Problem 64 - Chemistry The Central Science

Question

(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?

Step-by-Step Solution

Answer

The Lewis structure of \(SO_3\) has sulfur (S) atom in the center, surrounded by three oxygen (O) atoms with single and double bonds between S and each O atom. The hybridization at the S atom is sp2. There are multiple equivalent Lewis structures due to resonance, and \(SO_3\) exhibits delocalized π bonding.

Step 1: Draw the Lewis structure of \(SO_3\)

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 ```

Step 2: Identify the hybridization of the S atom

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.

Step 3: Determine the existence of other equivalent Lewis structures

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.

Step 4: Verify the existence of delocalized \(\pi\) bonding

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.

Key Concepts

Hybridization

Hybridization is a fundamental concept that helps explain the bonding in molecules such as \(SO_3\). In this case, to account for the molecule’s structure and bonding, sulfur (S) undergoes a process called hybridization. To form bonds with each of the three oxygen atoms surrounding it, sulfur needs to create three hybrid orbitals.

Hybrid orbitals are a mix of atomic orbitals that rearrange to create stronger bonds by improving the overlap between orbitals. In \(SO_3\), sulfur uses one \(s\) orbital and two \(p\) orbitals, resulting in sp2 hybridization, denoted as \(sp^2\). This means:

• The sulfur atom uses one \(s\) orbital and two \(p\) orbitals.
• It forms three equivalent sp2 hybrid orbitals.
• Each of these hybrid orbitals forms a sigma (\(\sigma\)) bond with an oxygen atom.

The sp2 hybridization results in a trigonal planar shape around the sulfur atom, providing a straightforward explanation of the geometry and bonding present in \(SO_3\). By understanding hybridization, we can confidently predict molecular geometries and bonding patterns.

Resonance

Resonance is a powerful concept in chemistry that explains how molecules can have multiple valid structures. For \(SO_3\), it suggests that the actual structure of the molecule is a hybrid of several resonance forms. These forms are different Lewis structures that illustrate the delocalization of electrons among atoms.

In \(SO_3\), each oxygen atom can reasonably form a double bond with sulfur. As a result, multiple Lewis structures, where the double bond seems to "move" between different oxygen atoms, can be drawn. However, it’s important to note that these structures are not distinct entities but representations that illuminate how:

• The double bonds are not fixed between sulfur and any particular oxygen.
• The molecule behaves as if the \(\pi\) electrons are spread out over the entire molecule.
• The resonance hybrid is more stable than any individual resonance structure.

Each resonance structure contributes to a blended or hybrid form, offering insight into the symmetry and uniformity of bond lengths in \(SO_3\). This resonance stabilization is crucial for understanding the true nature of these substances.

Delocalized π Bonding

Delocalized \(\pi\) bonding is a fascinating concept where \(\pi\) electrons are not confined to just one bond or one pair of atoms. In \(SO_3\), this type of bonding highlights the spread of \(\pi\) electrons across the entire molecule, facilitated by resonance.

Instead of \(\pi\) electrons being restricted to the sulfur-oxygen double bond, they are shared among all the oxygen atoms through resonance, which leads to:

• Increased stability of the molecule due to the energetic benefit of electron delocalization.
• Uniformity in bond lengths within the molecule, as all \(SO\) bond lengths are equivalent due to delocalization.
• Enhanced electron movement, providing a more accurate depiction of chemical bonding in \(SO_3\).

This delocalization not only strengthens the bonding but also aids in understanding properties like symmetrical bonding and stability in structures such as \(SO_3\). Observing how \(\pi\) electrons are shared over multiple bonds through resonance allows chemists to predict and explain molecular behavior more accurately.