Notes on Molecular Geometry and Bonding Theories

Chemistry: The Central Science

Chapter 9: Molecular Geometry and Bonding Theories

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9.1 Molecular Shapes

  • Lewis structures depict bonding and lone pairs in molecules but do not directly indicate their geometric shapes.

  • Despite not denoting shape, Lewis structures are instrumental in predicting and determining molecular shapes.

  • Common shapes for molecules consisting of two or three atoms connected to a central atom include:

    • Linear

    • Trigonal planar

    • Tetrahedral

9.2 The VSEPR Model

  • The shape of a molecule is determined by:

    • Bond angles

    • Bond lengths

  • Electron pairs repel each other and strive to maximize their distance from one another, leading to specific molecular shapes.

  • The model that reflects this behavior is called the valence-shell electron-pair repulsion (VSEPR) model.

Electron Domains

  • Electron domains refer to regions where electrons are most likely found:

    • Bonding electron domains: Include single, double, or triple bonds, counted as a single electron domain each.

    • Nonbonding electron domains: Nonbonding pairs of electrons associated with a single atom.

  • For example, in a molecule represented as AB$_3$, if A is the central atom, it may exhibit three electron domains.

Valence-Shell Electron-Pair Repulsion Model

  • The optimal arrangement of electron domains minimizes repulsions among them, leading to the lowest energy configuration.

  • An analogy involving balloons illustrates this concept: maximizing distance minimizes repulsions.

Electron-Domain Geometries

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  • Table 9.1 provides electron-domain geometries based on the number of electron domains around a central atom. Each arrangement corresponds to specific molecular shapes and bond angles.

  • To ascertain the electron-domain geometry, total the counts of bonding and nonbonding domains on the central atom, remembering that multiple bonds count as a single domain.

Electron-Domain Geometries
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Number of Electron Domains

Arrangement of Electron Domains

Electron Domain Geometry

Predicted Bond Angles

2

Linear arrangement

Linear

180 degrees

3

Trigonal arrangement

Trigonal planar

120 degrees

4

Tetrahedral arrangement

Tetrahedral

109.5 degrees

5

Trigonal bipyramidal arrangement

Trigonal bipyramidal

120 degrees (equatorial) and 90 degrees (axial)

6

Octahedral arrangement

Octahedral

90 degrees

Electron-Domain Geometries
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  • Coordination Number: Number of electron domains can also be referred to as the coordination number of the central atom in a molecule.

Applications of VSEPR for Molecular Shapes

  1. Construct the most accurate Lewis structure possible for the molecule.

  2. Determine the electron-domain geometry using electron domains.

  3. Infer the molecular geometry based on the arrangement of bonded atoms, referring to comprehensive tables for potential arrangements.

9.3 Molecular Shape and Polarity

  • Assess molecular polarity based on individual bond polarity using electronegativity values and how dipole moments align:

    • Polar molecules: Molecular dipoles do not cancel out, resulting in a net dipole.

    • Nonpolar molecules: Dipoles cancel out symmetrically, resulting in no overall dipole.

  1. Draw the Lewis structure.

  2. Count the number of electron pairs associated with the central atom to ascertain the electron-domain geometry.

  3. Distinguish between bonding and nonbonding electron domains to finalize the molecular geometry.

Polarity Comparison

  • Both polar and nonpolar molecules are compared based on molecular shapes and overall charge distribution, evidenced by molecular examples like BF$_3$ (nonpolar) and NH$_3$ (polar).

9.4 Covalent Bonding and Orbital Overlap

  • VSEPR alone does not characterize why bonds exist; this is better explained by valence-bond theory.

  • In this model, overlapping orbitals of two atoms allow electrons of opposing spins to occupy the overlapping space, leading to covalent bond formation.

9.5 Hybrid Orbitals

  • Hybrid orbitals form through the mixing of atomic orbitals in valence-bond theory, leading to equal-energy orbitals called degenerate orbitals.

  • The hybridization involves:

    • S and p orbitals mix to create new orbitals for bonding.

    • The shape differs from atomic orbitals, allowing for accurate representations of bonding configurations.

Examples of Hybridization

  • sp Hybridization (Beryllium): Mixing one s orbital and one p orbital creates linear bonds with bond angles of 180°.

  • sp$^2$ Hybridization (Boron): Results in three hybrid orbitals forming a trigonal planar geometry.

  • sp$^3$ Hybridization (Carbon): Produces four equivalent hybrid orbitals for tetrahedral geometry, such as in methane (CH$_4$).

Bonding in Molecules

  • In covalent bonding, single bonds function as sigma (σ) bonds characterized by head-on overlap, while multiple bonds consist of one σ bond and any additional bonds as pi (π) bonds characterized by sideways overlap.

  • In many molecules, electrons can be either localized (specific bonds between two atoms) or delocalized (shared by multiple atoms).

9.7 Molecular Orbitals

  • Molecular Orbital (MO) Theory: Addresses the limitations of VSEPR, asserting that bonding is not limited to discrete pairs of atoms but rather extends throughout the molecule's entirety. The key characteristics include:

    • Formation of bonding and antibonding orbitals based on atomic orbital overlap.

    • Each molecular orbital can accommodate a maximum of two electrons with opposite spins, following the Pauli exclusion principle.

MO Diagrams and Bonding

  • Bond Order: Calculated as the difference between the number of bonding and antibonding electrons divided by two. This helps determine the stability of bonds in diatomic molecules such as He$_2$.

Heteronuclear Diatomic Molecules

  • MO diagrams can reflect differing atomic energies in heteronuclear diatomic molecules, where the more electronegative atom will have orbitals of lower energy.

Practice Exercises

  • Exercises throughout the chapter test understanding of concepts like predicting molecular geometries and determining polarity based on molecular structure.

Important Notes

  • Consideration of lone pairs, bond angles, multiple bonds, and molecular geometry is crucial when applying VSEPR and bonding theories.

  • Understanding molecular orbitals can illuminate properties like magnetism in substances based on unpaired electron configurations.

Conclusion

This chapter synthesizes foundational knowledge about molecular geometry, bonding theories, and their implications in chemical systems, providing a comprehensive overview essential for advanced studies in chemistry.