Question

The correct bond order in the following species is:
Options are,
(A) $O_{2}^{+}$ < $O_{2}^{-}$ < $O_{2}^{2+}$
(B) $O_{2}^{-}$ < $O_{2}^{+}$ < $O_{2}^{2+}$
(C) $O_{2}^{2+}$ < $O_{2}^{+}$ < $O_{2}^{-}$
(D) $O_{2}^{2+}$ < $O_{2}^{-}$ < $O_{2}^{+}$

Answer 1

Bond order can be calculated with the help of molecular orbital theory. Understand the molecular orbital theory and the MOT diagram for oxygen molecules. The bond order can be calculated by knowing the number of electrons in bonding orbitals and number of electrons in antibonding orbitals. The formula depicting the relation is given below:
$B.O=\dfrac{({{e}^{-}}_{B}-{{e}^{-}}_{AB})}{2}$
Where,
B.O stands for bond order
${{e}^{-}}_{B}$ denotes number of electrons in bonding orbitals
${{e}^{-}}_{AB}$ denotes number of electrons in antibonding orbitals

Complete answer:
Bond order, as given by Linus Pauling can be defined as the difference between the number of bonds and antibonds present in a molecule.
Bond order can also be defined as half the difference between the number of bonding electrons and the number of antibonding electrons. This is in accordance with molecular orbital theory.
This definition often yields results similar to the bonds reaching equilibrium lengths. However, it is not applicable for stretched bonds.
In general, we say that the strength of the bond is directly proportional to the bond order. We will now determine the bond order of the molecules mentioned in options.
The below number of antibonding electrons and bonding electrons are in accordance to the molecular orbital theory:
$O_{2}^{2+}$:
Total number of electrons = 14
Number of electrons in bonding orbitals = 10
Number of electrons in antibonding orbitals = 4
B.O = 3
$O_{2}^{+}$:
Total number of electrons = 15
Number of electrons in bonding orbitals = 10
Number of electrons in antibonding orbitals = 5
B.O = 2.5
$O_{2}^{-}$ :
Total number of electrons = 17
Number of electrons in bonding orbitals = 10
Number of electrons in antibonding orbitals = 7
B.O = 1.5
Therefore, the correct order of bond order in the following species is $O_{2}^{-}$ < $O_{2}^{+}$ < $O_{2}^{2+}$.

The correct answer is option (B).

Note:
It is important to know that in molecules exhibiting resonance, the bond order need not be an integer. For example, the bond order of carbon atoms in benzene is 1.5.