Problem 60 - Chemistry An Atoms First Approach

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?

Step-by-Step Solution

Answer

In both SO₂ and SO₃, the sulfur atom is sp² hybridized, and π bonding occurs through the axial overlap of p orbitals. In SO₂, the bond order between sulfur and each oxygen is 1.5, while in SO₃, the bond order is 4/3. Both the localized electron model (hybrid orbital theory) and the molecular orbital model describe the π bonding consistently in these compounds.

Step 1: Analyzing SO₂ using hybrid orbital theory

To describe the bonding in SO₂ using hybrid orbital theory, we first need to determine the hybridization of the central sulfur atom. Sulfur has 6 valence electrons, and will form 2 single bonds with 2 oxygen atoms. The lone pair of electrons on sulfur participates in resonance, and thus, the hybridization of sulfur will be sp².

Step 2: Describing π bonding in SO₂ using hybrid orbital theory

In SO₂, the π bonding between sulfur (sp² hybridized) and the oxygen atom (also sp² hybridized) takes place by the axial overlap between the two p orbitals that are perpendicular to the plane formed by the three atoms (sulfur and two oxygens). The π electron cloud is distributed above and below this plane, forming a π bond. Due to resonance taking place, the bond order between sulfur and each oxygen atom is 1.5.

Step 3: Analyzing SO₃ using hybrid orbital theory

To describe the bonding in SO₃ using hybrid orbital theory, we first need to determine the hybridization of the central sulfur atom. Sulfur has 6 valence electrons and will form 3 single bonds with 3 oxygen atoms. The hybridization of sulfur will be sp².

Step 4: Describing π bonding in SO₃ using hybrid orbital theory

In SO₃, the π bonding between the central sulfur atom (sp² hybridized) and each of the oxygen atoms (also sp² hybridized) occurs by the axial overlap between their respective p orbitals, which are perpendicular to the plane formed by the four atoms (sulfur and three oxygens). The π electron cloud is distributed above and below this plane, forming π bonds. Due to resonance taking place among the sulfur-oxygen bonds, each sulfur-oxygen bond has an equal bond order of 4/3.

Step 5: Describing π bonding in SO₂ using molecular orbital theory

According to the molecular orbital model, the π bonding in SO₂ results from the combination of three 2p orbitals—one from the central sulfur atom and two from the oxygen atoms. This combination creates three molecular orbitals: one bonding π orbital and two antibonding π* orbitals. Because there are two of sulfur's electrons participating in the π bonding, the bonding order for each sulfur-oxygen bond in SO₂ is 1.5.

Step 6: Describing π bonding in SO₃ using molecular orbital theory

In molecular orbital theory, the π bonding in SO₃ results from the combination of four 2p orbitals—one from the central sulfur atom and three from the oxygen atoms. This combination creates four molecular orbitals: two bonding π orbitals and two antibonding π* orbitals. With four electrons taking part in the π bonding, the bond order for each sulfur-oxygen bond in SO₃ is 4/3. In conclusion, both the localized electron model (hybrid orbital theory) and the molecular orbital model describe the π bonding in SO₂ and SO₃ in a consistent way, with a bond order of 1.5 in SO₂ and 4/3 in SO₃.