Question

Which statements are correct for $CO$ and ${{N}_{2}}$ according to molecular orbital theory?
I.Bond order of $CO$ and ${{N}_{2}}$ are $3$ and $3$
II.Bond order of $CO$ and ${{N}_{2}}$ are same
III.During the formation of ${{N}_{2}}^{+}$ from ${{N}_{2}}$ bond length increases
IV.During the formation of $C{{O}^{+}}$ from $CO$ , the bond length decreases
A. $~II,\text{ }IV,I$
B. $~I,\text{ }II,\text{ }III,\text{ }IV$
C. $I,\text{ }III$
D. $I,\text{ }II,II$

Answer 1

We know that the bond order is a concept in the molecular orbital theory. The bond order of any molecule depends on the number of electrons in the bonding and antibonding orbital. The anti-bond formula used is $B.O=\dfrac{1}{2}$ Bonding electron antibonding electrons.

Complete step-by-step answer: Four statements are given for $CO$ and ${{N}_{2}}$ and we need to choose the correct option by applying molecular orbital theory. Let us first understand that molecular orbital theories are formed by the overlap of atomic orbitals. Molecular orbitals consist of bonding orbitals and antibonding orbitals. These orbitals are illustrated in the molecular orbital diagrams, which are useful for predicting the strength and existence of chemical bonds.
Bond order of a molecule is then calculated as;
$B.O\,=\,\dfrac{1}{2}({{N}_{b}}-{{N}_{a}})$
where, ${{N}_{b}}=$ Bonding electrons
${{N}_{a}}=$ Antibonding electrons
Both $CO$and ${{N}_{2}}$ are Iso electrons, that is they contain $14$ electrons in their molecular orbital. Calculating the bond order, we get the value $3$ for both the molecules.
Now, during the formation of ${{N}_{2}}^{+}$ from ${{N}_{2}}$ bond length increases, this is because an electron removed from pi bonding orbital. As outcome the bond order decreases. And we come to know that bond length and bond order are inversely proportional.
However, during the formation of $C{{O}^{+}}$ from $CO$ the bond length increases and do not decrease. This is because an electron is from pi bonding orbital as a result of which bond order decreases.

Hence, the option D is the correct option i.e. $I,\text{ }II,II$

Note: Note that the Molecular orbital theory is an important concept and students should go through it properly. With the help of this theory diagrams can be drawn which could further give us the information about the bond length and bond order.