)]^2[\pi(2p_y)]^2[π*(2px)]2[\pi^*(2p_y)]^1\)

Since the \(1s\) orbital of each oxygen atom is not involved in boding, the number of bonding electrons = \(8\) 
= \(N_b\) and the number of anti-bonding electrons = \(4\) = \(N_a\). 
Bond order =\(\frac{1}{2}(N_b-N_a)\)
=\(\frac{1}{2}(8-4)\)
=\(2\)

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 \(O_2^+=\frac{1}{2}(8-3)\)
= \(2.5\) 
Thus, the bond order of \(O_2^+\) is \(2.5\).

The electronic configuration of 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 \(O_2^-\)=\(\frac{1}{2}(8-5)\)
= \(1.5\) 
Thus, the bond order of \(O_2^-\) ion is \(1.5\).