(a) Write a single Lewis structure for \(S O_{3},\) and determine the hybridization at the S atom. (b) Are there other equivalent Lewis structures for the molecule? (c) Would you expect SO \(_{3}\) to exhibit delocalized \(\pi\) bonding?

First, we need to find the total number of valence electrons in the \(SO_3\) molecule. Sulfur (S) has 6 valence electrons, and each oxygen (O) atom has 6 valence electrons. Therefore, the total number of valence electrons for \(SO_3\) is 18: \(6 + 3 \times 6 = 18\). We will start by putting the sulfur atom in the center and arrange the three oxygen atoms around it. Next, we will add single bonds between S and each O atom, which consume 6 of the available 18 valence electrons. Now, distribute the remaining 12 valence electrons by placing them around each oxygen atom, so each O attains a stable 8-electron configuration (octet rule). Each oxygen atom gets an additional lone pair (2 electrons), resulting in the following Lewis structure: ``` O || S-O - S - O || O ```

In the \(SO_3\) molecule, the central S atom forms three sigma (\(\sigma\)) bonds, one with each of the three surrounding O atoms. In order to make three sigma bonds, it requires three hybrid orbitals. From hybridization theory, to have three hybrid orbitals, the central atom would implement the sp2 hybridization scheme (1 s orbital + 2 p orbitals = 3 sp2 hybrid orbitals). Therefore, the hybridization at the S atom is sp2.

A molecule can exhibit resonance if its electrons are delocalized throughout the structure, making it possible to have more than one valid Lewis structure. Considering the Lewis structure drawn in Step 1, it is possible to switch the double bonds and single bonds between the central S atom and O atoms without changing the overall electron distribution. For example, we can have the following alternative (but equivalent) Lewis structure: ``` O || O - S - O | O ``` These equivalent Lewis structures present a resonance within the \(SO_3\) molecule.

Delocalized \(\pi\) bonding occurs when the \(\pi\) electrons present within a molecule are spread across multiple adjacent bonds in a continuous chain. In the \(SO_3\) molecule, there are three equivalent resonance structures where the double bond between the S and O atoms can move between different O atoms, thus explaining the delocalization of π electrons throughout the molecule. Therefore, we would expect \(SO_3\) to exhibit delocalized π bonding.