Problem 23 - Chemistry and Chemical Reactivity

Question

Describe the \(\mathrm{O}-\mathrm{S}-\mathrm{O}\) angle and the hybrid orbital set used by sulfur in each of the following molecules or ions: (a) \(\mathrm{SO}_{2}\) (c) \(\mathrm{SO}_{3}^{2-}\) (b) \(\mathrm{SO}_{3}\) (d) \(\mathrm{SO}_{4}^{2-}\) Do all have the same value for the \(\mathrm{O}-\mathrm{S}-\mathrm{O}\) angle? Does the S atom in all these species use the same hybrid orbitals?

Step-by-Step Solution

Answer

No, not all have the same \( \text{O}-\text{S}-\text{O} \) angle or hybridization.

Step 1: Determine the Molecular Geometry of SO2

The molecule \( \text{SO}_2 \) has a bent structure due to the presence of lone pairs on the sulfur atom. There are two bonding domains and one lone pair. This leads to an \mathrm{O}-\mathrm{S}-\mathrm{O} angle of about 119.5° and \( sp^2 \) hybridization for sulfur.

Step 2: Determine the Molecular Geometry of SO3

The molecule \( \text{SO}_3 \) has a trigonal planar structure, with three oxygen atoms symmetrically placed around the sulfur atom. The \( \text{O}-\text{S}-\text{O} \) angle is exactly 120°, and the sulfur uses \( sp^2 \) hybridization.

Step 3: Determine the Molecular Geometry of SO3^{2-}

The ion \( \text{SO}_3^{2-} \) has a pyramidal structure due to the presence of lone pairs on the sulfur atom. The \( \text{O}-\text{S}-\text{O} \) bond angles are slightly less than 109.5° due to lone-pair repulsion, and the sulfur atom is \( sp^3 \) hybridized.

Step 4: Determine the Molecular Geometry of SO4^{2-}

The ion \( \text{SO}_4^{2-} \) has a tetrahedral structure. The \( \text{O}-\text{S}-\text{O} \) angles are all 109.5°, and the sulfur is \( sp^3 \) hybridized.

Step 5: Compare Angles and Hybridization

The \( \text{O}-\text{S}-\text{O} \) angles and hybridization differ among these compounds: \( \text{SO}_2 \) (119.5°, \( sp^2 \)), \( \text{SO}_3 \) (120°, \( sp^2 \)), \( \text{SO}_3^{2-} \) (less than 109.5°, \( sp^3 \)), \( \text{SO}_4^{2-} \) (109.5°, \( sp^3 \)). Not all have the same \( \text{O}-\text{S}-\text{O} \) angle or hybridization.

Key Concepts

Hybridization

Hybridization is a concept used in chemistry to describe the mixing of atomic orbitals to form new hybrid orbitals. These hybrid orbitals help explain the geometry of molecular bonding. The hybridization of an atom in a molecule tells us about the shape and angle of the bonds that form around the atom.
In this exercise, sulfur atoms utilize two different kinds of hybridization: \( sp^2 \) and \( sp^3 \).

• \( sp^2 \) hybridization involves mixing one \( s \) orbital with two \( p \) orbitals, resulting in three equivalent planar orbitals 120° apart.
• \( sp^3 \) hybridization involves one \( s \) orbital mixing with three \( p \) orbitals, creating four orbitals arranged tetrahedrally, 109.5° apart.

Understanding the concept of hybridization can help predict the geometry and angles of molecules.

SO2

Sulfur dioxide, \( \text{SO}_2 \), features a sulfur atom bonded to two oxygen atoms. It has a distinctive bent shape because of the lone pair of electrons present on sulfur, which requires space and affects bond angles.
Sulfur in \( \text{SO}_2 \) is \( sp^2 \) hybridized, meaning it uses three orbitals to form bonds and accommodate the lone pair.
The \( \text{O}-\text{S}-\text{O} \) bond angle is approximately 119.5°, slightly less than the ideal 120° of a perfect trigonal planar molecule, due to the lone pair pushing the bonds closer together. This illustrates how lone pairs can influence molecular geometry.

SO3

Sulfur trioxide, \( \text{SO}_3 \), is a molecule where sulfur is bonded symmetrically to three oxygen atoms. This arrangement gives \( \text{SO}_3 \) its trigonal planar geometry, with all \( \text{O}-\text{S}-\text{O} \) bond angles being exactly 120°.
In \( \text{SO}_3 \), sulfur is again \( sp^2 \) hybridized. There are no lone pairs on the sulfur, so the molecular symmetry is not disrupted.
This kind of geometry is common in molecules where there are only bonding pairs around the central atom with no non-bonding electron pairs to alter the shape.

SO4 2-

The sulfate ion, \( \text{SO}_4^{2-} \), presents a completely different picture. Here, sulfur forms a bond with four oxygen atoms, resulting in a tetrahedral geometry.
The sulfur atom is \( sp^3 \) hybridized, utilizing four equivalent hybrid orbitals, and all \( \text{O}-\text{S}-\text{O} \) angles are 109.5°, the ideal angle for a tetrahedral shape.
Unlike \( \text{SO}_2 \) and \( \text{SO}_3 \), the sulfate ion has no lone pairs on the sulfur atom. This allows the bond angles to be uniform, demonstrating the principle that lone pairs affect molecular geometry more than bonding pairs alone.