Problem 66
Question
(a) Describe the molecule xenon trioxide, \(\mathrm{XeO}_{3},\) using four possible Lewis structures, one each with zero, one, two, or three \(\mathrm{Xe}-\mathrm{O}\) double bonds. (b) Do any of these resonance structures satisfy the octet rule for every atom in the molecule? (c) Do any of the four Lewis structures have multiple resonance structures? If so, how many resonance structures do you find? (d) Which of the Lewis structures in part (a) yields the most favorable formal charges for the molecule?
Step-by-Step Solution
Verified Answer
The structure with two double bonds minimizes formal charges. Only some atoms in certain structures fulfill the octet rule. The structure with one double bond has three resonance forms.
1Step 1: Analyze the xenon trioxide molecule
Xenon trioxide 6eO_{3}7 consists of one Xenon (Xe) atom and three Oxygen (O) atoms. Xenon is a noble gas capable of expanding its octet to accommodate more than eight electrons.
2Step 2: Construct Lewis Structure with Zero Double Bonds
Place xenon (Xe) in the center with three oxygen atoms attached by single bonds (Xe-O). This uses 6 purely bonding electrons (3 single bonds = 6 electrons). Fill the outer octet for each oxygen with 6 electrons (3 lone pairs each), leaving xenon with 12 electrons total (6 bonding + 6 non-bonding lone pairs on O atoms).
3Step 3: Construct Lewis Structure with One Double Bond
Convert one Xe-O single bond to a double bond. Thus, one oxygen atom is connected through a double bond, two through single bonds. Place lone pairs around each oxygen: 4 electrons around the double-bonded oxygen and 6 around the single-bonded oxygens. This better satisfies the octet for more atoms.
4Step 4: Construct Lewis Structure with Two Double Bonds
Form two double bonds between xenon and two oxygen atoms, leaving one oxygen with a single bond. Assign lone pairs as necessary: 4 electrons around each double-bonded oxygen and 6 around the single-bonded oxygen.
5Step 5: Construct Lewis Structure with Three Double Bonds
Make all Xe-O bonds double bonds. With 6 electrons in bonding pairs (3 double bonds), complete each oxygen's octet by assigning 4 additional electrons. Xenon accommodates 12 electrons in its valence shell.
6Step 6: Evaluate Octet Rule Compliance
Structures from Steps 3, 4, and 5 allow oxygen atoms to fulfill the octet rule (8 electrons each). However, xenon in all cases exceeds the octet rule due to its capability to hold more electrons.
7Step 7: Analyze Resonance Structures
Each of the structures in steps 1-5 is a single resonance structure. Step 3 structure has multiple resonance forms; the two single-bond oxygens can exchange places, leading to 3 possible resonance forms.
8Step 8: Determine Most Favorable Structure
Consider formal charges for all structures: the structure with two double bonds (Step 4) holds the most favorable organization of formal charges, with minimal distribution across atoms and near zero total formal charge.
Key Concepts
Octet RuleResonance StructuresFormal ChargesXenon Trioxide
Octet Rule
The octet rule is a chemical principle that suggests atoms prefer to form bonds until they are surrounded by eight electrons, which gives them the electron configuration of a noble gas.
This rule is often applied to atoms in molecules to understand how they might bond.
In the case of xenon trioxide \(\mathrm{XeO}_{3}\), the situation is slightly more complex. While oxygen atoms adhere strictly to the octet rule (sharing or gaining electrons to achieve eight in their valence shell), xenon, as a noble gas, can exceed the octet rule.
This is because xenon has d-orbitals available for bonding, which allows it to accommodate more than eight electrons if necessary.
When constructing the Lewis structures for xenon trioxide, the primary aim is to ensure that the oxygen atoms satisfy the octet rule, while understanding that xenon may not. In the structures with one or two Xe-O double bonds, most octets are respected for oxygen, with xenon having expanded its octet beyond the typical eight electrons.
This rule is often applied to atoms in molecules to understand how they might bond.
In the case of xenon trioxide \(\mathrm{XeO}_{3}\), the situation is slightly more complex. While oxygen atoms adhere strictly to the octet rule (sharing or gaining electrons to achieve eight in their valence shell), xenon, as a noble gas, can exceed the octet rule.
This is because xenon has d-orbitals available for bonding, which allows it to accommodate more than eight electrons if necessary.
When constructing the Lewis structures for xenon trioxide, the primary aim is to ensure that the oxygen atoms satisfy the octet rule, while understanding that xenon may not. In the structures with one or two Xe-O double bonds, most octets are respected for oxygen, with xenon having expanded its octet beyond the typical eight electrons.
Resonance Structures
Resonance structures are a set of different Lewis structures that describe a molecule where the arrangement of electrons is delocalized.
These structures are not real but represent different forms a molecule can take to stabilize itself.
In xenon trioxide, each oxygen can form a single or double bond with the central xenon atom, creating various possible distributions of bonding and lone pairs.
For instance, when there is one double bond in the structure, the other oxygens being single-bonded can exchange places to create multiple representations of the same molecular situation, leading to three possible resonance forms.
These resonance structures illustrate that within the molecule, electrons are shared in various extents, but the actual molecule is a resonance hybrid, more stable than any individual form alone.
These structures are not real but represent different forms a molecule can take to stabilize itself.
In xenon trioxide, each oxygen can form a single or double bond with the central xenon atom, creating various possible distributions of bonding and lone pairs.
For instance, when there is one double bond in the structure, the other oxygens being single-bonded can exchange places to create multiple representations of the same molecular situation, leading to three possible resonance forms.
These resonance structures illustrate that within the molecule, electrons are shared in various extents, but the actual molecule is a resonance hybrid, more stable than any individual form alone.
Formal Charges
Formal charge is a tool used to evaluate the distribution of electrons within molecules, helping predict the most stable structure.
It is calculated with the formula: \[\text{Formal charge} = \text{Valence electrons} - \text{Non-bonding electrons} - \frac{1}{2} \times \text{Bonding electrons}\]In xenon trioxide, evaluating formal charges helps determine which Lewis structure is the most favorable.
Generally, the Lewis structure that minimizes formal charges, keeping them close to zero, is more stable.
Among the structures, the one with two double bonds to two oxygens yielded the most favorable formal charges, likely because it balances electron distribution without placing excessive burden on any single atom.
This minimal spread and near-zero charge distribution contribute to stability, making it the preferred configuration.
It is calculated with the formula: \[\text{Formal charge} = \text{Valence electrons} - \text{Non-bonding electrons} - \frac{1}{2} \times \text{Bonding electrons}\]In xenon trioxide, evaluating formal charges helps determine which Lewis structure is the most favorable.
Generally, the Lewis structure that minimizes formal charges, keeping them close to zero, is more stable.
Among the structures, the one with two double bonds to two oxygens yielded the most favorable formal charges, likely because it balances electron distribution without placing excessive burden on any single atom.
This minimal spread and near-zero charge distribution contribute to stability, making it the preferred configuration.
Xenon Trioxide
Xenon trioxide \(\mathrm{XeO}_{3}\) is an intriguing molecule. It features a central xenon atom bound to three oxygen atoms.
Despite xenon being a noble gas, capable of large valence expansions, this compound exists due to xenon's ability to form bonds with highly electronegative elements like oxygen.
Xenon trioxide is a strong oxidizing agent and is unstable in its pure form. It primarily exists in aqueous solution or as a crystalline solid under controlled conditions.
When analyzing \(\mathrm{XeO}_{3}\) through Lewis structures, each configuration shows xenon expanding its octet to accommodate bonding with all three oxygen ligands.
This aspect of xenon trioxide underscores the importance of understanding valence expansions in chemical bonding, beyond the constraints of the octet rule. Moreover, exploring xenon trioxide enriches learning about chemical reactivity and structural chemistry, highlighting how theoretical principles apply in practice.
Despite xenon being a noble gas, capable of large valence expansions, this compound exists due to xenon's ability to form bonds with highly electronegative elements like oxygen.
Xenon trioxide is a strong oxidizing agent and is unstable in its pure form. It primarily exists in aqueous solution or as a crystalline solid under controlled conditions.
When analyzing \(\mathrm{XeO}_{3}\) through Lewis structures, each configuration shows xenon expanding its octet to accommodate bonding with all three oxygen ligands.
This aspect of xenon trioxide underscores the importance of understanding valence expansions in chemical bonding, beyond the constraints of the octet rule. Moreover, exploring xenon trioxide enriches learning about chemical reactivity and structural chemistry, highlighting how theoretical principles apply in practice.
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