Chapter 18, Problem 58E

Interpretation Introduction

Interpretation: The bonding in NO, ${\text{NO}}^{\text{+}}$ , and ${\text{NO}}^{-}$ needs to be compared with the help of localized electron model and molecular orbital model.

Concept Introduction: Molecular orbital theory explained the bonding, magnetic and spectral properties of molecule. It is based on the formation of molecular orbitals by the combination of atomic orbitals. On the basis of energy and stability, these molecular orbitals can be further classified in three types:

• Bonding molecular orbitals (BMO): They have lesser energy than atomic orbital therefore, more stable compare to atomic orbital.
• Antibonding molecular orbitals (ABMO): They have higher energy than atomic orbital therefore less stable compared to atomic orbital.
• Non-bonding molecular orbitals (NBMO): They have same energy as atomic orbital.

Molecular orbital diagrams represent the distribution of electrons in different molecular orbitals in increasing order of their energy. Hence, lower energy molecular orbitals occupy the first then only electron moves in higher energy orbitals.

Answer to Problem 58E

The bond order of ${\text{NO}}^{\text{+}}$ and ${\text{NO}}^{\text{-}}$ are justified with molecular orbital theory but it is not according to theory for NO molecule which is due to presence of unpaired e- in NO molecule.

According to MOT, $\text{NO}$ and ${\text{NO}}^{\text{-}}$ are paramagnetic whereas ${\text{NO}}^{\text{+}}$ is diamagnetic but according to localized electron model, only NO is paramagnetic in nature.

Explanation of Solution

Given information: Bonding in NO, ${\text{NO}}^{\text{+}}$ , and ${\text{NO}}^{-}$ can be explained with MOT and localized electron model.

Both MO (molecular orbital model) and LE (Local electron model) represent the directional nature of covalent bond. They indicate that orbitals of minimum energy overlap with each other to form the chemical bond. The atomic orbitals of same energy and symmetry overlap effectively and form strong bond. LE model is based on hybridization whereas MO model is based on the formation of molecular orbitals. The molecular orbital electronic configuration of $\text{NO}$ , ${\text{NO}}^{\text{+}}$ and ${\text{NO}}^{\text{-}}$:

• Number of electrons in N = 7
• Number of electrons in O = 8
• Total number of electrons in $\text{NO}$ = 7 + 8 = 15
• Total number of electrons in ${\text{NO}}^{\text{-}}$ = 7 + 8 +1 = 16
• Total number of electrons in ${\text{NO}}^{\text{+}}$ = 7 + 8 -1 = 14
• $\text{NO}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^{\text{2}}{{\text{(π}}_{{}_{\text{2py}}}^{*}\text{)}}^{\text{1}}$
• ${\text{NO}}^{\text{+}}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^{\text{2}}$
• ${\text{NO}}^{\text{-}}$ = ${{\text{(σ}}_{\text{1s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{1s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2s}}\text{)}}^{\text{2}}{{\text{(σ}}_{{}_{\text{2s}}}^{\text{*}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2py}}\text{)}}^{\text{2}}{{\text{(π}}_{\text{2pz}}\text{)}}^{\text{2}}{{\text{(σ}}_{\text{2px}}\text{)}}^{\text{2}}{{\text{(π}}_{{}_{\text{2py}}}^{*}\text{)}}^1{{\text{(π}}_{{}_{\text{2pz}}}^{*}\text{)}}^1$

Calculate bond order:

  $\begin{array}{l}\text{Bond order = }\frac{{\text{bonding e}}^{\text{-}}{\text{- antibonding e}}^{\text{-}}}{2}\\ \text{Bond order in NO = }\frac{\text{10- 5}}{2}=2.5\\ {\text{Bond order in NO}}^{\text{+}}\text{ = }\frac{\text{10- 4}}{2}=3\\ {\text{Bond order in NO}}^{-}\text{ = }\frac{\text{8- 4}}{2}=2\end{array}$

According to localized electron model, the Lewis structure of $\text{NO}$ , ${\text{NO}}^{\text{+}}$ and ${\text{NO}}^{\text{-}}$

can be drawn as:

  

The bond order of ${\text{NO}}^{\text{+}}$ and ${\text{NO}}^{\text{-}}$ are justified with molecular orbital theory but it is not according to theory for NO molecule which is due to presence of unpaired e- in NO molecule.

According to MOT, $\text{NO}$ and ${\text{NO}}^{\text{-}}$ are paramagnetic whereas ${\text{NO}}^{\text{+}}$ is diamagnetic but according to localized electron model, only NO is paramagnetic in nature.

Conclusion

The bond order of ${\text{NO}}^{\text{+}}$ and ${\text{NO}}^{\text{-}}$ are justified with molecular orbital theory but it is not according to theory for NO molecule which is due to presence of unpaired e- in NO molecule.

According to MOT, $\text{NO}$ and ${\text{NO}}^{\text{-}}$ are paramagnetic whereas ${\text{NO}}^{\text{+}}$ is diamagnetic but according to localized electron model, only NO is paramagnetic in nature.