(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?

: 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.

: 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.

: 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.

: 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.