Question

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.

Short answer

In the localized electron model, the NO⁺ ion has a double bond with a bond order of 2, while the NO molecule has a double bond with a bond order of 2, and the NO⁻ ion has a triple bond with a bond order of 3. In contrast, the molecular orbital model predicts bond orders of 3 for NO⁺, 2.5 for NO, and 2 for NO⁻. The discrepancies between the models arise from the electron distribution in molecular orbitals, with the molecular orbital model better accounting for the actual correlation between the atoms and providing a more accurate description of bond orders and electron distribution.

Step-by-step solution

Localized Electron Model Analysis

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.

Molecular Orbital Model Analysis

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.

Compare the Models and Account for Discrepancies

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.

Key concepts

Localized Electron Model

The Localized Electron Model is a straightforward way to understand how atoms bond to form molecules. Here's how it works: you start by considering the valence electrons of atoms—those are the outermost electrons that are involved in bonding. In this model, electrons are either shared to form covalent bonds or transferred to form ionic bonds.
This model often uses Lewis structures, which are diagrams showing the connections between atoms and the locations of lone pairs of electrons around these atoms. In the case of nitrogen monoxide ( NO ), the uncharged molecule, you would represent it with Lewis structures that show its double bond and unpaired electrons. Similar structures can be drawn for the ions NO^+ and NO^- . However, this model assumes electrons are fixed in their positions around atoms, which has its limitations.

Molecular Orbital Theory

Molecular Orbital (MO) Theory takes a different approach by allowing electrons to delocalize over entire molecules, rather than being confined to fixed positions between specific atoms. This theory better captures the nature of electron interactions in molecules.
When applied to NO^+ , NO , and NO^- , the MO Theory provides a more dynamic picture. Electrons are placed into molecular orbitals created by the overlap of atomic orbitals. For example, NO^+ has its electrons filling orbitals like 1σ, 2σ , and 1π , resulting in a bond order of 3. In NO , the presence of an extra electron leads to a bond order of 2.5 due to the partly filled antibonding π^* orbitals. Similarly, NO^- has an even lower bond order of 2, highlighting how additional electrons in antibonding orbitals can weaken the overall bond strength.

Bond Order Discrepancies

Comparing the Localized Electron and Molecular Orbital models often reveals differences in predicted bond orders, especially in complex molecules like NO^+ , NO , and NO^- .
For NO^+ , the Localized Electron model might predict a bond order of 2 (double bond), while MO Theory finds a bond order of 3, indicating a stronger bond. The discrepancy arises because MO Theory considers the distribution of electrons across various molecular orbitals, including those that are antibonding.
In the case of NO , the models align more closely, with Localized Electron giving 2 and MO predicting 2.5, thanks to an extra unpaired electron in π^* orbital.
For NO^- , the Localized Electron model suggests a triple bond, or bond order of 3, whereas MO Theory predicts a bond order of 2, revealing that the occupation of antibonding orbitals indeed reduces bond strength, something the Localized model does not account for.
Thus, discrepancies highlight the intricacies of molecular bonding that only models considering electron delocalization, like MO Theory, can capture accurately.