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?

First, we need to determine the hybridization of sulfur atoms in both compounds, SO₂ and SO₃. For SO₂: Sulfur has 6 valence electrons and in SO₂, it is double bonded to one oxygen and single bonded to another oxygen atom. Therefore, sulfur uses 3 of its valence electrons to form bonds with oxygen atoms. To accommodate these 3 electron domains (double bond, single bond, and lone pair), sulfur must undergo sp² hybridization. For SO₃: Sulfur has 6 valence electrons and in SO₃, it is double bonded to each of the 3 oxygen atoms. This means, sulfur uses all its valence electrons to form bonds with the oxygen atoms. To accommodate these 3 electron domains (all double bonds), sulfur must undergo sp² hybridization as well.

For SO₂: In SO₂, sulfur undergoes sp² hybridization and forms 3 equivalent sp² hybrid orbitals. One of the sp² hybrid orbitals forms a σ bond with one oxygen atom's 2p orbital, and another sp² hybrid orbital forms a σ bond with the other oxygen atom's 2p orbital. The third sp² hybrid orbital of sulfur contains a lone pair of electrons. For SO₃: In SO₃, sulfur undergoes sp² hybridization and forms 3 equivalent sp² hybrid orbitals. Each sp² hybrid orbital forms a σ bond with one oxygen atom's 2p orbital. There are three σ bonds in total between sulfur and oxygen atoms in the SO₃ compound.

For SO₂: In SO₂, apart from the σ bonds as mentioned previously, sulfur and oxygen atoms also form π bonds. The double bond between sulfur and oxygen atom consists of one σ bond and one π bond. The π bond is formed through the sideways overlap between unhybridized 2p orbitals of sulfur and oxygen atoms. For SO₃: In SO₃, each sulfur-oxygen double bond consists of one σ bond and one π bond. The π bond is formed through the sideways overlap between the unhybridized 2p orbitals of sulfur and oxygen atoms. There are three π bonds in total in the SO₃ compound, and each π bond is distributed over all three sulfur-oxygen double bonds due to the resonance structures in SO₃.

In both SO₂ and SO₃, the π bonds are formed between the unhybridized 2p orbitals of sulfur and oxygen atoms through the sideways overlap. In SO₂, there is one π bond between the sulfur and one oxygen atom, whereas in SO₃, there are three π bonds distributed over all three sulfur-oxygen bonds due to resonance structures. In conclusion, the localized electron model (hybrid orbital theory) helps us describe the σ bonding in SO₂ and SO₃ compounds, while the molecular orbital model explains the π bonding nature in both compounds.