Question

(a) What is the shape of the \(\mathrm{XeF}_{2}\) molecule? (b) What values are expected for the FXeF bond angles?

Short answer

The shape of the XeF2 molecule is linear, with expected F-Xe-F bond angles of approximately 180 degrees.

Step-by-step solution

Determine the Electron Domain Geometry

First, count the valence electrons of Xenon (Xe) and Fluorine (F). Xenon has 8 valence electrons and each Fluorine has 7 valence electrons, which makes a total of 8+(2*7)=22 valence electrons. Factor in the 'octet rule' and note that Xenon can have more than 8 electrons. Thus, XeF2 forms with 2 bonding pairs and 3 lone pairs on Xenon, resulting in 5 electron domains. According to VSEPR theory, 5 electron domains correspond to a trigonal bipyramidal electron domain geometry.

Determine the Molecular Geometry

To minimize electron repulsion, the lone pairs occupy equatorial positions in the trigonal bipyramidal structure, leading to a linear molecular shape for the XeF2 molecule.

Predict the Bond Angles

The shape of the XeF2 molecule is linear, which means the F-Xe-F bond angle is expected to be approximately 180 degrees.

Key concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. Based on the Valence Shell Electron Pair Repulsion (VSEPR) theory, the physical basis for the shape of molecules is the electron domain geometry, which is influenced by the electron pairs surrounding the central atom. In the case of the \textbf{XeF}\(_2\) molecule, the central xenon atom is surrounded by a total of five electron domains: two shared with fluorine atoms (bonding pairs), and three that are unbonded (lone pairs).

Due to the electron repulsion, the lone pairs tend to occupy more space and will orient themselves in a way to minimize repulsion, which, for \textbf{XeF}\(_2\), leads to a linear molecular shape. This linear configuration is a result of the lone pairs occupying equatorial positions allowing the bonding pairs to be as far apart as possible, according to the VSEPR model. Visually, imagine a straight line with the xenon atom at the center and a fluorine atom at each end.

Electron Domain Geometry

Electron domain geometry focuses on the arrangement of electron domains (regions where electrons are most likely to be found), which include both bonding and nonbonding electron pairs. The arrangement is key to understanding the molecular geometry, as it directly influences the shape of the molecule. For \textbf{XeF}\(_2\), the electron domain geometry is a trigonal bipyramidal structure due to its five electron domains.

However, the actual molecular geometry is not always the same as the electron domain geometry, particularly when lone pairs are present because they repel more strongly than bonding pairs. This disparity is why despite having a trigonal bipyramidal electron domain geometry, the molecular shape of \textbf{XeF}\(_2\) is linear.

Bond Angles

Bond angles are the angles between adjacent lines representing bonds that come off the central atom in a molecule. The ideal bond angles for a given molecular shape are predicted by the VSEPR theory and vary based on the electron domain geometry. For a molecule with a linear shape, such as \textbf{XeF}\(_2\), the expected bond angle is 180 degrees.

This is because the lone pairs are situated in the equatorial positions of a trigonal bipyramid, thereby pushing the bonding pairs, which are in the axial positions, directly opposite each other to minimize repulsion. As a result, the bond angle between the two fluorine atoms and the central xenon atom in \textbf{XeF}\(_2\) is about 180 degrees, which is consistent with the linear geometry of the molecule.