Question

(a) An \(\mathrm{AB}_{2}\), molecule is linear. How many nonbonding electron pairs are around the A atom from this information? (b) How many nonbonding electrons surround the Xe in \(\mathrm{XeF}_{2} ?(\mathbf{c})\) Is \(\mathrm{XeF}_{2}\) linear?

Short answer

(a) In a linear AB2 molecule, there are no nonbonding electron pairs around the A atom. (b) There are six nonbonding electrons surrounding the Xe atom in XeF2. (c) Yes, XeF2 is a linear molecule.

Step-by-step solution

(a) Determining nonbonding electron pairs around the A atom in a linear AB2 molecule

According to VSEPR theory, the molecular geometry depends on the number of bonding and nonbonding electron pairs around the central atom. For a linear geometry, there must be two bonding pairs and no lone pairs around the central atom, or two bonding pairs and three lone pairs around the central atom. Since the molecule is linear, there are no nonbonding electron pairs around the A atom.

(b) Finding the number of nonbonding electrons surrounding Xe in XeF2

Xenon (Xe) is a noble gas and has 8 electrons in its valence shell. In XeF2, two of Xe's valence electrons will be used for bonding with the fluorine atoms, and the other six valence electrons will remain as nonbonding electrons. Therefore, there are six nonbonding electrons surrounding the Xe atom in XeF2.

(c) Checking if XeF2 is a linear molecule

Using the VSEPR theory, we can determine the molecular geometry of XeF2. The Xe atom has 2 bonding pairs (Xe-F) and 3 lone pairs (6 nonbonding electrons). In VSEPR notation, this is AX2E3, where A represents the central atom (Xe), X represents atoms bonded to the central atom (fluorine), and E represents lone pair electrons on the central atom (nonbonding electrons). The AX2E3 molecular shape minimizes electron pair repulsion and results in a linear molecular geometry. Consequently, XeF2 is a linear molecule.

Key concepts

Molecular Geometry

Understanding molecular geometry is crucial for predicting the shape and properties of molecules. At the heart of this concept is the VSEPR (Valence Shell Electron Pair Repulsion) theory. The main idea of VSEPR theory is that electron pairs around a central atom will repel each other and arrange themselves as far apart as possible to minimize this repulsion. In this way, the geometry of a molecule is determined by the number and type of electron pairs around the central atom.
For example, linear, trigonal planar, and tetrahedral are some fundamental shapes resulting from different arrangements of electron pairs. These geometries influence physical and chemical properties, such as boiling points and reactivity, making this concept essential in chemistry.

Nonbonding Electron Pairs

Nonbonding electron pairs, also known as lone pairs, consist of valence electrons that are not shared with another atom. Unlike bonding pairs, which are involved in chemical bonds, nonbonding pairs sit on a single atom.
They play a significant role in determining the shape of a molecule because they occupy space and can influence molecular geometry by repelling bonding pairs. According to VSEPR theory, the presence of lone pairs can alter idealized bond angles and geometries.

• Lone pairs tend to occupy more space than bonding pairs due to less restricted movement.
• This can cause distortions in shapes, making, for example, the difference between a tetrahedral and a pyramidal geometry.
• On central atoms like xenon, the space occupied by nonbonding pairs helps define the molecule's final shape.

Understanding nonbonding electron pairs is essential to mastering the prediction of molecular shapes and their subsequent chemical behavior.

Linear Molecule

A linear molecule is one of the simplest geometrical shapes observed in chemistry. It consists of a central atom bonded to two atoms, with all three atoms positioned in a straight line.
The angle between the bonds in a linear molecule is 180 degrees. Such geometry often occurs when a molecule has only bonding pairs of electrons around the central atom, or when the presence of lone pairs leads to a configuration where minimizing electron pair repulsions results in a linear arrangement.

• Examples of linear molecules include carbon dioxide (CO extsubscript{2}) and beryllium chloride (BeCl extsubscript{2}).
• The straightforward structure allows for predictions about properties like polarization and reactivity.
• Linear molecules can have either polar or nonpolar characteristics, depending on the symmetry and types of atoms involved.

Linear molecules' simplicity makes them an excellent starting point for understanding more complex molecular geometries.

XeF2

Xenon difluoride (XeF extsubscript{2}) is a fascinating example of a compound that forms despite involving a noble gas. The VSEPR theory offers insights into why XeF extsubscript{2} adopts its specific linear shape.
Xenon starts with eight valence electrons. In XeF extsubscript{2}, it forms bonds with two fluorine atoms, utilizing two of its electrons, leaving six as nonbonding electrons.
The XeF extsubscript{2} molecule is classified as AX extsubscript{2}E extsubscript{3} in VSEPR notation:

• Two bonding pairs formed by Xe-F bonds.
• Three lone pairs situated around the central xenon atom.
• This results in the repulsions aligning the fluorine atoms linearly, forming a 180-degree bond angle.

The presence of lone pairs results in a linear geometry for XeF extsubscript{2}, a prime example of how nonbonding electron pairs influence molecular geometry. Understanding XeF extsubscript{2} provides deeper insight into the behavior of molecules with unconventional bonding, expanding the boundaries of chemical bonding norms.