Question

Draw Lewis structures for ozone and for dioxygen. Using the data given below, qualitatively compare the bond enthalpies, bond orders, and bond lengths of these two compounds. $$ \begin{array}{rr} \mathrm{O}_{2}(g) \rightarrow 20(g) & \Delta H^{\circ}=+498 \mathrm{~kJ} \\ \mathrm{O}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{O}_{3}(g) & \Delta H^{\circ}=-105 \mathrm{kj} \end{array} $$

Short answer

O2 has a bond order of 2, shorter bonds, and higher bond enthalpy than O3, reflecting its stronger double bond.

Step-by-step solution

Draw the Lewis Structure for Dioxygen (O2)

Dioxygen (O2) is a simple diatomic molecule. Each oxygen atom has 6 valence electrons, allowing them to share two pairs of electrons to fulfill the octet rule. The Lewis structure for O2 shows a double bond between the two oxygen atoms, represented as O=O.

Draw the Lewis Structure for Ozone (O3)

Ozone (O3) is a triatomic molecule with a bent shape. To draw its Lewis structure: (1) Place the three oxygen atoms in a line; (2) Connect the first and second, and the second and third oxygens with single bonds; (3) Distribute the remaining 18 electrons to complete octets, this forms a single bond and a double bond between the structures. Note: Ozone has resonance structures with the bonds between the O atoms alternating between single and double. This means there are two structures that are averaged, showing that one double bond alternates position.

Bond Enthalpy and Energy Comparison

The bond enthalpy for O2 represents the energy required to break the O=O double bond, which is +498 kJ/mol. For forming O3 from O2 and O (otherwise indicating lower energy level) is -105 kJ/mol. This indicates that the bonds in O3, when compared to O2's double bond in dioxygen, are weaker and have lower enthalpy.

Bond Order and Its Implication

Bond order is the number of chemical bonds between a pair of atoms. In O2, the bond order is 2 (a double bond). In O3, due to resonance, the effective bond order is between 1 and 2 (commonly considered 1.5). This lower bond order suggests weaker bonds in O3 compared to O2.

Bond Length Analysis

Bond length is inversely proportional to bond order. Therefore, because O2 has a higher bond order (2), it has a shorter bond length than O3, which has a bond order of 1.5. In essence, the bonds in O3 are longer than those in O2.

Key concepts

Bond Enthalpy

Bond enthalpy, also known as bond dissociation energy, is the energy needed to break a chemical bond in a molecule. It is an essential concept that helps understand how stable a bond is. In the case of dioxygen, \( ext{O}_2 \), we see a double bond between the two oxygen atoms.
This requires an energy input of +498 kJ/mol to break, indicating a strong bond.

In contrast, when forming ozone \( ext{O}_3 \) from dioxygen and a single oxygen atom, the reaction actually releases energy (-105 kJ/mol).
This energy release suggests that the bonds in ozone are not as strong as the dioxygen bonds.

• The bonds in ozone are weaker compared to those in dioxygen.
• Lower bond enthalpy in ozone reflects its higher reactivity.

This aspect is crucial for understanding why dioxygen is more stable and less reactive than ozone in most chemical environments.

Bond Order

Bond order is an indicator of the number of chemical bonds between a pair of atoms. A higher bond order usually means a stronger bond.
In dioxygen (\( ext{O}_2 \)), we observe a double bond, giving it a bond order of 2, indicating a robust connection between the two oxygen atoms.

Ozone (\( ext{O}_3 \)), on the other hand, features resonance structures. Due to these alternating bonds, the effective bond order for ozone is somewhere between 1 and 2, often considered 1.5.

• This lower bond order in ozone indicates that these bonds are weaker than the double bond in dioxygen.
• The bond strength, as a result, is less in ozone compared to dioxygen.

Thus, understanding bond order helps predict molecule stability and reactivity.

Bond Length

Bond length is defined as the average distance between the nuclei of two bonded atoms within a molecule. It is inversely related to bond order.
In simple terms, the higher the bond order, the shorter the bond length. Dioxygen (\( ext{O}_2 \)), with its double bond (bond order of 2), has a shorter bond length compared to ozone (\( ext{O}_3 \)).

With ozone's bond order being approximately 1.5 due to its resonance structures, the bonds are longer.

• Shorter bond lengths in dioxygen imply stronger and more stable bonds.
• Longer bonds in ozone make it less stable and more reactive.

Bond length is a telling feature about the nature of the bond and corresponds to molecular stability.

Resonance Structures

Resonance structures occur when multiple valid Lewis structures can describe a molecule. This is a key concept in understanding molecules like ozone (\( ext{O}_3 \)).

Ozone does not have a stable single structure but instead resonates between two structures where the positions of the single and double bonds alternate.
This does not mean ozone flips back and forth but rather that the true structure is an average, or hybrid, of the possibilities.

• Resonance stabilizes the molecule by allowing electron density to be spread over multiple atoms.
• The bond lengths in resonating molecules like ozone are also averaged, resulting in a consistent but intermediate bond length.

Understanding resonance provides critical insight into why some molecules might show unexpected properties or reactivity due to electron delocalization.