Question

The reaction of three molecules of fluorine gas with a Xe atom produces the substance xenon hexafluoride, \(\mathrm{XeF}_{6}\) : $$\mathrm{Xe}(g)+3 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{XeF}_{6}(s) $$ (a) Draw a Lewis structure for \(\mathrm{XeF}_{6}\). (b) If you try to use the VSEPR model to predict the molecular geometry of \(\mathrm{XeF}_{6}\), you run into a problem. What is it? (c) What could you do to resolve the difficulty in part \((\mathrm{b}) ?(\mathbf{d})\) The molecule \(\mathrm{IF}_{7}\) has a pentagonalbipyramidal structure (five equatorial fluorine atoms at the vertices of a regular pentagon and two axial fluorine atoms). Based on the structure of \(\mathrm{IF}_{7}\), suggest a structure for \(\mathrm{XeF}_{6}\).

Short answer

(a) The Lewis structure for XeF6 has Xe at the center, connected to 6 F atoms with single bonds. (b) The VSEPR model has a problem with predicting molecular geometry for XeF6 due to having an odd number (7) of electron domains. (c) One possible solution is to consider alternative models like Molecular Orbital Theory (MOT) or Gillespie-Nyholm VSEPR-steric number theory. (d) Based on the structure of IF7, XeF6 could have a distorted pentagonal pyramidal structure with 5 F atoms in a pentagonal plane and one additional F atom in the axial position.

Step-by-step solution

(a) Draw the Lewis structure for XeF6.

To draw the Lewis structure for XeF6, first count the total number of valence electrons. Xenon (Xe) has 8 valence electrons, and each fluorine (F) atom has 7 valence electrons. Since there are 6 fluorine atoms, the total number of valence electrons is: $$8 + 6 \times 7 = 50$$ Place the Xe atom in the center and arrange 6 F atoms around it. Connect each F atom to the Xe atom with a single bond, accounting for 12 valence electrons (2 per bond). Now, distribute the remaining 38 electrons among the outer F atoms (giving each F a full octet). The Lewis structure for XeF6 is complete.

(b) Identify the problem with predicting molecular geometry using the VSEPR model.

The Valence Shell Electron Pair Repulsion (VSEPR) model is based on the assumption that electron pairs will arrange themselves in a way that minimizes repulsion between them, thus determining the molecule's overall shape. However, when you try to apply the VSEPR model to XeF6, there is a problem: the compound has an odd number (7) of electron domains. The VSEPR model does not have a standard geometry for compounds with 7 electron domains.

(c) Suggest a solution to the problem identified in part (b).

One possible solution to this problem is to consider an alternative model or approach that can handle compounds with 7 electron domains. There are other models like the Molecular Orbital Theory (MOT) or Gillespie-Nyholm VSEPR-steric number theory that can provide a resolution for calculating molecular geometries with odd numbers of electron domains.

(d) Suggest a structure for XeF6 based on the structure of IF7.

IF7, or iodine heptafluoride, has a pentagonal bipyramidal structure. In this structure, there are five fluorine atoms surrounding the central iodine atom in a planar pentagonal arrangement and two additional fluorine atoms above and below the plane (axial positions). Given that XeF6 also has a central atom (Xe) with multiple surrounding F atoms and an odd number of electron domains, it is possible to propose a structure similar to IF7, but with one less fluorine atom. One option is to maintain the pentagonal plane of 5 F atoms and add one additional F atom in the axial position, forming a distorted pentagonal pyramidal structure.

Key concepts

Lewis Structure

The Lewis structure is an essential tool in chemical education that allows students to visualize the arrangement of electrons around atoms in a molecule.

To draw a Lewis structure, one must first count the total number of valence electrons available, which in the case of \textbf{XeF}\(_6\) is 50. These electrons are then distributed to satisfy the octet rule for each fluorine atom, leading to a central xenon atom with six fluorines attached via single bonds. What remains unique about xenon compounds like \textbf{XeF}\(_6\) is that xenon can expand its valence shell to accommodate more than eight electrons, a concept that deviates from the octet rule typically applied to the second-period elements.

Teaching tip: Encourage students to verify their Lewis structures by counting electrons to ensure they match the total number of valence electrons and by checking that each atom satisfies the octet rule (or the respective rule for expanded octet elements like xenon).

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. The VSEPR model helps predict the geometry by considering electron domains—regions where electrons are most likely to be found, such as in bonds or lone pairs.

For \textbf{XeF}\(_6\), applying VSEPR is challenging due to its seven electron domains (six bonding pairs and one lone pair). This odd number of electron domains strays from the standard geometries VSEPR typically covers, such as tetrahedral or trigonal bipyramidal.

Exercise Improvement Tip

It's beneficial to show examples of molecular geometries for compounds with various numbers of electron domains, thereby giving students a better understanding of how electron domains influence molecular shape.

Molecular Orbital Theory

While the VSEPR model has limitations, Molecular Orbital Theory (MOT) offers a more nuanced understanding of how electrons are distributed in a molecule. MOT considers the combination of atomic orbitals to form molecular orbitals that can be occupied by electrons. This theory can handle molecules with an odd number of electron domains, providing a more accurate description of bonding and antibonding electrons.

In the case of \textbf{XeF}\(_6\), MOT could predict the distribution of electrons in molecular orbitals formed from the overlap of xenon and fluorine atomic orbitals. It's important to note that MOT is a more advanced concept, typically introduced at a higher education level.

Electron Domains

Electron domains are used in models like VSEPR to predict molecular shapes. A single electron domain could be a lone pair, a single bond, a double bond, or even a triple bond. In \textbf{XeF}\(_6\), we consider each bond between Xenon and Fluorine as one electron domain, plus the one lone pair on Xenon, totaling seven electron domains.

When teaching this concept, highlight that multiple bonds are counted as one electron domain. This simplifies the process, making it easier for students to determine the electron domain count for predicting molecular geometry. However, odd numbers of electron domains, like in \textbf{XeF}\(_6\), present a challenge not adequately accounted for by VSEPR, which emphasizes the theory's limitations and the need for alternative approaches or advanced theories like MOT.