Question

Use VSEPR theory to predict the probable geometric structures of (a) \(\mathrm{XeO}_{3} ;\) (b) \(\mathrm{XeO}_{4} ;\) (c) \(\mathrm{XeF}_{5}^{+}\).

Short answer

Using the VSEPR theory: (a) \(\mathrm{XeO}_{3}\) predicts a trigonal pyramidal structure. (b) \(\mathrm{XeO}_{4}\) predicts a tetrahedral structure. (c) \(\mathrm{XeF}_{5}^{+}\) predicts a square pyramidal structure.

Step-by-step solution

Determine the Total Number of Electrons

Count the total number of valence electrons around the central atom (Xe). For \(\mathrm{XeO}_{3}\), the count is 8 (from Xe) + 3(6) (from each O) = 26 electrons. For \(\mathrm{XeO}_{4}\), the count is 8 (from Xe) + 4(6) (from each O) = 32 electrons. For \(\mathrm{XeF}_{5}^{+}\), the count is 8 (from Xe) + 5(7) (from each F) = 43 electrons, but we subtract one electron due to the +1 charge for a total of 42 electrons.

Place Electrons and Determine the Steric Number

For \(\mathrm{XeO}_{3}\), placing the electrons, we have 1 bond with each O (6 electrons), and one lone pair on Xe (2 electrons). This gives us a steric number of 4. For \(\mathrm{XeO}_{4}\), we have one bond with each O (8 electrons), and no lone pairs giving us a steric number of 4. For \(\mathrm{XeF}_{5}^{+}\), we have one bond with each F (10 electrons), and one lone pair on Xe (2 electrons). This gives us a steric number of 6.

Predict the Shape

Using the steric number, we can predict the shape. For \(\mathrm{XeO}_{3}\) with a steric number of 4 and 1 lone pair, the shape is trigonal pyramidal. For \(\mathrm{XeO}_{4}\) with a steric number of 4 and no lone pairs, the shape is tetrahedral. For \(\mathrm{XeF}_{5}^{+}\) with a steric number of 6 and 1 lone pair, the shape is square pyramidal.

Key concepts

Molecular Geometry

Understanding molecular geometry is essential for predicting the shapes of molecules. According to VSEPR theory, molecular geometry is determined by the number of electron pairs surrounding the central atom. These can be bonding pairs (shared with another atom) or lone pairs (not shared). The arrangement of these electron pairs around the central atom will minimize repulsions, leading to specific geometric shapes.
This geometric arrangement helps in predicting the physical and chemical properties of the molecules, such as polarity, reactivity, and even biological activity in some cases. For example, the molecular geometry of water (H₂O) is bent due to its two lone pairs, leading to its well-known properties.

• Bonding pairs: Electrons involved in covalent bonds.
• Lone pairs: Non-bonding electrons residing on the central atom.

Each geometric shape correlates with different steric numbers and the presence or absence of lone pairs.

Valence Electrons

Valence electrons are the outermost electrons in an atom and play a crucial role in chemical bonding. They are the electrons that are involved in forming bonds with other atoms. To determine the molecular geometry using VSEPR theory, one must first identify the total number of valence electrons in the compound.
For instance, in \(XeO_3\), xenon (Xe) contributes 8 valence electrons, and each oxygen (O) contributes 6, totaling 26 valence electrons. Correct accounting of these electrons is vital for predicting the correct shape and reactivity of the molecule.

• The periodic table can help identify the number of valence electrons.
• Valence electrons are often visualized as dots in Lewis structures.

This calculation is the first step towards understanding molecular structures using VSEPR theory.

Steric Number

The steric number is a key concept in VSEPR theory used to predict the molecular shape. It is calculated by adding the number of atoms bonded to the central atom with the number of lone pair electrons on the central atom.
For example, for \(XeO_3\), xenon is bonded to three oxygens and has one lone pair. Therefore, the steric number is 4. Each steric number corresponds to a geometric shape, indicating the spatial arrangement of the bonds and lone pairs.

• Steric number 2: linear geometry.
• Steric number 3: trigonal planar geometry.
• Steric number 4: tetrahedral or trigonal pyramidal geometry (depending on lone pairs).
• Steric number 5: trigonal bipyramidal geometry.

Analyzing the steric number is crucial for predicting and understanding complex molecular shapes.

Trigonal Pyramidal

The trigonal pyramidal molecular geometry arises when a central atom is surrounded by three bonded atoms and one lone pair, giving a steric number of 4. This structure is a common example of how lone pairs can affect molecular geometry.
In a trigonal pyramidal shape, the lone pair on the central atom pushes the bonds down, creating a somewhat 3D pyramid structure. \(NH_3\) (ammonia) is a classic example, with nitrogen at the center bonded to three hydrogen atoms and one lone pair influencing its pyramidal shape.

• Lone pair repels bonding pairs more than bonding pairs repel each other.
• Results in angles slightly less than \120^\circ\ due to this repulsion.

This geometry is fundamental in understanding interactions and reaction mechanisms in chemistry.

Tetrahedral

A tetrahedral molecular geometry features a central atom surrounded by four atoms, with all bonding pairs and no lone pairs, resulting in a symmetrical arrangement. This shape occurs often in organic molecules and is critical in determining molecular function.
The ideal bond angles in a perfect tetrahedron are \109.5^\circ\, which provide maximal separation between electron pairs. This shape contributes to the stability and properties of the molecule. An example is methane \(CH_4\) where carbon is centrally positioned among four hydrogens.

• Provides a balanced shape for maximizing space between electron pairs.
• Common in simple molecular structures, especially hydrocarbons.

The \CH_4// molecule is the perfect illustration of how this geometry is deduced and why it matters in chemistry.