Question

Describe the bonding in \(\mathrm{SO}_{2}\) and \(\mathrm{SO}_{3}\) using the localized electron model (hybrid orbital theory). How would the molecular orbital model describe the \(\pi\) bonding in these two compounds?

Short answer

In both SO₂ and SO₃, sulfur undergoes sp² hybridization, forming sigma bonds with each oxygen atom using its sp² hybrid orbitals. In SO₂, there's a lone pair on sulfur, and a double bond is formed between the sulfur and each oxygen atom due to two π bonds. In SO₃, a trigonal planar geometry is formed with three equivalent S-O resonance structures due to the delocalization of electrons in π bonds. According to the molecular orbital model, the π bonding in SO₂ and SO₃ involves the combination of p-orbitals on sulfur and oxygen atoms, creating molecular orbitals. In SO₂, one bonding and one antibonding π molecular orbitals are formed. In SO₃, a set of four π molecular orbitals is formed, with three bonding and one antibonding orbitals, resulting in delocalized π bond formation and resonance.

Step-by-step solution

(Step 1: Determine the electron configuration for sulfur and oxygen)

Sulfur is in group 16, and so has an electron configuration of [Ne]3s²3p⁴. Oxygen is also in group 16, and has an electron configuration of [He]2s²2p⁴.

(Step 2: Determine the hybridization for Sulfur)

In SO₂, there are two sigma bonds between the S and O atoms and one lone pair on S. Sulfur needs three hybrid orbitals to accommodate these three electron pairs, leading to sp² hybridization. In SO₃, there are three sigma bonds between the S and O atoms and no lone pair on S. Sulfur needs three hybrid orbitals to accommodate the three sigma bonds, also leading to sp² hybridization.

(Step 3: Describe the sigma bonding framework)

In both SO₂ and SO₃, sulfur forms sigma bonds with each oxygen atom using its sp² hybrid orbitals. In SO₂, there is an additional lone pair occupying one of the sp² orbitals. In SO₃, each of the three oxygen atoms forms a sigma bond with the central sulfur atom, creating a trigonal planar geometry.

(Step 4: Identify π bond formation in SO₂ and SO₃)

In both molecules, the remaining unhybridized p-orbital on sulfur overlaps laterally with the unhybridized p-orbital of each oxygen atom. For SO₂, there are two π bonds formed within the molecule, making a double bond between the sulfur and each oxygen atom. For SO₃, there are three π bonds formed in the molecule due to the redistribution of electrons. Each S-O bond is weaker than a double bond but stronger than a single bond due to this delocalization. This results in three equivalent S-O resonance structures.

(Step 5: Describe the Molecular Orbital model for π bonding)

According to the molecular orbital model, the π bonding in both SO₂ and SO₃ involves the combination of p-orbitals on sulfur and oxygen atoms to create molecular orbitals. In SO₂, one bonding π molecular orbital is formed from the in-phase overlap of two p-orbitals. The remaining electrons create one antibonding π molecular orbital. In SO₃, three p-orbitals on the oxygen atoms combine with the p-orbital on sulfur to create a set of four π molecular orbitals. Mixing creates three bonding and one antibonding molecular orbitals. The six π electrons are distributed among the bonding orbitals, which results in delocalized π bond formation and resonance.

Key concepts

Localized Electron Model

The localized electron model is a way to describe how electrons are shared between atoms in a molecule. In simpler terms, it helps us understand how atoms like sulfur (\(\mathrm{S}\)) and oxygen (\(\mathrm{O}\)) connect in molecules like \(\mathrm{SO}_{2}\) and \(\mathrm{SO}_{3}\). This model focuses on identifying which orbitals hold the pairs of electrons.
The main objective is to find out how atoms bond together; each bond is seen as sharing of two electrons. In \(\mathrm{SO}_{2} \), sulfur forms two sigma bonds with oxygen and has a lone pair, hinting an sp² hybridization.
Whereas for \(\mathrm{SO}_{3} \), sulfur utilizes three sigma bonds with no lone pairs on sulfur, also resulting in sp² hybridization. This model provides a clear and detailed view of individual bonds within a molecule, giving insights into their geometries and hybridizations.

Hybrid Orbital Theory

Hybrid orbital theory is essential for understanding how atomic orbitals mix to form new hybrid orbitals, which accommodate electron pairs forming bonds. For \(\mathrm{SO}_{2}\), sulfur needs three hybrid orbitals to make bonds with oxygen and hold its lone pair, resulting in sp² hybridization. It uses three atomic orbitals, one \(s\), and two \(p\) orbitals, leading to a set of three equivalent sp² hybrid orbitals.
In \(\mathrm{SO}_{3}\), sulfur also adopts an sp² hybridization. Here, all three hybrid orbitals are used to form sigma bonds with oxygen atoms, giving a flat trigonal planar structure. Hybrid orbital theory simplifies visualizing complex bonding interactions by merging atomic orbitals into new forms focused on bonding.

Molecular Orbital Theory

Molecular orbital theory offers a more global perspective on bonding compared to localized models. It elucidates how atoms in a molecule share electrons across the whole molecule. This theory views electrons not as localized pairs but as forming molecular orbitals that spread over different atoms.
For \(\mathrm{SO}_{2}\), it creates one bonding \(\pi\) molecular orbital and one antibonding \(\pi\) molecular orbital due to the overlap of p-orbitals from sulfur and oxygen.
In \(\mathrm{SO}_{3}\), the p-orbital on sulfur overlaps with three p-orbitals on oxygen, resulting in four \(\pi\) molecular orbitals. This involves three bonding and one antibonding orbital, contributing to a resonance and delocalized bonding, where the \(\pi\) electrons roam over multiple bonds rather than being fixed.

Pi Bonding

Pi bonding occurs when unhybridized p-orbitals overlap side-by-side on neighboring atoms. It is distinct from sigma bonding, which involves head-on overlap of orbitals. In \(\mathrm{SO}_{2}\), sulfur exhibits lateral overlap with oxygen’s p-orbitals forming two \(\pi\) bonds. These bonds contribute to double bond characteristics for each S-O connection.
In \(\mathrm{SO}_{3}\), three delocalized \(\pi\) bonds are formed, each linking one pair of orbitals from sulfur and one of the oxygen atoms. This setup results in every S-O bond being stronger than a single bond, but weaker than a classic double bond due to the global electron sharing, known as resonance.

Hybridization

Hybridization is the process where atomic orbitals mix to create new, equivalent hybrid orbitals ideal for bonding. It helps rationalize the molecular structure of compounds like \(\mathrm{SO}_{2}\) and \(\mathrm{SO}_{3}\). In the case of \(\mathrm{SO}_{2}\), the central sulfur atom hybridizes its 3s and 3p orbitals into three sp² orbitals to accommodate the two sigma bonds and one lone pair.
For \(\mathrm{SO}_{3}\), the hybridization results in three sp² orbitals utilized for sigma bonding with the oxygen atoms, resulting in a trigonal planar geometry. This approach simplifies understanding how molecules retain their stability and form specific shapes based on energy-efficient electron arrangements.