Problem 12 - Chemistry and Chemical Reactivity

Question

Draw the Lewis structure, and then specify the electron-pair and molecular geometries for each of the following molecules or ions. Identify the hybridization of the central atom. (a) \(\mathrm{XeOF}_{4}\) (c) central \(\mathrm{S}\) in \(\mathrm{SOF}_{4}\) (b) \(\mathrm{BrF}_{5}\) (d) central Br in \(\mathrm{Br}_{3}^{-}\)

Step-by-Step Solution

Answer

(a) Square pyramidal, \(sp^3d^2\); (b) Square pyramidal, \(sp^3d^2\); (c) Trigonal bipyramidal, \(sp^3d\); (d) Linear, \(sp^3d\).

Step 1: Count Valence Electrons for XeOF4

The valence electrons are counted as follows: Xe (8 electrons), O (6 electrons), and each F (7 electrons) for a total of 4 F atoms. Thus, the total is \(8 + 6 + 4(7) = 42\) valence electrons.

Step 2: Draw Lewis Structure for XeOF4

Place Xe in the center bonded to O and four F atoms, with Xe having an expanded octet to accommodate all peripheral atoms. O has one double bond with Xe. Distribute electrons to satisfy the octet rule.

Step 3: Determine Electron-Pair Geometry of XeOF4

With 6 regions of electron density around Xe (4 single bonds with F, 1 double bond with O, and 1 lone pair), the electron-pair geometry is octahedral.

Step 4: Determine Molecular Geometry of XeOF4

Considering the lone pair, the geometry of XeOF4 is square pyramidal.

Step 5: Identify Hybridization of Xe in XeOF4

The central Xe with 6 regions of electron density undergoes \(sp^3d^2\) hybridization.

Step 6: Count Valence Electrons for Central S in SOF4

Sulfur has 6 valence electrons, O adds 6, and each F contributes 7 electrons with 4 F atoms. Total: \(6 + 6 + 4(7) = 40\) valence electrons.

Step 7: Draw Lewis Structure for SOF4

S is centered with a double bond to O and single bonds to four F atoms. Distribute electrons to fulfill the octet rule across all atoms.

Step 8: Determine Electron-Pair Geometry of Central S in SOF4

With 5 regions of electron density (1 double bond with O and 4 single bonds with F), the geometry is trigonal bipyramidal.

Step 9: Determine Molecular Geometry of Central S in SOF4

The actual shape without lone pairs matches the electron pair geometry, so the molecular geometry is also trigonal bipyramidal.

Step 10: Identify Hybridization of Central S in SOF4

The S atom with 5 areas of electron density uses \(sp^3d\) hybridization.

Step 11: Count Valence Electrons for BrF5

Br has 7 valence electrons. Each F atom also has 7, contributing 5 F atoms. Total: \(7 + 5(7) = 42\) valence electrons.

Step 12: Draw Lewis Structure for BrF5

Br is central with single bonds to each F atom, possessing one lone pair. Distribute electrons to ensure all atoms fulfill their octet requirements.

Step 13: Determine Electron-Pair Geometry of BrF5

With 6 regions of electron density around Br (5 single bonds to F and 1 lone pair), the geometry is octahedral.

Step 14: Determine Molecular Geometry of BrF5

Considering one lone pair, BrF5 has a square pyramidal molecular geometry.

Step 15: Identify Hybridization of Br in BrF5

The central Br atom has \(sp^3d^2\) hybridization to accommodate 6 electron pairs.

Step 16: Count Valence Electrons for Central Br in \(Br_3^-\)

Each Br atom has 7 valence electrons, with 3 of them plus an extra electron for the negative charge, totaling \(3(7) + 1 = 22\) valence electrons.

Step 17: Draw Lewis Structure for \(Br_3^-\)

A linear structure is drawn with Br as central, each outer Br atom having a single bond with 3 lone pairs. The added electron (negative charge) is considered as a lone electron pair on the central Br.

Step 18: Determine Electron-Pair Geometry of Central Br in \(Br_3^-\)

With 5 regions of electron density (2 single bonds and 3 lone pairs), the geometry is trigonal bipyramidal.

Step 19: Determine Molecular Geometry of Central Br in \(Br_3^-\)

With three lone pairs in equatorial positions, the molecular geometry of the ion is linear.

Step 20: Identify Hybridization of Central Br in \(Br_3^-\)

The Br atom with 5 electron pairs adopts \(sp^3d\) hybridization.

Key Concepts

Understanding Electron-Pair Geometry

Electron-pair geometry is a concept that helps us understand the three-dimensional distribution of electrons around a central atom in a molecule. To determine this, one must count the number of regions of electron density, which include bonding and lone pairs around the central atom. For example, in the case of \(\mathrm{XeOF}_{4}\), with six regions of electron density due to four single bonds with fluorine, one double bond with oxygen, and one lone pair, the electron-pair geometry is octahedral. This term describes the general spatial arrangement that accounts for all regions of electrons, not just those involved in bonding.

• Importance: Electron-pair geometry provides a basis for predicting molecular shapes by considering all electron pairs equally.
• Common Geometries: Linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral.

Understanding electron-pair geometry is foundational for grasping molecular shapes and is a key step in applying VSEPR (Valence Shell Electron Pair Repulsion) theory.

Deciphering Molecular Geometry

Molecular geometry, distinct from electron-pair geometry, focuses on the shape of the molecule as defined by the positions of nuclei in relation to one another, excluding lone pairs. This concept is crucial because it dictates the actual physical shape of the molecule which impacts properties such as reactivity and polarity. In our previous discussion of \(\mathrm{XeOF}_{4}\), although its electron-pair geometry is octahedral, the presence of a lone pair alters the molecular geometry to square pyramidal. The absence of lone pairs would often allow the electron-pair and molecular geometries to match, like the trigonal bipyramidal arrangement found in \(\mathrm{SOF}_{4}\).

• Molecular Geometry Types: Linear, bent, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral are common types.
• Function: Molecular geometry affects how a molecule interacts with others, influencing its function and behavior in reactions.

Recognizing how lone pairs modify geometry helps in predicting molecular properties and understanding their behavior.

Exploring Hybridization

Hybridization is a concept used to describe the mixing of atomic orbitals in an atom to form new hybrid orbitals. These are used when atoms form chemical bonds. Understanding hybridization involves recognizing how these hybrids arrange themselves to allow a molecule to achieve its geometry. For instance, the central xenon atom in \(\mathrm{XeOF}_{4}\) undergoes \(sp^3d^2\) hybridization, allowing the electron pairs to adopt an octahedral arrangement. Each type of hybridization corresponds to a specific shape:

• Types: Common types include \(sp\), \(sp^2\), \(sp^3\), \(sp^3d\), and \(sp^3d^2\), each representing different arrangements.
• Correlations: The hybridization type can often indicate the electron-pair geometry, such as \(sp^3\) for tetrahedral or \(sp^3d^2\) for octahedral structures.

Grasping hybridization is crucial for visualizing how molecular geometry shapes up during the formation of compounds and explains the covalent bonding nature.

Counting Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom and are crucial in defining how that atom bonds with others. Counting valence electrons accurately is the first step in drawing Lewis structures, as these diagrams depict the arrangement of valence electrons around atoms within molecules. Let's consider \(\mathrm{XeOF}_{4}\) again:

• Xenon: 8 electrons
• Oxygen: 6 electrons
• Fluorine: 7 per atom, with four atoms, totaling 28

Giving a total of 42 valence electrons. This counting process helps in determining how electrons are distributed, thereby aiding the accurate depiction of a molecule's ideal Lewis structure. Understanding which electrons participate in bonding and which ones remain as lone pairs is key in predicting a molecule's geometry.