chapter 8 part 1

Advanced Theories of Covalent Bonding

Valence Bond Theory

Valence Bond (VB) Theory is a quantum mechanical model that explains how atoms form covalent bonds by the overlap of atomic orbitals. It provides insight into the nature of chemical bonds and the geometry of molecules, complementing the predictions made by Lewis structures and VSEPR theory.

• Molecular Geometry: The three-dimensional arrangement of atoms in a molecule, determined experimentally by measuring bond lengths and angles.

• VSEPR Theory: Predicts the geometry of molecules based on the repulsion between electron pairs in the valence shell, but does not explain the nature of bonding.

• Bond Differences: Bonds in different molecules (e.g., H2 vs. F2 vs. HF) have different bond enthalpies and lengths, indicating differences in bond strength and character.

• VB vs. MO Theory:

  • Valence Bond Theory (VB): Electrons occupy atomic orbitals of individual atoms; bonds form by overlap of these orbitals.

  • Molecular Orbital Theory (MO): Atomic orbitals combine to form molecular orbitals that are delocalized over the entire molecule.

• Bond Formation: When two half-filled atomic orbitals overlap, their electrons pair with opposite spins, resulting in energy stabilization and bond formation.

• Geometry from Overlap: The geometry of a molecule is determined by the spatial orientation of the overlapping orbitals.

Key Features of Valence Bond Theory:

• Bonds form when singly occupied atomic orbitals on two atoms overlap.

• The two electrons in a bond must have opposite spins.

• Bond formation lowers the potential energy of the system.

Example: In F2, the bond forms by overlap of two 2p orbitals, each containing one electron. In HF, the bond forms by overlap of the 1s orbital of H and the 2p orbital of F.

Hybrid Atomic Orbitals

Hybridization is the concept of mixing atomic orbitals to form new, equivalent hybrid orbitals that explain the observed shapes and bond angles in molecules, especially polyatomic ones.

• Need for Hybridization: Simple atomic orbitals cannot always explain the observed molecular geometries (e.g., BeCl2, CO2).

• Hybridization Types:

  • sp Hybridization: Linear geometry, 180° bond angle (e.g., BeH2).

  • sp2 Hybridization: Trigonal planar geometry, 120° bond angle (e.g., BF3).

  • sp3 Hybridization: Tetrahedral geometry, 109.5° bond angle (e.g., CH4).

• Hybridization and Lone Pairs: Lone pairs occupy hybrid orbitals and affect bond angles (e.g., NH3 has a bond angle of ~107° due to one lone pair; H2O has a bond angle of ~105° due to two lone pairs).

• Procedure for Determining Hybridization:

  1. Draw the Lewis structure of the molecule or ion.

  2. Predict the arrangement of electron pairs using VSEPR theory.

  3. Match the number of electron domains to the type of hybridization:

     Number of Electron Pairs	Hybridization	Geometry
     2	sp	Linear
     3	sp2	Trigonal planar
     4	sp3	Tetrahedral
     5	sp3d	Trigonal bipyramidal
     6	sp3d2	Octahedral

• Hybridization with d Orbitals: For elements in the third period and beyond, d orbitals can participate in hybridization (e.g., SF6 uses sp3d2 hybridization for an octahedral geometry).

Examples:

• SF6: S uses sp3d2 hybridization to form six equivalent bonds in an octahedral arrangement.

• PBr5: P uses sp3d hybridization to form five bonds in a trigonal bipyramidal geometry.

Multiple Bonds: Sigma and Pi Bonds

Multiple bonds (double and triple bonds) involve both sigma (σ) and pi (π) bonds, which arise from different types of orbital overlap.

• Sigma (σ) Bonds: Formed by end-to-end (axial) overlap of orbitals; all single bonds are sigma bonds.

• Pi (π) Bonds: Formed by sideways (lateral) overlap of unhybridized p orbitals; present in double and triple bonds.

• Bond Energies: Sigma bonds are generally stronger than pi bonds (e.g., in C2H4, σ bond enthalpy ≈ 350 kJ/mol, π bond enthalpy ≈ 270 kJ/mol).

• Double Bond: Consists of one sigma and one pi bond.

• Triple Bond: Consists of one sigma and two pi bonds.

Examples:

• Ethylene (C2H4): Each C atom is sp2 hybridized (trigonal planar). The unhybridized p orbitals on each C overlap to form a pi bond, resulting in a double bond between the C atoms.

• Acetylene (C2H2): Each C atom is sp hybridized (linear). Two unhybridized p orbitals on each C form two pi bonds, resulting in a triple bond between the C atoms.

• Formaldehyde (CH2O): The C atom is sp2 hybridized, forming two sigma bonds with H atoms and one sigma bond with O. The remaining p orbital on C and O overlap to form a pi bond (double bond between C and O).

• Isomerism: In compounds like 1,2-dichloroethane (C2H4Cl2), free rotation is possible about single bonds. In 1,2-dichloroethylene (C2H2Cl2), no rotation is possible about the double bond, leading to cis-trans isomerism.

Summary Table: Hybridization, Geometry, and Bonding

Hybridization	Number of Electron Domains	Geometry	Bond Angle	Example
sp	2	Linear	180°	BeCl2, C2H2
sp2	3	Trigonal planar	120°	BF3, C2H4
sp3	4	Tetrahedral	109.5°	CH4, NH3, H2O
sp3d	5	Trigonal bipyramidal	90°, 120°	PBr5
sp3d2	6	Octahedral	90°	SF6

Key Equations and Concepts

• Bond Order: Number of chemical bonds between a pair of atoms.

  • Single bond: bond order = 1

  • Double bond: bond order = 2

  • Triple bond: bond order = 3

• Hybridization Notation: sp, sp2, sp3, sp3d, sp3d2

• Bond Energy: Energy required to break a bond; varies with bond type and atoms involved.

• Sigma and Pi Bonds:

  • Single bond: 1 σ

  • Double bond: 1 σ + 1 π

  • Triple bond: 1 σ + 2 π

Procedure for Determining Bonding and Hybridization

1. Draw the Lewis structure using VSEPR theory.

2. Determine the required geometry (linear, trigonal planar, tetrahedral, etc.).

3. Assign the correct hybridization to the central atom to match the number of electron domains.

4. Identify leftover p electrons for possible pi bond formation.

Additional info: The notes above expand on the original lecture content by providing definitions, stepwise procedures, and summary tables for clarity and completeness. The explanations of hybridization and multiple bonding are supplemented with examples and a summary table for quick reference.