Question

Construct the molecular orbital diagram for N2 and then identify the bond order. What is the ground state electron configuration and the bond order for c_2+? (sigma_1s)^2(sigma_1s*)^2 (sigma_2s)^2 (sigma_2s*)^2(pi_2p)^3

Answer 1

Concepts and reason

The concept used to solve this question is based on the calculation of bond order from molecular orbital diagram.

Bond order of a molecule is half of the difference of the number of electrons present in bonding and antibonding orbitals in the molecular orbital diagram.

Fundamentals

The sum of total number of electrons present in the outermost shell of both atoms involved in bonding are filled in the molecular orbital diagram of a particular molecule.

Bond order is calculated by the expression as follows:

${\rm{Bond}}\;{\rm{order}} = \frac{{{\rm{Number}}\;{\rm{of}}\;{\rm{bonding}}\;{\rm{electrons}} - {\rm{Number}}\;{\rm{of}}\;{\rm{antibonding}}\;{\rm{electrons}}}}{2}$ …… (1)

(1.1)

The molecular orbital diagram of ${{\rm{N}}_2}$ molecule is shown as follows:

(1.2)

The bond order of ${{\rm{N}}_2}$ molecule is calculated from the equation (1) as follows:

$\begin{array}{c}\\{\rm{Bond}}\;{\rm{order}} = \frac{{8 - 2}}{2}\\\\ = 3\\\end{array}$

(2.1)

The number of electrons present in ${\rm{C}}_2^ +$ molecule is $11$ .

The ground state electronic configuration of ${\rm{C}}_2^ +$ molecule is given as follows:

${\rm{Electronic}}\;{\rm{configuration}}\;{\rm{of}}\;{\rm{\;C}}_2^ + = {\left( {{\sigma _{1{\rm{s}}}}} \right)^2}{\left( {\sigma _{{\rm{1s}}}^*} \right)^2}{\left( {{\sigma _{{\rm{2s}}}}} \right)^2}{\left( {\sigma _{2{\rm{s}}}^*} \right)^2}{\left( {{\pi _{{\rm{2}}{{\rm{p}}_x}}} - {\pi _{{\rm{2}}{{\rm{p}}_y}}}} \right)^3}$

(2.2)

The bond order of ${\rm{C}}_2^ +$ molecule is calculated from the equation (1) as follows:

$\begin{array}{c}\\{\rm{Bond}}\;{\rm{order}} = \frac{{7 - 4}}{2}\\\\ = 1.5\\\end{array}$

Ans: Part 1.1

The molecular orbital diagram of ${{\bf{N}}_{\bf{2}}}$ molecule is as follows:

Part 1.2

The bond order of ${{\bf{N}}_{\bf{2}}}$ molecule is ${\bf{3}}$ .

Part 2.1

The ground state electronic configuration of ${\bf{C}}_{\bf{2}}^{\bf{ + }}$ molecule is ${\left( {{{\bf{\sigma }}_{{\bf{1s}}}}} \right)^{\bf{2}}}{\left( {{\bf{\sigma }}_{{\bf{1s}}}^{\bf{*}}} \right)^{\bf{2}}}{\left( {{{\bf{\sigma }}_{{\bf{2s}}}}} \right)^{\bf{2}}}{\left( {{\bf{\sigma }}_{{\bf{2s}}}^{\bf{*}}} \right)^{\bf{2}}}{\left( {{{\bf{\pi }}_{{\bf{2p}}}}} \right)^{\bf{3}}}$ .

Part 2.2

The bond order of ${\bf{C}}_{\bf{2}}^{\bf{ + }}$ molecule is ${\bf{1}}{\bf{.5}}$ .