Problem 57 - Chemistry and Chemical Reactivity

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 \(S-O\) bonds in this compound?

Step-by-Step Solution

Answer

\(\mathrm{SO}_2\) has two resonance structures with \(\mathrm{S-O}\) bond order of 1.5, rationalized by MO theory showing electrons in bonding and antibonding orbitals.

Step 1: Identify Resonance Structures

To find the resonance structures of \(\mathrm{SO}_{2}\), we start by drawing the Lewis structures of \(\mathrm{SO}_{2}\). The structure of \(\mathrm{SO}_{2}\) involves sulfur and oxygen atoms bonded together. First, draw one sulfur atom in the center with two oxygen atoms bonded to it. For the first resonance structure, you can draw one double bond between sulfur and one oxygen (\(\mathrm{S}\text{=}\mathrm{O}\)), and a single bond with the other oxygen (\(\mathrm{S-O}\)). Then assign formal charges and distribute lone pairs accordingly.

Step 2: Draw Second Resonance Structure

To draw the second resonance structure, move the double bond from one sulfur-oxygen bond to the other. Now you have \(\mathrm{O=S-O}\) for the second resonance structure. Again, assign formal charges and distribute lone pairs properly so that the overall charge remains the same as in the first structure.

Step 3: Explain Resonance Using Lewis Structures

The two resonance structures, \(\mathrm{O=S-O}\) and \(\mathrm{O-S=O}\), suggest that neither structure fully represents the actual molecule. Instead, \(\mathrm{SO}_2\) is best described as a resonance hybrid of these two structures, where the \(\mathrm{S-O}\) bonds are equivalent and have a bond order between a single and a double bond.

Step 4: Apply MO Theory for Bonding

To understand the bonding in \(\mathrm{SO}_2\) using MO theory, consider the molecular orbitals formed by the combination of atomic orbitals from sulfur and oxygen. The \(\mathrm{SO}_2\) molecule has 18 valence electrons. These electrons are placed in the molecular orbitals formed from the linear combinations of atomic orbitals from sulfur and the oxygens.

Step 5: Determine Bond Order with MO Theory

In MO theory, each \(\mathrm{S-O}\) bond is described by the combination of bonding and antibonding molecular orbitals. The bond order is calculated by taking the difference between the number of electrons in bonding orbitals and antibonding orbitals, divided by two. For \(\mathrm{SO}_2\), this approach results in a bond order of 1.5 for each \(\mathrm{S-O}\) bond, as some of the electrons are also present in antibonding orbitals.

Step 6: Rationalize Bond Order Using MO

The experimentally determined bond order of 1.5 for each \(\mathrm{S-O}\) bond is rationalized by considering the partial inclusion of double bond characteristics and resonance stabilization in the molecular orbital framework. This partial bond character is represented by equal sharing of electrons across the two possible bonding states identified in resonance structures, illustrating fractional bond orders evident in MO theory.

Key Concepts

Lewis structures

Lewis structures are diagrams that represent the valence electrons of atoms within a molecule, focusing on illustrating how these electrons are arranged around individual atoms.This method helps to predict the geometry, reactivity, and polarity of the molecule.
In the case of sulfur dioxide (\(SO_2\)), we start by acknowledging that sulfur and oxygen share electrons to fulfill their desire for a noble gas electron configuration.
Sulfur sits at the center of the molecule, being less electronegative compared to oxygen.

• The first step is to create a skeleton structure with sulfur bonded to two oxygen atoms.
• Next, distribute electrons in the form of bonds (single or double) to meet the octet rule for each atom.
• For \(SO_2\), typical resonance structures involve one double bond and one single bond between sulfur and oxygen, with a switch in their positions for each resonance form.
• Don't forget to assign formal charges to ensure both structures maintain a neutral charge.

This concept forms the basis for understanding the resonance in \(SO_2\).

molecular orbital theory

Unlike the localized approach of Lewis structures, molecular orbital (MO) theory treats electrons in molecules as delocalized over the entire molecule. It is a quantum-chemical model that explains the formation of chemical bonds via overlap of atomic orbitals. In the \(SO_2\) molecule, MO theory helps us understand how the p orbitals of sulfur and oxygen overlap to form molecular orbitals.

• Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO), which could either enhance bonding (bonding MOs) or weaken it (antibonding MOs).
• The 18 valence electrons of \(SO_2\) are filled into these molecular orbitals following the Aufbau principle, starting with the lowest energy level.
• This filling results in some electrons occupying antibonding orbitals, reducing overall molecule stability.
• Nevertheless, resonance and delocalization provide stability, directly influencing calculated bond orders.

This delocalized electron approach provides a more comprehensive understanding of molecular behavior compared to localized models like Lewis structures.

bond order

Bond order is a concept that essentially measures the bond strength between two atoms. It indicates the number of chemical bonds between a pair of atoms. Traditionally, a single bond has a bond order of 1, a double bond 2, and a triple bond 3. However, when examining both resonance and MO theory, you can have fractional bond orders such as 1.5 in the case of \(SO_2\).

• Under MO theory, bond order is determined by the formula: \( \frac{(\text{number of bonding electrons}) - (\text{number of antibonding electrons})}{2} \).
• Bond order in \(SO_2\) is particularly interesting because it is found to be 1.5, owing to the partial double bond character shared across each \(S-O\) bond.
• This emerges from electrons being distributed across both bonding and antibonding MOs, reflecting the shared electron characteristic in resonance hybrid structures.
• The concept of bond order helps explain physical properties such as bond length and bond strength - higher bond order implies shorter, stronger bonds.

Thus, bond order provides a quantitative understanding of molecular structure, integrating both the Lewis and MO approach.

sulfur dioxide (SO2)

Sulfur dioxide (\(SO_2\)) is a common chemical compound with significant applications in industry and the environment. It serves as a classic example in studying molecular representations and bonding theories.

• From an atmospheric chemistry perspective, \(SO_2\) is known for its role as a significant pollutant, contributing to acid rain.
• Chemically, \(SO_2\) showcases how resonance structures depict delocalized pi bonding, contributing to a more stable molecule.
• In practical industrial uses, \(SO_2\) is utilized in processes like bleaching, refrigeration, and as a preservative.
• The understanding of its bonds through theories like MO and its fractional bond orders helps chemists predict reactivity and interactions with other compounds.

Through its study, \(SO_2\) expands knowledge on the applications and implications of molecular structures and their predictions.