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?

First, let's draw the resonance structures for the O3 and NO2- molecules. For O3 molecule: 1. Draw the Lewis structure (O=O-O). 2. Identify the bond pairs in a single and double bond. 3. Alternate the double and single bond to create another possible structure (O-O=O). For NO2- ion: 1. Draw the Lewis structure (O-N=O with a lone pair on N atom). This ion has a negative charge, so one extra electron is added to the nitrogen atom. 2. Identify the bond pairs in a single and double bond. 3. Alternate the double and single bond to create another possible structure (O=N-O with a lone pair on N atom).

In the localized electron model, electrons are considered to occupy specific orbitals within the molecule. O3 has resonance structures, so there is a delocalization of π electrons between the O atoms. The average of the resonance structures is taken into account to describe the actual structure. In O3, the bond order of the O-O bond is a fractional number between 1 and 2, as it fluctuates between a single and double bond. The bond lengths are also intermediate between a single and double bond.

Similarly, for NO2-, we need to consider the resonance structures to determine the bond order and bond characteristics. In NO2-, the bond order of the N-O bond lies between 1 and 2, fluctuating between a single and double bond. The bond lengths are intermediate between a single and double bond. The nitrogen atom has a free lone pair, contributing to its charge.

In the molecular orbital model, electrons are considered delocalized, moving freely within the molecule. We will specifically focus on π bonding. For O3: - Three 2p orbitals from the O atoms can combine to form three molecular orbitals: one bonding (lower energy), one non-bonding (intermediate energy), and one anti-bonding (higher energy) orbital. - Four π electrons are available within the molecule, so they fill the bonding and nonbonding orbitals. - The delocalization of π electrons contributes to the stability of the O3 molecule. For NO2-: - Two 2p orbitals from the O atoms and the 2p orbital from the N atom combine to form three molecular orbitals: one bonding (lower energy), one nonbonding (intermediate energy), and one anti-bonding (higher energy) orbital. - Four π electrons are available within the ion, so they fill the bonding and nonbonding orbitals. - The delocalization of π electrons contributes to the stability of the NO2- ion. In conclusion, the localized electron model allows us to describe the bond order and bond lengths in the O3 and NO2- molecules, while the molecular orbital model provides a better understanding of the delocalization of π electrons that contribute to the stability of these species.