Question

Draw the two resonance structures that describe the bonding in \(\mathrm{SO}_{2}\). Then describe the bonding in this compound using MO theory. How does MO theory rationalize the bond order of 1.5 for the two \(\mathrm{S}-\mathrm{O}\) bonds in this compound?

Short answer

SO₂ has two resonance structures with S=O and S-O forms. MO theory shows a bond order of 1.5 by spreading electrons across bonding orbitals.

Step-by-step solution

Understanding Resonance Structures

First, recall that resonance structures are different ways to represent the position of electrons in a molecule without changing the overall arrangement of atoms. In the case of SO₂, we need to draw structures that distribute the electron pairs around the sulfur (S) and oxygen (O) atoms, while ensuring the octet rule is observed.

Drawing the First Resonance Structure

For the first resonance structure, draw sulfur (S) in the center with two oxygen atoms (O) on either side. Allocate a double bond between sulfur and one oxygen (S=O) and a single bond between sulfur and the other oxygen (S-O). Ensure that lone pairs on the oxygen atoms are added to satisfy their octet.

Drawing the Second Resonance Structure

The second resonance structure is a mirror image of the first. This time, have a single bond (S-O) with the left oxygen and a double bond (S=O) with the right oxygen, again ensuring both oxygen atoms have complete octets with lone pairs.

Introduction to Molecular Orbital (MO) Theory

Molecular Orbital (MO) theory describes bonds in terms of overlapping atomic orbitals to form molecular orbitals, which can be filled with electrons just like atomic orbitals are filled in individual atoms. This theory gives a more comprehensive understanding of the bonding in terms of electron distributions.

Applying MO Theory to SO₂

In SO₂, the sulfur atom uses its available 3s and 3p orbitals, and the oxygen atoms use their 2p orbitals to form molecular orbitals. Consider the combination of these orbitals to form bonding and antibonding molecular orbitals. Electrons in SO₂ are distributed across these molecular orbitals.

Rationalizing a Bond Order of 1.5

According to MO theory, bond order is calculated as the difference between the number of electrons in bonding orbitals and antibonding orbitals, divided by two. For SO₂, this distribution results in a bond order of 1.5 for each S-O bond since the bonding electrons are not equally distributed among simple single or double bonds, instead spread across molecular orbitals encompassing both resonance structures.

Key concepts

Resonance Structures

Resonance structures are alternative ways of drawing a molecule's structure by shifting electrons without moving the atoms themselves. This concept helps in illustrating the different electron positions possible in a molecule, providing a better idea of electron delocalization. In the case of the sulfur dioxide molecule ( SO₂ ), resonance structures are particularly relevant.
To form these structures, consider placing sulfur ( S ) at the center, with oxygen ( O ) on either side. Draw one resonance structure with a double bond between sulfur and one oxygen ( S=O ), and a single bond with the other oxygen ( S-O ). The reverse formation, with the double bond on the opposite side, is the second resonance structure. Each oxygen atom should maintain its octet, thus having lone pairs of electrons where needed.
Resonance structures for SO₂ show that neither single structure accurately depicts the electron distribution. Instead, the true electron configuration is a hybrid of these resonance forms. This understanding is key to grasping why resonance structures are used and how they provide insight into a molecule's characteristics.

Bond Order

Bond order is an important concept often used to describe the stability of a chemical bond. It is calculated by subtracting the number of electrons in antibonding orbitals from the number of electrons in bonding orbitals, and then dividing by two. In simpler terms, bond order gives us an idea of how many bonds, on average, exist between two atoms in a molecule.
For the SO₂ molecule, each sulfur-oxygen bond has a bond order of 1.5. This fractional bond order arises from the molecule's resonance structures. In these structures, there are both double and single bonds between sulfur and oxygen. Therefore, neither bond is entirely double nor single but a blend of both. The bond order of 1.5 indicates a bond that is somewhat stronger than a single bond but not as strong as a double bond.
Bond order can be correlated with bond length and bond energy. Generally, higher bond order means shorter, stronger bonds, implying more shared electron density between atoms, leading to enhanced bonding interaction.

SO₂ Molecule

The sulfur dioxide ( SO₂ ) molecule is an example of a compound featuring central sulfur bonded to two oxygen atoms. As a gas at room temperature, SO₂ is used in multiple industrial processes and can also be a harmful air pollutant, contributing to acid rain formation.
The molecule has a bent shape due to the sp² hybridization of sulfur, which leads to an approximate 120^ angle between the sulfur-oxygen bonds. The presence of lone pairs on sulfur causes electron pair repulsion, resulting in the bend.
Another crucial aspect of the SO₂ molecule is its polar nature. Despite being symmetric in terms of having two oxygen atoms attached to a central atom, the bent shape means the dipoles from the S-O bonds don't cancel out entirely, providing the molecule a net dipole moment.

Chemical Bonding in SO₂

Chemical bonding in SO₂ is best described through a combination of resonance structures and molecular orbital theory. Each bond between sulfur and oxygen can be seen as a resonance hybrid of single and double bonds, giving rise to a bond order of 1.5.
Molecular orbital theory provides a more detailed picture of this bonding. In SO₂ , sulfur's 3s and 3p orbitals combine with the 2p orbitals of oxygen to form molecular orbitals. These include bonding orbitals that stabilize the molecule by holding the atoms together, and antibonding orbitals that, if filled, can destabilize the molecule.
The electrons in SO₂ are delocalized over the entire molecule, adding to the bonding strength and making the description of its bonding more nuanced than what a simple Lewis structure can illustrate. This understanding through MO theory captures the real distribution of electrons more effectively.

Sulfur Dioxide Structure

The structure of sulfur dioxide ( SO₂ ) is a key element in understanding its chemical behavior. The molecule consists of a sulfur atom centrally bonded to two oxygen atoms. A significant part of understanding SO₂ comes from examining its geometrical arrangement and electron distribution.
Sulfur dioxide has a bent molecular geometry resulting from the sp² hybridization of sulfur, which causes a bond angle of about 120^ . This bent shape, influenced by the lone pair on sulfur, leads to the polar nature of the molecule.
Electrons in SO₂ are described not just by simple bonds but are spread across resonance structures. These structures show that neither a single nor a double bond exclusively exists between sulfur and oxygen, making the S-O bond order 1.5 as evidenced by MO theory. Thus, SO₂ is a great example of how molecular geometry and electron distribution impact a molecule's properties, including its reactivity and interaction with other molecules.