Question

Describe the bonding in the \(\mathrm{O}_{3}\) molecule and the \(\mathrm{NO}_{2}^{-}\) ion using the localized electron model. How would the molecular orbital model describe the \(\pi\) bonding in these two species?

Short answer

In the localized electron model, the bonding in O₃ consists of single bonds between the central oxygen atom and each of the peripheral oxygen atoms, as well as resonance that leads to a 1.5 bond nature. Similarly, in NO₂⁻, the bonding involves single bonds between the nitrogen atom and each oxygen atom as well as resonance that results in a 1.5 bond nature. In both cases, the π bonding is described using resonance structures. In contrast, the molecular orbital model considers bonding on a molecular level, treating electrons as they occupy delocalized molecular orbitals that extend over the entire molecule. In both O₃ and NO₂⁻, the π orbitals combine to form a continuous set of molecular orbitals distributed over the whole molecule, resulting in a delocalized distribution of electron density in the π system across all bonds.

Step-by-step solution

First, we need to determine the Lewis structures for both the O₃ and NO₂⁻ species. These structures show the arrangement of atoms and the valence electron distribution among the atoms in the molecule. For O₃: 1. Count the number of valence electrons: three oxygen atoms with 6 valence electrons each, totaling 18 electrons. 2. Place the least electronegative atom in the center: one oxygen as the central atom. 3. Connect the other atoms to the central oxygen with single bonds and assign remaining electrons, maintaining the octet rule: The two peripheral oxygens each form a single bond with the central oxygen and are left with two lone pairs each. For NO₂⁻: 1. Count the number of valence electrons: nitrogen with 5 valence electrons, two oxygen atoms with 6 valence electrons each, and one extra electron from the negative charge, totaling 18 electrons. 2. Place the least electronegative atom in the center: Nitrogen as the central atom. 3. Connect the other atoms to the central nitrogen with single bonds and assign remaining electrons, maintaining the octet rule: The two oxygen atoms form single bonds with the central nitrogen and are left with three lone pairs each, while the central nitrogen has one lone pair. #Step 2: Describe bonding using localized electron model#

In the O₃ molecule: 1. Single bond between the central oxygen atom and each of the peripheral oxygen atoms, formed by the overlap of their 2p orbitals. 2. Double bond formed between the central oxygen atom and one of the peripheral oxygens, due to resonance; this bond is distributed over both oxygen-oxygen bonds, creating a 1.5 bond nature. In the NO₂⁻ ion: 1. Single bond between the nitrogen atom and each of the oxygen atoms, formed by the overlap of their 2p orbitals. 2. There is also a double bond due to resonance, resulting in a 1.5 bond nature between the nitrogen atom and each of the oxygen atoms. #Step 3: Describe π bonding in localized electron model using resonance#

In both cases, the π bonding can be described using resonance structures in the localized electron model. - In O₃, resonance structures show the π bonding distributed evenly between both oxygen-oxygen bonds, which results in a 1.5 bond nature in each bond. - In NO₂⁻, resonance structures show the π bonding distributed evenly between the nitrogen-oxygen bonds, also resulting in a 1.5 bond nature in each bond. #Step 4: Describe π bonding using molecular orbital model#

The molecular orbital model considers bonding on a molecular level rather than an atomic level, treating electrons as they occupy delocalized molecular orbitals that extend over the entire molecule. In both O₃ and NO₂⁻, the π orbitals from the 2p orbitals of the constituent atoms combine to form a continuous set of molecular orbitals distributed over the whole molecule. These bonding and anti-bonding molecular orbitals result in the delocalized distribution of electron density in the π system across all bonds in the molecule. To sum up, the localized electron model describes the bonding in O₃ and NO₂⁻ through resonance structures with partial double bond character, while the molecular orbital model presents a more continuous, delocalized description of the π bonding in these species.

Key concepts

Lewis structures

Lewis structures are crucial for understanding the basic arrangement of atoms within a molecule and how electrons are shared or distributed among them. They help in visualizing the connectivity between atoms and the distribution of valence electrons.

To construct a Lewis structure, begin by counting all valence electrons from the atoms involved. For example, in the ozone (\( \mathrm{O}_{3} \)) molecule, each oxygen atom contributes six valence electrons, totaling 18 electrons that must be accounted for in the structure. Next, arrange the atoms with the least electronegative atom typically at the center. This helps in distributing electrons to fulfill the octet rule (where feasible).

For linear molecules like the nitrate ion (\(\mathrm{NO}_{2}^{-}\)), nitrogen serves as the central atom, connecting to oxygen atoms. Considering charge, adjust the electron count with an extra electron for the negative charge, ensuring all atoms achieve a stable electronic configuration. Ultimately, connecting atoms with single or sometimes double bonds forms a framework for understanding molecular interactions.

resonance

Resonance is a concept employed to describe delocalization of electrons within molecules. Some molecules cannot be represented by a single, definitive Lewis structure. Instead, they have multiple contributing structures, known as resonance structures, that depict electron distribution.

In ozone (\( \mathrm{O}_{3} \)) and the nitrite ion (\( \mathrm{NO}_{2}^{-} \)), resonance plays a vital role. Traditional Lewis structures show single/double bonds between atoms, but resonance structures illustrate a hybridization of these bonds. For both molecules, neither the single nor double bonds fully exist separately.

This complex array results in partial (1.5) bond characteristics between atoms. Essentially, the true structure of the molecule is an average or blend of all resonance structures, leading to more accurate representations of bond lengths and strengths. The concept of resonance helps to explain chemical properties and is pivotal for understanding electron behavior in more complex molecular systems.

molecular orbital model

The molecular orbital model offers a detailed view by considering electrons as moving within molecular orbitals formed by the combination of atomic orbitals throughout the entire molecule. Unlike the localized electron model, it allows for the treatment of electrons as delocalized across the entire molecule.

In molecules like \(\mathrm{O}_{3}\) and \(\mathrm{NO}_{2}^{-}\), \(\pi\) bonds are formed through the overlap of \(2p\) orbitals of neighboring atoms, creating a set of molecular orbitals. These molecular orbitals include bonding, non-bonding, and anti-bonding orbitals.

This model describes the bonding interactions not as confined to just two atoms but distributed over several atoms, which results in electron density spread over the entire molecule skeleton. As such, the molecular orbital approach provides a comprehensive description of electron delocalization and energy levels that explain molecular stability and reactivity.

π bonding

\(\pi\) bonding occurs from the sideways overlap of p orbitals and is critical in understanding complex molecules with multiple bonding scenarios. Unlike \(\sigma\) bonds, which arise from head-on overlap and are stronger and more stable, \(\pi\) bonds add a secondary layer of bonding, contributing to the molecular structure's rigidity and reactivity.

In the case of ozone (\( \mathrm{O}_{3} \)) and the nitrite ion (\( \mathrm{NO}_{2}^{-} \)), \(\pi\) bonds, alongside resonance, explain why these molecules exhibit partial bond character and not distinct single or double bonds.

When applied in molecular orbital theory, \(\pi\) bonds arise from the interaction of \(p\) orbitals, creating a system of delocalized electrons above and below the plane of the atoms involved. This delocalization is responsible for certain chemical properties, such as stability and bond length, which differ from expectations based strictly on local electron pair interactions. Understanding \(\pi\) bonding is essential for predicting how molecules will interact within various chemical environments.