For each of the following, draw the Lewis structure, predict the ONO bond angle, and give the hybridization of the nitrogen. You may wish to review the chapters on chemical bonding and advanced theories of covalent bonding for relevant examples. (b) \(\mathrm{NO}_{2}^{-}\) (c) \(\mathrm{NO}_{2}^{+}\)

VSEPR theory, or Valence Shell Electron Pair Repulsion theory, is a model used to predict the shape of individual molecules based on the idea that electron pairs around a central atom will repel each other and thus, arrange themselves as far apart as possible to minimize this repulsion. This results in geometric arrangements that can be used to predict molecular shapes.

For instance, when looking at the molecule \textbf{NO}\(_2^-\), we observe that there are three regions of electron density around the nitrogen atom. According to VSEPR theory, these areas of density repel one another, arranging themselves around the central atom in a way that creates a 'bent' shape. This is due to one of the regions being a lone electron, which has a different repulsion compared to lone pairs or bonded electron pairs. This asymmetry influences the ONO bond angle to be slightly less than 120 degrees, which deviates from the typical trigonal planar angle.

Similarly, for the \textbf{NO}\(_2^+\) molecule, there are no lone pairs on the nitrogen, resulting in two bonded pairs that align opposite each other, forming a linear shape with a 180-degree bond angle.

Covalent bonding is a type of chemical bond where atoms share pairs of electrons. In covalent bonds, the shared electrons occupy the outermost shell (or valence shell) of the atoms, allowing each atom to gain a noble gas configuration or to fulfill the octet rule — which states that atoms are generally more stable when they have eight electrons in their valence shell.

In the examples of \textbf{NO}\(_2^-\) and \textbf{NO}\(_2^+\), the atoms of nitrogen and oxygen share electrons to form covalent bonds. In the Lewis structure for these molecules, lines represent shared electron pairs between nitrogen and oxygen atoms, while dots represent unshared electrons.

• In \textbf{NO}\(_2^-\), there's an odd number of electrons leading to a radical presence, which is a species with an unpaired electron.
• In \textbf{NO}\(_2^+\), all electrons are paired, but the nitrogen atom lacks a lone pair, contrasting \textbf{NO}\(_2^-\) which has one lone pair and one unpaired electron.

Understanding covalent bonding is crucial to predict the molecular structure and reactivity of these molecules.

Hybridization is a concept in molecular chemistry that describes how atomic orbitals mix to form new, equivalent hybrid orbitals, which can then be used to form covalent bonds with other atoms. An important aspect of hybridization is the prediction of both the geometric layout of atoms and the types of bonds formed between them.

For nitrogen in both \textbf{NO}\(_2^-\) and \textbf{NO}\(_2^+\), we observe different hybridization states that explain the molecular geometry. In \textbf{NO}\(_2^-\), the nitrogen exhibits sp\(^2\) hybridization, which involves the mixing of one s orbital and two p orbitals to form three hybrid orbitals, and corresponds to three areas of electron density; this hybridization supports the 'bent' molecular shape of the molecule. In contrast, for \textbf{NO}\(_2^+\), nitrogen is sp hybridized where one s orbital and one p orbital mix, forming two hybrid orbitals that align linearly, fitting with the linear shape of the molecule.

The type of hybridization is closely tied to the molecule’s electron configuration and highly influences the chemical properties and bond angles observed in these nitrogen oxide ions.