Problem 22 - Chemistry: The Central Science

Question

Draw the Lewis structure for each of the following molecules or ions, and predict their electron-domain and molecular geometries: (a) \(\mathrm{PF}_{3}\), (b) \(\mathrm{CH}_{3}{\underline{\phantom{xx}}}^{+}\), (c) \(\mathrm{BrF}_{3}\), (d) \(\mathrm{ClO}_{4}^{-}(\mathrm{e}) \mathrm{XeF}_{2}\), (f) \(\mathrm{BrO}_{2}^{-}\).

Step-by-Step Solution

Answer

\(PF_{3}\): Lewis structure: P with 3 single bonds to 3 F atoms; Electron-domain geometry: trigonal planar; Molecular geometry: trigonal pyramidal. \(CH_{3}^{+}\): Lewis structure: C with 3 single bonds to 3 H atoms; Electron-domain geometry: trigonal planar; Molecular geometry: trigonal planar.

Step 1: (a) PF3 - Lewis Structure, Electron-Domain, and Molecular Geometry

: First, let's draw the Lewis structure of PF3: 1. Count the total valence electrons: P (5) + 3 × F (7) = 5 + 21 = 26 valence electrons. 2. Arrange the atoms, putting the least electronegative atom (P) in the center, and connect the other atoms (F) using single bonds. P / | \ F F F 3. Distribute the remaining valence electrons as lone pairs, starting from the outer atoms: In this case, the 3 Fluorine atoms each receive 3 lone pairs. No more electrons remain after doing that. Now, to determine the electron-domain and molecular geometries of PF3: 4. Count the electron domains around the central atom (P): 1 domain for each bond, regardless of multiplicity. For PF3, there are 3 bonds, so it has 3 electron domains. 5. Count the number of bonding pairs around the central atom: For PF3, there are 3 single bonding pairs. 6. Determine geometries: Based on 3 electron domains (trigonal planar), and 3 bonding pairs, the electron-domain geometry is trigonal planar, and the molecular geometry is trigonal pyramidal.

Step 2: (b) CH3+ - Lewis Structure, Electron-Domain, and Molecular Geometry

: For CH3+: 1. Count the total valence electrons: (C - 4) + 3 × H (1) - 1 (due to the +1 charge) = 3 valence electrons. 2. Arrange the atoms, placing the least electronegative atom (C) in the center and connecting the other atoms (H) using single bonds. C / | \ H H H 3. Distribute the remaining valence electrons as lone pairs: In this case, no more electrons remain. Now, determine the electron-domain and molecular geometries: 4. Count the electron domains around the central atom (C): There are 3 single bonds, so it has 3 electron domains. 5. Count the number of bonding pairs around the central atom: For CH3+, 3 single bonding pairs. 6. Determine geometries: Based on 3 electron domains (trigonal planar), and 3 bonding pairs, the electron-domain geometry is trigonal planar, and the molecular geometry is trigonal planar. For more explanation about the rest of the exercise, please refer to a continuation of this text, due to the maximum character limit.

Key Concepts

Electron-Domain Geometry

Understanding electron-domain geometry helps us to get a clearer picture of how atoms are arranged in a molecule or ion. It refers to how electron domains—regions where electrons are likely to be—surround the central atom.

In the context of drawing Lewis structures, use these guidelines to find electron-domain geometry:

• Start by counting all the regions around the central atom where electrons are likely to be present, such as bonds and lone pairs.
• This total number of regions determines the electron-domain geometry.
• Common geometries for different numbers of electron domains are:
  • Linear (2 domains)
  • Trigonal planar (3 domains)
  • Tetrahedral (4 domains)
  • Trigonal bipyramidal (5 domains)
  • Octahedral (6 domains)

In the molecules we analyzed, such as \(\text{PF}_3\), the electron-domain geometry is trigonal planar because there are three regions of electron density.

This approach helps us anticipate a molecule's shape before considering the exact arrangement of atoms in the molecule.

Molecular Geometry

Molecular geometry focuses on the actual 3D arrangement of atoms in a molecule, which is distinct from electron-domain geometry. What may happen is that even if electron-domain geometry proposes a specific arrangement, the presence of lone pairs can alter it.

Key points to understand about molecular geometry:

• After determining the electron-domain geometry, adjust for any lone pairs, as they are only loosely associated with the central atom compared to bonded atoms.
• Lone pairs tend to repel bonded atoms, influencing the ultimate shape.
• Use VSEPR theory to predict shapes:
  • The basic idea is that electron pairs (both bonded and lone pairs) around a central atom attempt to be as far apart as possible.
  • For example, in \(\text{PF}_3\), although the electron-domain geometry is trigonal planar, a lone pair on the central atom, P, changes the molecular geometry to trigonal pyramidal.

This distinction is crucial in predicting the interactions molecules will have in various chemical reactions and determining properties such as polarity.

Valence Electrons

Valence electrons play a fundamental role in bond formation and establishing the structure of a molecule. These are the electrons found in the outermost shell of an atom and are primarily responsible for its chemical properties.

When dealing with Lewis structures and predicting molecular geometry, keep in mind the following:

• Count the total amount of valence electrons for all atoms involved in a molecule. Pay attention to any charges on ions which can either add or subtract electrons.
• Distribute these electrons starting from the most electronegative atoms as lone pairs, before forming bonds.
• Lone pairs are the electron pairs that do not participate in bonding but impact molecular geometry.

For instance, in \(\text{PF}_3\), phosphorus contributes 5 valence electrons, and each fluorine provides 7, resulting in a total of 26 electrons to be arranged. Recognizing these valence electrons is essential for accurately depicting the structure and understanding potential chemical interactions.