Chemical Bonding: Molecular Shapes and VSEPR Theory

Chemical Bonding I: Molecular Shapes, VSEPR Theory

Introduction to VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a fundamental model used to predict the three-dimensional shapes of molecules. It is based on the idea that electron groups around a central atom will arrange themselves as far apart as possible to minimize repulsion.

• Electron groups include both bonding pairs (single, double, or triple bonds) and lone pairs of electrons.

• Repulsion between electron groups determines the geometry and bond angles in a molecule.

• The resulting arrangement allows chemists to predict molecular shapes and properties.

Electron Groups and Lewis Structures

Lewis structures help identify the number of electron groups around a central atom, which is essential for applying VSEPR theory.

• Lone pairs of electrons count as one electron group each.

• Bonds (single, double, or triple) also count as one electron group each.

• Example: In the nitrite ion ($NO_2^-$), nitrogen has three electron groups: one lone pair, one single bond, and one double bond.

Electron Group Geometry

Electron group geometry describes the spatial arrangement of all electron groups (bonding and lone pairs) around the central atom.

• Two electron groups: Linear geometry ($180^ ext{o}$ bond angle)

• Three electron groups: Trigonal planar geometry ($120^ ext{o}$ bond angle)

• Four electron groups: Tetrahedral geometry ($109.5^ ext{o}$ bond angle)

• Five electron groups: Trigonal bipyramidal geometry ($90^ ext{o}$, $120^ ext{o}$ bond angles)

• Six electron groups: Octahedral geometry ($90^ ext{o}$ bond angle)

Electron Geometry vs. Molecular Geometry

While electron geometry considers all electron groups, molecular geometry describes the arrangement of only the atoms (excluding lone pairs).

• CH4 (Methane): Electron geometry is tetrahedral; molecular geometry is also tetrahedral.

• NH3 (Ammonia): Electron geometry is tetrahedral; molecular geometry is trigonal pyramidal (due to one lone pair).

• H2O (Water): Electron geometry is tetrahedral; molecular geometry is bent (due to two lone pairs).

Bond Angle Distortion and Lone Pairs

Lone pairs occupy more space than bonding pairs, leading to deviations from ideal bond angles.

• Relative repulsion: Lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair.

• This causes bond angles to decrease as the number of lone pairs increases.

Molecule	Lone Pairs	Bond Angle
CH4	0	109.5°
NH3	1	107°
H2O	2	104.5°

Lone Pairs in Trigonal Bipyramidal and Octahedral Geometries

In molecules with five or six electron groups, lone pairs preferentially occupy positions that minimize repulsion.

• Trigonal bipyramidal: Lone pairs take equatorial positions, leading to molecular shapes such as see-saw, T-shaped, and linear.

• Octahedral: Lone pairs can lead to square pyramidal or square planar molecular geometries.

Example: BrF3 Geometries

For BrF3:

• Electron geometry: Trigonal bipyramidal

• Molecular geometry: T-shaped (due to two lone pairs)

Describing Multicenter Molecules

Complex molecules may have multiple central atoms, each with its own geometry.

• Example: In amino acids, the nitrogen may be trigonal pyramidal, the carbonyl carbon trigonal planar, and the oxygen bent.

Representing 3D Shapes on Paper

Chemists use conventions to depict three-dimensional molecular shapes:

• Straight line: Bond in the plane of the paper

• Hatched wedge: Bond going into the page

• Solid wedge: Bond coming out of the page

Polarity of Molecules

Molecular polarity depends on both the presence of polar bonds and the overall shape of the molecule.

• To be polar, a molecule must:

  • Have polar bonds (difference in electronegativity)

  • Have an unsymmetrical shape (so dipoles do not cancel)

• Polarity affects intermolecular forces, boiling points, and solubility ("like dissolves like").

Molecular Dipole Moment

The net dipole moment of a molecule is the vector sum of all individual bond dipoles.

• Example: CO2 is linear and nonpolar (dipoles cancel); H2O is bent and polar (dipoles add).

Quiz Example: Bond Angles

Order the following molecules by increasing X-Se-X bond angle:

Molecule	Bond Angle
SeCl6	Smallest
SeF2	Intermediate
SeO2	Largest

Correct order: SeCl6 < SeF2 < SeO2

Quiz Example: Nonpolar Molecules

Which of the following molecules is nonpolar?

• NH3

• XeF4 (correct answer: nonpolar, due to square planar geometry and cancellation of dipoles)

• H2O

• CH3Cl

• CH2Cl2

Key Equations

• Bond dipole moment: $\vec{\mu} = q \times r$

• Net molecular dipole: $\vec{\mu}_{\text{net}} = \sum \vec{\mu}_{\text{bond}}$

Summary Table: Electron Group and Molecular Geometries

Electron Groups	Electron Geometry	Molecular Geometry (no lone pairs)
2	Linear	Linear
3	Trigonal planar	Trigonal planar
4	Tetrahedral	Tetrahedral
5	Trigonal bipyramidal	Trigonal bipyramidal
6	Octahedral	Octahedral

Additional info: Lone pairs alter molecular geometry and bond angles, leading to shapes such as bent, trigonal pyramidal, see-saw, T-shaped, square pyramidal, and square planar.