Question

Xenon forms well-characterized compounds (4 page 400 ). Two xenon-oxygen compounds are \(\mathrm{XeO}_{3}\) and \(\mathrm{XeO}_{4} .\) Draw the Lewis structures of these compounds, and give their electron-pair and molecular geometries. What are the hybrid orbital sets used by xenon in these two oxides?

Short answer

XeO3: Trigonal pyramidal, sp3 hyb.; XeO4: Tetrahedral, sp3 hyb.

Step-by-step solution

Determine XeO3 Lewis Structure

Xenon trioxide, XeO3, consists of 1 xenon (Xe) atom and 3 oxygen (O) atoms. Xenon has 8 valence electrons, and each oxygen has 6. Therefore, the total valence electrons are 26. Xe is the central atom, with three double bonds to oxygen to satisfy the octet for O and utilize all valence electrons, leaving Xe with a lone pair.

Determine Electron-Pair and Molecular Geometry of XeO3

The Valence Shell Electron Pair Repulsion (VSEPR) theory is used here. XeO3 has three bonding pairs and one lone pair around Xe, thus having an electron geometry of tetrahedral and a molecular geometry of trigonal pyramidal.

Determine Hybridization of Xe in XeO3

For tetrahedral electron geometry, xenon uses sp3 hybridization for its orbitals since there are four regions of electron density.

Determine XeO4 Lewis Structure

Xenon tetroxide, XeO4, consists of 1 xenon (Xe) atom and 4 oxygen (O) atoms. Xenon has 8 valence electrons, and each oxygen has 6, totaling 32 valence electrons. The structure involves Xe forming four double bonds with four oxygen atoms to complete the octets.

Determine Electron-Pair and Molecular Geometry of XeO4

XeO4 has four bonding pairs and zero lone pairs around Xe. Thus, its electron and molecular geometry are both tetrahedral according to VSEPR theory.

Determine Hybridization of Xe in XeO4

As there are four regions of electron density around the xenon in XeO4, the xenon is sp3 hybridized for its orbitals.

Key concepts

Lewis Structures

Lewis structures offer a visual method to represent the distribution of electrons among atoms in a molecule. For Xenon trioxide ( XeO_3 ), it's crucial to recognize xenon (Xe) as the central atom because xenon can accommodate more electrons due to its large size and d-orbitals involvement. To construct the Lewis structure for XeO_3 , we start by recognizing the number of valence electrons:

• Xenon contributes 8 electrons.
• Each of the three oxygen atoms provides 6 electrons.

In total, this gives us 26 valence electrons to distribute. The structure must have every oxygen atom paired in a double bond with xenon. This satisfies the full octet for oxygen and uses up all electrons, resulting in xenon having one lone pair remaining.
For Xenon tetroxide ( XeO_4 ), xenon forms double bonds with all four oxygen atoms, using 32 electrons. This setup completes the octet rule for each oxygen and leaves no lone pairs on the xenon atom.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory helps in predicting the shapes of molecules based on the idea that electron pairs around a central atom will position themselves as far apart as possible to minimize repulsion. In XeO_3 , the presence of three bonding pairs (from the double bonds with oxygen) and one lone pair of electrons contributes to the overall shape. According to VSEPR, the electron pair geometry is tetrahedral due to four electron domains, but the molecular geometry is trigonal pyramidal because of the lone pair.
For XeO_4 , the absence of any lone pairs around the xenon atom simplifies the analysis. With four bonding pairs (double bonds to oxygen), both the electron pair and molecular geometries remain tetrahedral, creating a symmetrical shape.

Molecular Geometry

Understanding molecular geometry allows us to visualize the three-dimensional arrangement of atoms within a molecule. The molecular geometry is crucial in determining properties like polarity and reactivity.
For Xenon trioxide ( XeO_3 ), even though the electron pair geometry is tetrahedral due to four electron regions, its molecular geometry is trigonal pyramidal because one of these regions is a non-bonding lone pair. This leads to a slightly distorted shape from the ideal tetrahedral form.
In contrast, Xenon tetroxide ( XeO_4 ) has a perfect tetrahedral molecular geometry because all four electron regions are bonding pairs with no lone pairs to cause distortion. This results in a highly symmetrical three-dimensional structure.

Hybridization

Hybridization describes the mixing of atomic orbitals to form new, equivalent hybrid orbitals for bonding. In the case of xenon compounds, understanding hybridization helps explain how xenon can form multiple bonds despite having a filled outer electron shell.
In XeO_3 , xenon undergoes sp^3 hybridization because there are four areas of electron density: three from the Xe-O double bonds and one from the lone pair on xenon. This results in four hybrid orbitals, all equivalent, which accommodate these electron domains.
For XeO_4 , xenon also exhibits sp^3 hybridization. Even though all four regions are bonding pairs, the process remains the same, resulting in four equivalent hybrid orbitals that help form the double bonds with oxygen atoms for stable molecular formation.