Describe the bonding in \(\mathrm{NO}^{+}, \mathrm{NO}^{-}\), and NO using both the localized electron and molecular orbital models. Account for any discrepancies between the two models.

The localized electron model uses Lewis structures to determine the bonding between atoms. In this model, the bonds are formed by shared electron pairs between the atoms, and each atom aims to achieve the octet rule. 1. NO⁺: In the NO⁺ ion, oxygen has 6 valence electrons and nitrogen has 5 valence electrons, with the positive charge accounting for 1 less electron. Hence, there are 10 valence electrons in this system. Construct a Lewis structure that satisfies the octet rule for both atoms using these 10 valence electrons. The resulting NO⁺ ion has a double bond between nitrogen and oxygen and an unpaired electron on the nitrogen. 2. NO: Nitrogen has 5 and oxygen has 6 valence electrons, making a total of 11 valence electrons in the NO molecule. Construct a Lewis structure that satisfies the octet rule for oxygen and the exception of nitrogen having 7 valence electrons. There is a double bond between nitrogen and oxygen and an unpaired electron on each atom. 3. NO⁻: Nitrogen has 5 and oxygen has 6 valence electrons, with the negative charge accounting for 1 additional electron. Hence, there are 12 valence electrons in the system. Construct a Lewis structure that satisfies the octet rule for both atoms using these 12 valence electrons. The resulting NO⁻ ion has a triple bond between nitrogen and oxygen. In summary, the localized electron model suggests the following bond types for these systems: - NO⁺: Double bond, 1 unpaired electron on nitrogen, bond order 2. - NO: Double bond, 1 unpaired electron on each atom, bond order 2. - NO⁻: Triple bond, bond order 3.

The molecular orbital model is based on the combination of atomic orbitals on different atoms to form molecular orbitals that are shared between the atoms involved. The bonding and anti-bonding molecular orbitals can provide insight into the bond order and stability of the molecule. 1. NO⁺: The molecular orbital diagram of NO⁺ ion consists of 10 electrons occupying the molecular orbitals in this order: \(1\sigma, 1\sigma^{*}, 2\sigma, 2\sigma^{*}, 3\sigma, 1\pi\). Here, there are 8 bonding electrons and 2 anti-bonding electrons, giving a bond order of (8-2)/2 = 3. 2. NO: The molecular orbital diagram of NO molecule consists of 11 electrons filling the molecular orbitals in this order: \(1\sigma, 1\sigma^{*}, 2\sigma, 2\sigma^{*}, 3\sigma, 1\pi, 1\pi^{*}\). There are 8 bonding electrons and 3 anti-bonding electrons, resulting in a bond order of (8-3)/2 = 2.5. 3. NO⁻: The molecular orbital diagram of NO⁻ ion consists of 12 electrons occupying the molecular orbitals in this order: \(1\sigma, 1\sigma^{*}, 2\sigma, 2\sigma^{*}, 3\sigma, 1\pi, 1\pi^{*}\). Here, there are 8 bonding electrons and 4 anti-bonding electrons, giving a bond order of (8-4)/2 = 2. In summary, the molecular orbital model suggests the following bond orders for these systems: - NO⁺: Bond order 3. - NO: Bond order 2.5. - NO⁻: Bond order 2.

Comparing the results obtained from both the localized electron and molecular orbital models, we can see that there are discrepancies in the bond orders of NO⁺ and NO⁻ ions: - NO⁺: The localized electron model predicts a bond order of 2, while the molecular orbital model predicts a bond order of 3. The discrepancy arises due to the distribution of electrons in molecular orbitals, allowing NO⁺ to have a higher bond order than predicted by the localized electron model, which assumes only fixed double bonds. - NO: Both models are in close agreement, with the localized electron model predicting a bond order of 2 and the molecular orbital model predicting a bond order of 2.5. This slight difference can be attributed to the presence of unpaired electrons in the molecular orbital model. - NO⁻: The localized electron model predicts a triple bond (bond order 3), while the molecular orbital model predicts a bond order of 2. The discrepancy results from the distribution and partial occupation of anti-bonding molecular orbitals, which reduces the bond strength compared to the localized electron model, which assumes a fixed triple bond. In conclusion, the molecular orbital model provides a more accurate description of the complex electron distribution and the bond order for these systems compared to the localized electron model.