Chapter 11: Molecular Geometries and Bonding Theories – Study Notes

Molecular Geometries and Bonding Theories

Molecular Shapes

Molecular shape refers to the three-dimensional arrangement of atoms in a molecule. While Lewis structures show the connectivity of atoms, they do not indicate the spatial orientation. The geometry of a molecule is determined by the arrangement of electron pairs around the central atom, which influences bond angles and molecular polarity.

• Lewis Structures: Show how atoms are connected but not their spatial arrangement.

• Bond Angles: The angle between two bonds originating from the same atom.

• VSEPR Theory: Predicts molecular geometry based on electron pair repulsion.

Examples of Molecular Shapes:

• CO2: AB2, linear

• SO2: AB2, bent

• SO3: AB3, trigonal planar

• NF3: AB3, trigonal pyramidal

• ClF3: AB3, T-shaped

Valence Shell Electron Pair Repulsion (VSEPR) Theory

The VSEPR theory is used to predict the geometry of molecules based on the repulsion between electron pairs in the valence shell of the central atom. Electron pairs (bonding and lone pairs) arrange themselves to minimize repulsion, resulting in specific geometries.

• Each electron pair repels all others, leading to maximum separation.

• Electron Domain Geometry: Determined by the total number of electron domains (bonding and lone pairs) around the central atom.

• Molecular Geometry: Determined by the arrangement of only the bonding pairs (ignoring lone pairs).

Electron-Domain Geometries

Electron-domain geometry depends on the number of electron domains around the central atom. The main types are:

Number of Electron Domains	Arrangement	Electron Domain Geometry	Predicted Bond Angles
2	Linear	Linear	180°
3	Trigonal planar	Trigonal planar	120°
4	Tetrahedral	Tetrahedral	109.5°
5	Trigonal bipyramidal	Trigonal bipyramidal	120°, 90°
6	Octahedral	Octahedral	90°

Electron Pair and Molecular Geometries

The molecular geometry is derived from the electron-domain geometry by considering only the positions of the atoms (bonding pairs), not the lone pairs.

Electron Domains	Bonding Domains	Lone Pairs	Molecular Geometry	Example
2	2	0	Linear	CO2
3	3	0	Trigonal planar	BF3
3	2	1	Bent	SO2
4	4	0	Tetrahedral	CH4
4	3	1	Trigonal pyramidal	NH3
4	2	2	Bent	H2O
5	5	0	Trigonal bipyramidal	PCl5
5	4	1	Seesaw	SF4
5	3	2	T-shaped	ClF3
5	2	3	Linear	I3-
6	6	0	Octahedral	SF6
6	5	1	Square pyramidal	BrF5
6	4	2	Square planar	XeF4

Polarity of Molecules

The polarity of a molecule depends on both its geometry and the polarity of its individual bonds. Molecular dipoles are vector sums of bond dipoles, and the overall molecular polarity is determined by adding these vectors in three dimensions.

• Bond Dipole: A measure of the separation of positive and negative charges in a bond.

• Molecular Dipole: The vector sum of all bond dipoles in a molecule.

• Nonpolar molecules: Symmetrical geometry cancels out bond dipoles (e.g., CO2, CCl4).

• Polar molecules: Asymmetrical geometry results in a net dipole (e.g., H2O, NH3).

Example: CH2Cl2 is polar because the bond dipoles do not cancel out due to its tetrahedral geometry.

Covalent Bonding and Orbital Overlap

Covalent bonds are formed when atomic orbitals from different atoms overlap in space, allowing electrons to be shared between atoms. The strength of the bond depends on the extent of orbital overlap and the charges on the nuclei.

• Orbital Overlap: The region where atomic orbitals from two atoms intersect, leading to electron sharing.

• Sigma (σ) Bond: Formed by end-to-end overlap of orbitals (e.g., s-s, s-p, or p-p).

• Pi (π) Bond: Formed by sideways overlap of p orbitals.

Example: In H2, the 1s orbitals of two hydrogen atoms overlap to form a σ bond.

Hybridization of Molecular Orbitals

Hybridization is the mixing of atomic orbitals to form new, equivalent hybrid orbitals that are used in bonding. This concept explains the observed molecular geometries and the equivalence of bonds in molecules like CH4.

• sp Hybridization: Mixing one s and one p orbital forms two sp hybrid orbitals (linear geometry, 180° bond angle).

• sp2 Hybridization: Mixing one s and two p orbitals forms three sp2 hybrid orbitals (trigonal planar geometry, 120° bond angle).

• sp3 Hybridization: Mixing one s and three p orbitals forms four sp3 hybrid orbitals (tetrahedral geometry, 109.5° bond angle).

Atomic Orbitals Set	Hybrid Set	Geometry	Examples
sp	Two sp	Linear (180°)	BeCl2, HgCl2
sp2	Three sp2	Trigonal planar (120°)	BF3, SO3
sp3	Four sp3	Tetrahedral (109.5°)	CH4, NH3, H2O

Hybrid Orbitals in Multiple Bonds

Multiple bonds involve both σ and π bonds. The σ bond is formed by the overlap of hybrid orbitals, while π bonds are formed by the sideways overlap of unhybridized p orbitals.

• Ethene (C2H4): Each carbon is sp2 hybridized; the double bond consists of one σ and one π bond.

• Acetylene (C2H2): Each carbon is sp hybridized; the triple bond consists of one σ and two π bonds.

• Benzene (C6H6): Delocalized π bonds due to resonance, with each carbon sp2 hybridized.

Molecular Orbital Theory and Energy Level Diagrams

Molecular Orbital (MO) Theory describes the formation of molecular orbitals from the combination of atomic orbitals. These orbitals can be bonding, antibonding, or non-bonding, and their arrangement can be shown in energy level diagrams.

• Bonding MO: Lower in energy, electron density between nuclei.

• Antibonding MO: Higher in energy, electron density outside the region between nuclei (denoted with an asterisk, e.g., σ1s*).

• Bond Order (BO): Indicates the strength and stability of a bond.

Bond Order Formula:

$\text{Bond Order (BO)} = \frac{(\text{number of electrons in bonding MOs}) - (\text{number of electrons in antibonding MOs})}{2}$

Example: For H2, BO = (2 - 0)/2 = 1 (single bond). For He2, BO = (2 - 2)/2 = 0 (no bond).

Molecule	Bond Order	Bond Energy (kJ/mol)	Bond Length (Å)	Magnetic Behavior
B2	1	290	1.59	Paramagnetic
C2	2	602	1.24	Diamagnetic
N2	3	945	1.10	Diamagnetic
O2	2	498	1.21	Paramagnetic
F2	1	159	1.42	Diamagnetic
Ne2	0	0	--	--

Additional info: Paramagnetic molecules have unpaired electrons and are attracted to magnetic fields; diamagnetic molecules have all electrons paired and are weakly repelled by magnetic fields.

Summary Table: Electron Domain and Molecular Geometries

Electron Domains	Bonding Domains	Lone Pairs	Electron Geometry	Molecular Geometry	Example
2	2	0	Linear	Linear	CO2
3	3	0	Trigonal planar	Trigonal planar	BF3
3	2	1	Trigonal planar	Bent	SO2
4	4	0	Tetrahedral	Tetrahedral	CH4
4	3	1	Tetrahedral	Trigonal pyramidal	NH3
4	2	2	Tetrahedral	Bent	H2O
5	5	0	Trigonal bipyramidal	Trigonal bipyramidal	PCl5
5	4	1	Trigonal bipyramidal	Seesaw	SF4
5	3	2	Trigonal bipyramidal	T-shaped	ClF3
5	2	3	Trigonal bipyramidal	Linear	I3-
6	6	0	Octahedral	Octahedral	SF6
6	5	1	Octahedral	Square pyramidal	BrF5
6	4	2	Octahedral	Square planar	XeF4