(a) What is the difference between a localized \(\pi\) bond and a delocalized one? (b) How can you determine whether a molecule or ion will exhibit delocalized \(\pi\) bonding? (c) Is the \(\pi\) bond in \(\mathrm{NO}_{2}^{-}\) localized or delocalized?

A localized π bond is a covalent bond formed between two adjacent atoms, resulting from the side-to-side overlap of the adjacent p orbitals. These π bonds exist exclusively between the two atoms and are not shared with other atoms in the molecule. In contrast, a delocalized π bond is a bond where π electrons are shared and distributed across three or more atoms within a molecule. These electrons are not confined to just two atoms, and contribute to the bonding structure of multiple atoms, resulting in a more stable molecular structure. This phenomenon is often seen in molecules or ions with resonance structures.

To determine whether a molecule or ion exhibits delocalized π bonding, consider the following points: 1. Identify if the molecule/ion has any resonance structures. If there are multiple valid Lewis structures where double bonds are located in different positions, it can indicate delocalized π bonding is present. 2. Look for conjugated (alternating single and double) bonds within the molecule or ion. In a conjugated system, the π electrons can delocalize across the entire system, forming delocalized π bonds. 3. Assess the molecule/ion's stability. Delocalized π bonding contributes to the stability of a molecule or ion due to the distribution of bonding electrons over multiple atoms. If a molecule/ion is relatively more stable than expected, it could be due to delocalized π bonding.

To determine if the π bond in NO2- ion is localized or delocalized, let's follow the points discussed in step (b). 1. The Lewis structure of the NO2- ion exhibits resonance, meaning there are multiple valid ways to represent its bonding structure with double bonds in different positions. In this case, the double bond can be either between the nitrogen atom and one of the oxygen atoms, or between the nitrogen atom and the other oxygen atom. 2. There is a conjugated system in NO2- ion, due to the presence of alternating single and double bonds in the resonance structures. 3. A delocalized π bond allows for better distribution of electrons and greater stability in the overall ion. Given these reasons, we can conclude that the π bond in the NO2- ion is delocalized.