Write the Lewis structure, including resonance structures where appropriate, for (a) the oxalate ion, \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\) (there is a \(\mathrm{C}-\mathrm{C}\) bond with two oxygen atoms attached to each carbon atom); (b) \(\mathrm{BrO}^{+}\); (c) the acetylide ion, \(\mathrm{C}_{2}{ }^{2-}\). Assign formal charges to each atom.

When learning to draw Lewis structures, it is essential to understand that certain molecules or ions can have multiple valid dot structures, known as resonance structures. These alternate arrangements of electrons depict the same molecule where the position of electrons varies, while the position of the nuclei remains unchanged. In a sense, resonance structures are like different snapshots of a molecule that show different possible ways electrons can be distributed in a molecule.

For instance, the oxalate ion, \( \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \), exhibits resonance because the double bonds between carbon and oxygen atoms can be on different pairs of oxygen atoms. To illustrate these alternatives, we draw several Lewis structures. This also emphasizes the concept of electron delocalization in the molecule where electrons are not fixed in one place but can move within a certain framework of the molecular structure.

It's important for students to recognize that no single resonance structure is the 'real' structure on its own. Instead, the actual structure of the molecule is a hybrid that shares characteristics of all the resonance structures.

Calculating the formal charge on an atom within a molecule or ion is a critical step in drawing accurate Lewis structures. The formal charge is the hypothetical charge an atom would have if all the bonding electrons are equally shared between the bonded atoms. This concept is vital because it helps us determine the most probable electron configuration in the molecule and which resonance structure is more stable.

To calculate the formal charge on an atom, use the formula:\[ Formal\ Charge = (Valence\ Electrons) - (Non-bonding\ Electrons) - \frac{(Bonding\ Electrons)}{2} \]

This formula accounts for the valence electrons the atom brings into the molecule, the electrons that are not involved in bonding (non-bonding electrons or lone pairs), and half of the bonding electrons, as bonding electrons are shared between two atoms. For instance, in the resonance structures of the oxalate ion, the formal charges must be calculated for each atom in each structure to ascertain the most stable arrangement of electrons.

The fundamental concept that underpins the Lewis structure practice is that of valence electrons. These are the electrons located in the outermost shell of an atom and are involved in forming bonds. Every element has a characteristic number of valence electrons that can be found using the group number for elements in the main group on the periodic table.

For example, carbon, being in group 14 of the periodic table, has four valence electrons, while oxygen has six as it is in group 16. This information is essential when determining how atoms will bond and what the final electron configuration will look like in a molecule. In the context of the acetylide ion, \( \mathrm{C}_{2}{ }^{2-} \), understanding that each carbon atom offers four valence electrons, and considering the extra electrons due to the negative charge, allows us to properly draw the Lewis structure with a triple bond between the carbon atoms and assign the correct formal charges.