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..3..
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..4..
Complete this molecular orbital diagram for CN– then determine the bond order. Note that the 1s orbital is not shown in this problem. To add arrows to the MO diagram, click on the blue boxes.
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Bond order of CN–
-
0
-
0.5
-
1
-
1.5
-
2
-
2.5
-
3
♦ Relevant knowledge
The molecular orbital configuration aids in determining the bonding order of molecules. The electrons are filled into molecules’ molecular orbits in the same manner that they are filled within the atomic orbitals of atoms. The bond order of molecules can be in the following manner:
Bond order = (Bonding electrons−Anti-bonding electrons) ⁄ 2
* The molecular orbital theory describes the bonding by explaining the organization and combination of atomic orbitals within an atom that are linked in a molecule to create molecular orbitals.
* The number molecular orbitals formed from atomic orbitals will always be equal to the number that they contain. There are two types of orbitals: anti-bonding and bonding orbitals.
* A molecular orbital that contains more electrons than the anti-bonding molecular orbitals will be considered stable.
* The difference between the number electrons in antibonding orbitals and bonding orbitals is half of the bond order.
Two molecular orbitals form when two atomic orbitals collide. The bonding molecular orbal is one, and the anti-bonding molecular orbal is another.
[katex]\begin{array}{l}\\{\rm{Antibonding}}\,{\rm{MO: }}\,{\rm{\sigma ×2s}}\,\,\,{\rm{\sigma ×2}}{{\rm{p}}_{\rm{z}}}\,{\rm{\pi ×2}}{{\rm{p}}_{\rm{x}}}\,{\rm{\pi ×2}}{{\rm{p}}_{\rm{y}}}\\\\{\rm{Bonding}}\,\,{\rm{MO: }}\,\,{\rm{\sigma 2s}}\,\,\,{\rm{\sigma 2}}{{\rm{p}}_{\rm{z}}}\,{\rm{\pi 2}}{{\rm{p}}_{\rm{x}}}\,{\rm{\pi 2}}{{\rm{p}}_{\rm{y}}}\\\end{array}[/katex]
The energies of different molecular orbitals in [katex]{\rm{C}}{{\rm{N}}^ – }[/katex]
[katex]{\rm{\sigma 1s}}\,{\rm{ < }}\,{\rm{\sigma ×1s}}\,{\rm{ < \sigma 2s}}\,{\rm{ < \sigma ×2s}}\,{\rm{ < }}\left( {{\rm{\pi 2}}{{\rm{p}}_{\rm{x}}}{\rm{ = \pi 2}}{{\rm{p}}_{\rm{y}}}} \right)\,{\rm{ < }}\,{\rm{\sigma 2}}{{\rm{p}}_{\rm{z}}}\,{\rm{ < }}\,\left( {{\rm{\pi ×2}}{{\rm{p}}_{\rm{x}}}{\rm{ = \pi ×2}}{{\rm{p}}_{\rm{y}}}} \right)\,{\rm{ < }}\,{\rm{\sigma ×2}}{{\rm{p}}_{\rm{z}}}[/katex]
[katex]{\rm{Bond}}\,{\rm{order}}\,{\rm{ = }}\,\frac{{\rm{1}}}{{\rm{2}}}\left( {{\rm{number}}\,{\rm{of}}\,{\rm{bonding}}\,{\rm{electron}}\,{\rm{ – }}\,{\rm{number}}\,{\rm{ofantibonding}}\,{\rm{electron}}} \right)[/katex]
Electronic configuration of [katex]{\rm{C}}{{\rm{N}}^{\rm{ – }}}[/katex]
[katex]{\rm{\sigma 1}}{{\rm{s}}^{\rm{2}}}\,{\rm{,}}\,{\rm{\sigma ×1}}{{\rm{s}}^{\rm{2}}}\,{\rm{,\sigma 2}}{{\rm{s}}^{\rm{2}}}\,{\rm{,\sigma ×2}}{{\rm{s}}^{\rm{2}}}\,{\rm{,}}\left( {{\rm{\pi 2p}}_{\rm{x}}^{\rm{2}}{\rm{ = \pi 2p}}_{\rm{y}}^{\rm{2}}} \right)\,{\rm{,}}\,{\rm{\sigma 2p}}_{\rm{z}}^{\rm{2}}\,{\rm{,}}\,\left( {{\rm{\pi ×2}}{{\rm{p}}_{\rm{x}}}{\rm{ = \pi ×2}}{{\rm{p}}_{\rm{y}}}} \right)\,{\rm{,}}\,{\rm{\sigma ×2}}{{\rm{p}}_{\rm{z}}}[/katex]
The molecular orbital diagram for [katex]{\rm{C}}{{\rm{N}}^{\rm{ – }}}[/katex]
The number of electrons in anti-bonding orbitals is 2
The number of electrons in the bonding orbitals is 8
[katex]\begin{array}{c}\\{\rm{therefore}}\,{\rm{bond}}\,{\rm{order}}\,{\rm{ = }}\,\frac{{{\rm{8 – 2}}}}{{\rm{2}}}\\\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{ = }}\,{\rm{3}}\\\end{array}[/katex]Ans:
The complete molecular orbital diagram for [katex]{\rm{C}}{{\rm{N}}^{\rm{ – }}}[/katex]