Which has the greater bond lengths: \(\mathrm{NO}_{2}^{-}\) or \(\mathrm{NO}_{3}^{-}\) ? Explain.

When attempting to understand the properties of molecules, Lewis structures are an excellent starting point. These structures are a way to represent molecules to show how the atoms are arranged and how they share electrons. By drawing dots to represent electrons, and lines for bonds between atoms, we can visualize the electron distribution within a molecule.

For example, in the exercise comparing the bond lengths of \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{NO}_{3}^{-}\), the Lewis structures reveal the initial electron sharing between nitrogen (N) and oxygen (O) atoms. An important point when drawing these structures for polyatomic ions is remembering to include the extra electrons that come from the negative charge. For \(\mathrm{NO}_{2}^{-}\), we add one extra electron, while for \(\mathrm{NO}_{3}^{-}\), an additional electron is also added to complete the structures.

Resonance structures are a set of two or more Lewis structures that collectively describe the bonding in a molecule for which a single Lewis structure fails to accurately represent the electron distribution. These structures are crucial as they can influence properties such as the bond lengths and the stability of the molecule.

In the nitrogen-oxygen compounds case, resonance structures explain how the electron density is delocalized over different oxygen atoms. For \(\mathrm{NO}_{2}^{-}\), there are two resonance structures that differ in the position of the double bond. The \(\mathrm{NO}_{3}^{-}\) ion shows even more delocalization, with three resonance structures each having a different oxygen atom double-bonded to the nitrogen. This delocalization of charge plays a direct role in determining the bond order, hence affecting the bond lengths.

Bond order is a concept that helps us understand the strength and length of a bond between two atoms by reflecting how many chemical bonds exist between them. Typically, a higher bond order means a stronger and shorter bond, since more electrons are being shared between the atoms.

In practice, bond order can be calculated by dividing the total number of bonding electrons between two atoms by the number of bonds. For instance, in the exercise, we calculated the average bond order for \(\mathrm{NO}_{2}^{-}\) and for \(\mathrm{NO}_{3}^{-}\) by dividing the total bond orders by the number of resonance structures. The lower bond order of \(\mathrm{NO}_{3}^{-}\) compared to \(\mathrm{NO}_{2}^{-}\) suggests that \(\mathrm{NO}_{3}^{-}\) has longer bond lengths, as it has a more delocalized bonding arrangement.

The nitrogen-oxygen bond is a fundamental chemical bond that can be found in various compounds, each having distinct characteristics based on the bonding environment. The length of nitrogen-oxygen bonds can vary depending on factors such as resonance, bond order, and the presence of formal charges.

In the given exercise, we compared the bond lengths of two nitrogen-oxygen compounds, \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{NO}_{3}^{-}\). Due to the greater average bond order in \(\mathrm{NO}_{2}^{-}\), the electrons are held more closely to the nucleus, leading to shorter bonds. On the other hand, the \(\mathrm{NO}_{3}^{-}\) ion's electrons are more spread out across the molecule due to its resonance structures, resulting in longer bond lengths. This directly correlates to the idea that the strength of the bond is inversely proportional to its length.