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?

Short answer

Among the four possible Lewis structures for xenon trioxide (XeO3), the one with zero Xe-O double bonds satisfies the octet rule for every atom. The structure with one Xe-O double bond has two resonance structures, and the structure with two Xe-O double bonds also has two resonance structures. The most favorable formal charges are in the structure with one Xe-O double bond, which has formal charges of +2 on Xe, 0 on the doubly-bonded O, and -1 on each singly-bonded O atom.

Step-by-step solution

(Step 1: Drawing Four Lewis structures with different Xe-O bonds)

: First, let's draw four possibilities for the Lewis structures of XeO3, with zero, one, two, or three Xe-O double bonds in each structure. 1. Zero Xe-O double bonds: O | Xe-O-O 2. One Xe-O double bond: O | Xe=O-O 3. Two Xe-O double bonds: O=Xe-O | O 4. Three Xe-O double bonds: O=Xe=O | O Now we have drawn four possible Lewis structures of XeO3.

(Step 2: Determining if any structures satisfy the Octet Rule)

: Now, let's examine each structure to see if it satisfies the octet rule for every atom in the molecule. 1. Zero Xe-O double bonds: Xe has 8 electrons, and each O has 8 electrons surrounding them, so this structure satisfies the octet rule. 2. One Xe-O double bond: Xe has 10 electrons, and each O has 8 electrons surrounding them, so this structure does not satisfy the octet rule. 3. Two Xe-O double bonds: Xe has 10 electrons, and each O has 8 electrons surrounding them, so this structure does not satisfy the octet rule. 4. Three Xe-O double bonds: Xe has 12 electrons, and each O has 8 electrons surrounding them. This structure does not satisfy the octet rule. Only the structure with zero Xe-O double bonds satisfies the octet rule for every atom in the molecule.

(Step 3: Determining if any structures have multiple resonance structures)

: Let's see if any of the four Lewis structures have multiple resonance structures. 1. Zero Xe-O double bonds: The structure has no double bonds, so there are no resonance structures. 2. One Xe-O double bond: There are two possible resonance structures because the double bond can be between Xe and the second O atom or Xe and the third O atom. 3. Two Xe-O double bonds: There are two possible resonance structures because the Xe can form double bonds with either the second and third O atoms or with the first and second O atoms. 4. Three Xe-O double bonds: The structure has no alternative positions for the double bonds, so there are no resonance structures.

(Step 4: Determining the most favorable formal charges for the molecule)

: Now, we need to calculate the formal charges for each structure to determine the most favorable one. 1. Zero Xe-O double bonds: Formal charge of Xe: \( 8 - 3 - 2 = 3\) Formal charge of each O: \( 6 - 3 - 4 = -1\) The structure has formal charges of +3 on Xe and -1 on each O atom. 2. One Xe-O double bond: Formal charge of Xe: \( 8 - 4 - 1 \times 2 = 2\) Formal charge of doubly-bonded O: \( 6 - 2 - 4 = 0\) Formal charge of singly-bonded O: \( 6 - 3 - 4 = -1\) The structure has formal charges of +2 on Xe, 0 on the doubly-bonded O, and -1 on each singly-bonded O atom. 3. Two Xe-O double bonds: Formal charge of Xe: \( 8 - 5 - 0 = 3\) Formal charge of each doubly-bonded O: \( 6 - 1 - 4 = 1\) Formal charge of singly-bonded O: \( 6 - 3 - 4 = -1\) The structure has formal charges of +3 on Xe, +1 on each doubly-bonded O, and -1 on the singly-bonded O atom. 4. Three Xe-O double bonds: Formal charge of Xe: \( 8 - 6 + 3 = 5\) Formal charge of each doubly-bonded O: \( 6 - 0 - 4 = 2\) The structure has formal charges of +5 on Xe and +2 on each O atom. The most favorable formal charges are in the structure with one Xe-O double bond, which has formal charges of +2 on Xe, 0 on the doubly-bonded O, and -1 on each singly-bonded O atom.

Key concepts

Octet Rule

The octet rule is a key principle in chemistry that suggests atoms tend to form bonds until they are surrounded by eight electrons, giving them a configuration similar to that of noble gases. This concept helps chemists predict the types and numbers of bonds that atoms will form in a molecule. For example, in xenon trioxide (\( \mathrm{XeO}_3 \)), the goal is to arrange the electrons so that each atom ideally has eight electrons around it, satisfying the octet rule.

In most cases, oxygen atoms prefer to follow the octet rule by forming two bonds each, accommodating 6 valence electrons plus the 2 shared electrons from a bond. Xenon, however, is an exception. Being a noble gas, xenon can expand its octet due to the availability of empty 5d orbitals. In \( \mathrm{XeO}_3 \), the structure with zero Xe−O double bonds satisfies the octet rule for all atoms, offering each atom the required eight electrons.

This violation largely occurs because xenon can form more than five bonds, leading to a greater electron count around itself. Therefore, while \( \mathrm{XeO}_3 \) involves structures that challenge the octet rule, it showcases xenon's unique capability of expanding beyond eight electrons. This illustrates how elements in the lower periods can sometimes disobey the octet rule due to their expanded valence shells.

Resonance Structures

Resonance structures are multiple ways to draw a molecule's Lewis structure, showcasing different positions for a given pair of electrons. In essence, these are the structures that cannot be defined by a single Lewis structure due to the delocalization of electrons.

For xenon trioxide (\( \mathrm{XeO}_{3} \) ), there are a few resonance structures arising from the possible placements of double bonds between xenon and oxygen atoms. In the case of one or two Xe-O double bonds, the molecule can have differing structures by shifting the locations of these double bonds. For instance, with one Xe-O double bond, moving this bond among the three oxygen atoms results in two possible resonance structures. The same logic applies to \( \mathrm{XeO}_3 \)  with two Xe-O double bonds, leading to more resonance possibilities.

These resonance structures do not imply real positional changes of the bonds, but rather a hybrid of all possible drawings, where electron distribution is spread across the structure's bonds. It's crucial to understand that each resonance form is a way to represent the molecule’s overall electron distribution, which is essentially a combination or "average" of all potential structures.

Formal Charges

The concept of formal charges helps determine which Lewis structure is the most stable by assessing the hypothetical charge an atom would have if all bonding electrons were equally shared. The calculation helps discern whether electrons are being evenly distributed across a molecule.

For xenon trioxide (\( \mathrm{XeO}_{3} \) ), optimal formal charges are determined through calculations where the goal is to have the lowest possible charges, ideally close to zero. To calculate formal charges, use the formula:

- Formal charge = (Valence electrons in free atom) - (Non-bonding electrons) - 1/2(Bonding electrons)

Applied to our molecule, among the four Lewis structures drawn, the structure with one Xe-O double bond fares best in terms of formal charges. It distributes the charges across the molecule with Xe having a +2, one O as 0, and the other two O atoms as -1. This configuration keeps the formal charges minimal, thereby suggesting it's the most stable representation for \( \mathrm{XeO}_{3} \) .

Formal charges help not only in identifying the most plausible structure but also aid in understanding polar characteristics of molecules and their reactive behavior, providing critical insights into molecular chemistry.