How was the \(\mathrm{N}-\mathrm{O}\) bond order of \(4 / 3\) calculated for \(\mathrm{NO}_{3}^{-}\) ?

When studying molecules, the Lewis structure serves as a valuable tool for visualizing the bonding between atoms and the lone pairs of electrons that may exist around atoms. To draw a Lewis structure, we generally follow specific rules to distribute electrons and show the bond connectivity within the molecule.

For polyatomic ions like the nitrate ion ((NO_{3}^{-})), it is crucial to account for the extra electrons from the negative charge when drawing the structure. The nitrate ion, for instance, includes one nitrogen atom (N) and three oxygen atoms (O), with nitrogen being the central atom. After assigning electrons based on the octet rule, which states that atoms are stable with eight electrons in their valence shell, and accounting for the extra electron from the negative charge, we achieve a structure with one single N-O bond and two N=O double bonds. However, it is essential to understand that this representation is not static; it is part of a set of possible structures called resonance structures.

The nitrate ion ((NO_{3}^{-})) is a polyatomic ion commonly found in various chemical compounds, including fertilizers and explosives. It consists of one nitrogen atom and three oxygen atoms, carrying an overall negative charge. Understanding the nitrate ion's structure and behavior is fundamental in many branches of chemistry, such as inorganic and environmental chemistry.

In the context of Lewis structures and bond order calculations, the nitrate ion is an excellent example of a molecule that exhibits resonance. It cannot be accurately represented by a single Lewis structure because the electrons are delocalized over the entire molecule. This delocalization provides stability to the ion and is a key concept in understanding the chemical bonding within the nitrate ion.

Resonance structures are multiple ways of drawing a Lewis structure for a particular molecule or polyatomic ion where electron pairing or bonding can vary. These structures do not represent different forms of a molecule; instead, they depict the same molecule with electrons delocalized in different positions. The actual structure of the molecule is a hybrid, or a combination, of all the possible resonance forms.

For the nitrate ion ((NO_{3}^{-})), resonance occurs because the electron pairs can be spread out in different ways to form one single and two equivalent double bonds with the nitrogen atom. When calculating the bond order, we consider all resonance forms equally. This results in the fractional bond order of 4/3 for the N-O bonds in the nitrate ion, meaning that each bond is not a single or a double bond but a hybrid with characteristics of both.