Question

(a) Draw a Lewis structure for the ozone molecule, \(\mathrm{O}_{3}\). (The order of atom attachment is \(\mathrm{O}-\mathrm{O}-\mathrm{O}\), and they do not form a ring.) Chemists use ozone to cleave carboncarbon double bonds (Section 6.5C). (b) Draw four contributing resonance structures; include formal charges. (c) How does the resonance model account for the fact that the length of each \(\mathrm{O}-\mathrm{O}\) bond in ozone \((128 \mathrm{pm})\) is shorter than the \(\mathrm{O}-\mathrm{O}\) single bond in hydrogen peroxide (HOOH, \(147 \mathrm{pm}\) ) but longer than the \(\mathrm{O}-\mathrm{O}\) double bond in the oxygen molecule \((123 \mathrm{pm})\) ?

Short answer

Answer: The resonance model accounts for the bond length of O-O bond in ozone by demonstrating that multiple resonance structures contribute to an averaged bond length. This means that the bond in ozone is intermediate between a single bond and a double bond, resulting in a shorter bond length than a single bond but longer than a double bond.

Step-by-step solution

1. Draw the Lewis structure for O3

To draw the Lewis structure for ozone, we first need to determine the total number of valence electrons in the molecule. Oxygen has six valence electrons, and since there are three oxygen atoms in ozone (O3), we have a total of 18 valence electrons (6*3=18). Now, let's arrange the oxygen atoms. The order of atom attachment is O-O-O, and they do not form a ring. We put the central O in the middle and connect two other O atoms. Then, we can complete the octets on each oxygen atom. To do this, we need to put two lone pairs of electrons on each external O atom, so they have six electrons each. After that, we need to distribute the remaining eight electrons between the middle and the exterior oxygen atoms. Central O would have a double bond to each exterior O atom with one lone pair each.

2. Draw four contributing resonance structures and show formal charges

To draw the contributing resonance structures for ozone, we need to consider the different ways the double bond and lone pairs of electrons can be distributed among the oxygen atoms while maintaining overall formal charges. 1. First resonance structure: central O has a double bond with the left exterior O and a single bond with the right exterior O. We add a lone pair to the central O and two lone pairs to the right O. Left O has a formal charge of 0, central O has a formal charge of +1, and right O has a formal charge of -1. 2. Second resonance structure: central O has a double bond with the right exterior O and a single bond with the left exterior O. We add a lone pair to the central O and two lone pairs to the left O. Left O has a formal charge of -1, central O has a formal charge of +1, and right O has a formal charge of 0. 3. Third resonance structure: central O has a single bond with both exterior O atoms and two lone pairs. Each exterior O atom has a double bond to the other exterior O atom (forming a loop) with one lone pair each. Left O has a formal charge of 0, central O has a formal charge of -1, and right O has a formal charge of +1. 4. Fourth resonance structure: similar to the third resonance structure, but with the left O having a formal charge of +1 and right O having a formal charge of 0.

3. Explain the bond length differences using the resonance model

The resonance model accounts for the fact that the length of each O-O bond in ozone is shorter than the O-O single bond in hydrogen peroxide and longer than the O-O double bond in the oxygen molecule. In ozone, the presence of multiple contributing resonance structures results in a blending or averaging of the individual bond lengths and strengths. Thus, the resulting bond length in ozone reflects a bond that is intermediate between a single bond and a double bond, as the electron density in the bonding region is distributed over more than one location. This blending of bonding characteristics makes the O-O bond in ozone shorter than a single bond but longer than a double bond, resulting in a bond length of 128 pm.

Key concepts

Resonance Structures

In chemistry, resonance structures are multiple ways of expressing the same molecule’s electron distribution. For ozone (\(\text{O}_3\)), resonance is particularly important. Ozone has four contributing resonance structures, which characterize variations in how electrons can be localized among the three oxygen atoms.

Resonance structures do not exist separately. Instead, they represent snapshots of extreme electron positions. Collectively, these structures describe an average actual state of the electrons, known as the resonance hybrid. In ozone, we can shift electrons to form different bonds while maintaining the overall molecule's stability.

• In one structure, the central oxygen shares a double bond with one of the external oxygens, forming a single bond with the other.
• Another structure does the opposite by shifting the double bond to the other external oxygen.
• A resonance structure may also depict both external oxygens sharing a double bond, resembling a delocalized loop, though this is not stable.
• Finally, forms with shifted charges adjust to keep each oxygen's valence shell filled with 8 electrons.

Each structure may carry different formal charges, maintaining neutrality for the overall molecule. These variations highlight the flexibility of electron position, showing why ozone adopts a more stable and average electron configuration.

Formal Charges

Formal charges are hypothetical charges assigned to atoms in a molecule, calculated based on their valence electron contribution. In ozone's resonance structures, formal charges help us understand electron distribution and stability.

The formal charge for an atom can be calculated using the formula:\[\text{Formal Charge} = \text{Valence Electrons} - \text{Non-Bonding Electrons} - \frac{\text{Bonding Electrons}}{2}\]For ozone, each oxygen typically has six valence electrons. By applying this formula, you can assign charges to the different resonance structures.

• When a central oxygen atom forms a double bond with one neighboring oxygen, it might carry a +1 formal charge.
• The bonded external oxygen with more lone pairs might hold a \(-1\) formal charge.
• By switching the positions of double and single bonds, the formal charges adjust between the oxygens, emphasizing how electrons are spread.

Recognizing and calculating formal charges help predict the most stable resonance structures, which are crucial for understanding molecular interaction and behavior.

Bond Length Differences

Bond length differences in molecules like ozone can seem confusing. However, these differences are key to understanding molecular stability. We compare the bond lengths of ozone's \(\text{O}-\text{O}\) bonds to those in hydrogen peroxide and molecular oxygen.

In hydrogen peroxide, the \(\text{O}-\text{O}\) bond measures 147 pm, typical for a single bond. In the oxygen molecule (\(\text{O}_2\)), a double bond measures 123 pm, being shorter due to more shared electrons and stronger attraction.

Ozone has a measured \(\text{O}-\text{O}\) bond length of 128 pm. This value suggests a bond order between a single and double bond, explained by resonance. Resonance effectively spreads electrons across all oxygens, distributing bond characteristics evenly. This resonance model account is why the bond length is longer than a double but shorter than a single bond.

• This average bond length arises as electrons participate in resonance, yielding a fractional bond order beyond typical single or double bonds.
• The bond length reflects a partial double bond character due to electron delocalization and shared density.

Understanding these differences in bond lengths helps explain how resonance models predict the structure and behavior of molecules like ozone.