In 1999, Karl Christe synthesized and characterized a salt that contained the \(\mathrm{N}_{5}{ }^{+}\)cation, in which the five \(\mathrm{N}\) atoms are connected in a long chain. This cation is the first all-nitrogen species to be isolated in more than 100 years. Draw the most important Lewis structure for this ion, including all equivalent resonance structures. Calculate the formal charges on all atoms.

Understanding the formal charge on atoms within a molecule or ion is crucial to identifying the most stable Lewis structure. Formal charge is the charge an atom would have if all bonding electrons were shared equally between the bonded atoms. The formula to calculate it is quite straightforward:
\[\text{Formal Charge} = (\text{Valence electrons}) - (\text{Non-bonding electrons}) - \frac{1}{2}(\text{Bonding electrons})\]
For the \(\mathrm{N}_{5}{}^{+}\) cation in our exercise, each nitrogen atom initially has 5 valence electrons. To find the formal charge for a specific nitrogen atom, you need to count the number of non-bonding electrons it hosts (those not involved in bonding) and half the number of bonding electrons (those shared with other atoms). With this information, you will be able to see which resonance structure presents the overall lowest possible formal charges for the system, which often corresponds to the most stable structure.

Resonance structures are alternate ways of drawing the Lewis structure of a molecule that differ only in the placement of electrons, not the arrangement of atoms. These structures represent different potential electronic configurations that contribute to the actual, observed structure of the molecule, known as the resonance hybrid.
The intriguing part of resonance is that no single structure can accurately depict the real molecule; instead, the actual structure is an average of all the resonance forms. In the case of the \(\mathrm{N}_{5}{}^{+}\) ion, drawing all equivalent resonance structures would involve shifting electron pairs to form different arrangements of double and single bonds, while ensuring that the overall distribution abides by the rules of chemical bonding. This aids in visualizing the electron delocalization within the molecule.

Valence electrons are the electrons in the outermost shell of an atom and are crucial to the atom’s chemical properties. They are responsible for the formation of chemical bonds because they can be lost, gained, or shared with other atoms. For nitrogen (\(\text{N}\)), with an atomic number of 7, there are 5 valence electrons as it belongs to group 15 of the periodic table (also known as the pnictogens).
When constructing Lewis structures or determining formal charges, it’s essential to know the number of valence electrons as they dictate the bonding behavior of the atom. For the \(\mathrm{N}_{5}{}^{+}\) cation, knowing that each nitrogen atom contributes 5 valence electrons is the starting point for deducing the total number of electrons we have to work with and how they may be shared or paired in bonds.

Chemical bonding is the force that holds atoms together in molecules or compounds. There are several types of chemical bonds, but the ones relevant to discussing the \(\mathrm{N}_{5}{}^{+}\) ion are covalent bonds, which involve the sharing of electron pairs between atoms. Each pair of shared electrons constitutes a single bond, and multiple shared pairs can form double or even triple bonds.
In Lewis structures, these bonds are represented by lines connecting atoms, and the pattern of these bonds must satisfy each atom's need for a complete octet of electrons whenever possible. However, some species like \(\mathrm{N}_{5}{}^{+}\) are exceptions to the octet rule, leading to fascinating bonding arrangements. The presence of resonance in such species is indicative of multiple bonding scenarios contributing to the overall stability and structure of the ion.