Question

Antimony pentafluoride $\left({\mathrm{SbF}}_5\right)$ reacts with ${\mathrm{XeF}}_4$ and ${\mathrm{XeF}}_6$ to form ionic compounds, ${\mathrm{XeF}}_3^{+}{\mathrm{SbF}}_6^{-}$ and ${\mathrm{XeF}}_5^{+}$ ${\mathrm{SbF}}_6^{-}$. Describe the geometries of the cations and anions in these two compounds.

Short answer

${\text{XeF}}_3^{+}$ is T-shaped, ${\text{XeF}}_5^{+}$ is square pyramidal, ${\text{SbF}}_6^{-}$ is octahedral.

Step-by-step solution

Identify the species

In the given reactions, the ionic compounds formed are ${\text{XeF}}_3^{+}{\text{SbF}}_6^{-}$ and ${\text{XeF}}_5^{+}{\text{SbF}}_6^{-}$. The species we need to determine the geometry of are ${\text{XeF}}_3^{+}$, ${\text{XeF}}_5^{+}$, and ${\text{SbF}}_6^{-}$.

Determine the geometry of ${\text{XeF}}_3^{+}$

The ${\text{XeF}}_3^{+}$ ion has a central xenon atom bonded to three fluoride ions. Since xenon can have expanded octets, we consider the electron geometry which includes three bond pairs and two lone pairs, totaling five regions of electron density. This corresponds to a trigonal bipyramidal electron geometry, with the lone pairs occupying equatorial positions, resulting in a T-shaped molecular geometry.

Determine the geometry of ${\text{XeF}}_5^{+}$

For the ${\text{XeF}}_5^{+}$ ion, xenon is bonded to five fluoride ions. With five bond pairs and one lone pair (six regions of electron density), the electron geometry is octahedral. The lone pair assumes an axial position, leading to a square pyramidal molecular geometry.

Determine the geometry of ${\text{SbF}}_6^{-}$

The ${\text{SbF}}_6^{-}$ anion consists of antimony surrounded by six fluoride ions with no lone pairs, which gives it an octahedral geometry since it has six regions of electron density all occupied by bonding pairs.

Key concepts

Expanded Octets

Expanded octets occur when an atom has more than eight electrons in its valence shell. While this concept may initially seem confusing, it's a normal phenomenon in elements that have d orbitals available, such as those found in the third period or higher.
Certain elements like phosphorus, sulfur, and xenon can expand their octet. This is because they possess empty d orbitals that can accommodate additional electrons. In the case of xenon tetrafluoride (${\text{XeF}}_4$), xenon can have expanded octets allowing it to form compounds with more than the usual eight electrons around it.
Understanding expanded octets is crucial for predicting and rationalizing more advanced molecular geometries—like those found in xenon compounds, as discussed in this exercise.

Trigonal Bipyramidal

The trigonal bipyramidal geometry is a type of molecular geometry where a central atom is bonded to five other atoms in such a way that it forms two distinct planes.
It consists of two axial positions and three equatorial positions that total five regions of electron density. Typically, lone pairs of electrons prefer equatorial positions as they are further apart, reducing electron-electron repulsion. This configuration is seen in the ${\text{XeF}}_3^{+}$ cation.
Here's why: it has three bonds and two lone pairs. The result is a trigonal bipyramidal electron geometry where the molecular shape due to the lone pairs is T-shaped.

• The three fluoride ions create the T-shape as they remain in the equatorial plane.
• The electron lone pairs reside on the equatorial plane minimizing repulsive forces.

Square Pyramidal

The square pyramidal geometry is an exciting structure that emerges when a molecule has five single bonds and one lone pair of electrons.
This adds up to six electron domains, which is characteristic of octahedral electron geometry. For the ${\text{XeF}}_5^{+}$ cation, this specific arrangement forms because of the lone pair's preference to take one of the axial positions. This reduces the repulsion with other electron pairs as much as possible.
Its significant features:

• Five bonding pairs form a square base, often resembling a pyramid.
• The lone pair is positioned to minimize any electron-pair repulsions.

This is why the square pyramidal shape is prevalent in species containing expanded octets, like many xenon compounds.

Octahedral Geometry

Octahedral geometry is frequently encountered in coordination compounds and molecules forming with a central atom bonded to six other atoms or groups.
In an octahedral configuration, the electron pairs are at equal distances from each other. The ${\text{SbF}}_6^{-}$ anion perfectly demonstrates this, consisting of antimony at the center surrounded by six fluoride ions.
Key aspects of octahedral geometry:

• There are six regions of electron density, all occupied by bonding pairs, ensuring maximal symmetry and minimal repulsion.
• It remarkably allows all angles to be 90°, granting the geometry its characteristic shape.

Octahedral arrangements are fundamental and appear in many structural representations across chemistry, highlighting the coordination chemistry of metals and larger nonmetals.