Problem 13 - Chemistry The Central Science In Si Units

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?

Step-by-Step Solution

Answer

(a) There can be 0 or 1 nonbonding pairs on A. (b) Xe has 6 nonbonding electrons. (c) Yes, \( \mathrm{XeF}_2 \) is linear.

Step 1: Determine the molecular geometry

For an \( \mathrm{AB}_2 \) molecule that is linear, the molecule must have a linear electron geometry. This means there are three electron regions surrounding the central atom: 2 bonding pairs (i.e., bonds to the \( \mathrm{B} \) atoms) and 1 nonbonding pair of electrons if the central atom is surrounded by three electron pairs in total. Therefore, the central atom \( \mathrm{A} \) in \( \mathrm{AB}_2 \) has 0 or 1 nonbonding electron pair, dependent on additional context not given in this problem.

Step 2: Identify the nonbonding electrons in XeF2

The molecular formula \( \mathrm{XeF}_2 \) suggests that the xenon \( \mathrm{Xe} \) atom is the central atom with two fluorine \( \mathrm{F} \) atoms bonded to it. Xenon has a total of 8 valence electrons. After forming two bonds with fluorine atoms (using 2 electrons), there are 6 electrons remaining as nonbonding electrons, which form 3 lone pairs.

Step 3: Determine if XeF2 is linear

The structure of \( \mathrm{XeF}_2 \) is determined by the VSEPR theory. Xenon in \( \mathrm{XeF}_2 \) has 2 bonding pairs and 3 nonbonding pairs of electrons around it, resulting in 5 regions of electron density. The electron geometry is trigonal bipyramidal, with the lone pairs occupying equatorial positions, minimizing repulsion. The molecular shape is linear due to the two bonding pairs in the axial positions.

Key Concepts

Nonbonding Electron Pairs

Nonbonding electron pairs, also known as lone pairs, are pairs of valence electrons that are not shared with another atom in a molecule. These electrons belong solely to one atom and do not participate in bonding. These lone pairs are important because they influence the shape and properties of the molecule.
The presence of lone pairs affects the molecular geometry by taking up space around the central atom. This can change the angles between the atoms. For example:

• In a tetrahedral molecule, introducing a lone pair can result in a trigonal pyramidal shape.
• In \( \mathrm{XeF}_2 \), xenon has three lone pairs and two bond pairs, creating a linear shape with the lone pairs positioned to minimize repulsion.

When solving problems involving molecular shapes, it is vital to count these electron pairs correctly to predict the most accurate geometry using guidelines like the VSEPR theory.

VSEPR Theory

VSEPR stands for Valence Shell Electron Pair Repulsion theory. This theory is a model used to determine the geometry of molecules based on the idea that electron pairs surrounding a central atom will arrange themselves as far apart as possible to minimize repulsion.
The steps in using VSEPR theory are generally:1. Draw the Lewis structure of the molecule.2. Count the number of bonding and nonbonding electron pairs around the central atom.3. Predict the molecule's geometry by minimizing the repulsion between these pairs.
For example, in \( \mathrm{XeF}_2 \), xenon has two bond pairs and three lone pairs. The five regions of electron density form a trigonal bipyramidal electron geometry. The nonbonding pairs occupy the equatorial positions, which minimizes repulsion, leading to a linear arrangement of the bonded atoms.
Understanding VSEPR theory is vital for predicting and explaining molecular structures and is widely used in chemistry to visualize molecules.

Linear Molecules

Linear molecules are those in which atoms are arranged in a straight line. This is often seen when there are two bonding pairs and no lone pairs, or when lone pairs are positioned to balance out repulsions symmetrically around the central atom.
In linear geometry, the bond angles are generally \( 180^\circ \), making them highly symmetrical and their shape easy to predict when applying VSEPR theory. For a molecule to be linear like \( \mathrm{XeF}_2 \), it must have specific arrangements:

• Two atoms bonded to the central atom (as in diatomic molecules).
• Multiple bonds, like double or triple bonds, can also maintain linearity if they occur between three atoms.
• Electron pairs positioned to cancel out repulsions, often seen in cases with lone pairs on a central atom like in \( \mathrm{XeF}_2 \).

Linear molecules are straightforward in structure but crucial in understanding more complex molecular geometry scenarios.