Molecular Geometry Shapes

Why This Matters

Molecular geometry is the foundation for understanding polarity, intermolecular forces, and reactivity throughout AP Chemistry. When you're asked why water has a high boiling point or why $\text{CO}_2$ is nonpolar despite having polar bonds, you're really being tested on how electron pair repulsion, lone pair effects, and three-dimensional arrangement determine molecular behavior. These concepts connect directly to Unit 2's focus on compound structure and Unit 3's emphasis on how molecular shape influences physical properties like solubility and boiling point.

The key principle is VSEPR theory (Valence Shell Electron Pair Repulsion): electron pairs around a central atom arrange themselves to minimize repulsion, and lone pairs repel more strongly than bonding pairs. This creates predictable distortions from ideal geometries. Don't just memorize that water is bent at 104.5°. Understand why lone pairs compress bond angles and how that bent shape creates a dipole moment that explains water's remarkable properties.

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Geometries with No Lone Pairs: Ideal Shapes

When a central atom has only bonding pairs, electron groups spread out symmetrically to maximize distance from each other. These "ideal" geometries have predictable bond angles because there's no lone pair repulsion to distort them.

Linear

• Two electron groups at 180°, arranged in a straight line
• Nonpolar when substituents are identical (e.g., $\text{CO}_2$), because bond dipoles cancel perfectly in opposite directions
• Multiple bonds (double or triple) count as a single electron group, so $\text{CO}_2$ has two electron groups even though it has four total bonds

Trigonal Planar

• Three electron groups at 120°, all lying in the same plane
• Nonpolar when all three substituents are identical (e.g., $\text{BF}_3$), since the three bond dipoles cancel symmetrically
• Also appears in polyatomic ions like carbonate ($\text{CO}_3^{2-}$)

Tetrahedral

• Four electron groups at 109.5°, the most common geometry in organic chemistry
• The three-dimensional arrangement maximizes separation of electron pairs in all directions (e.g., $\text{CH}_4$)
• This is the geometry of carbon in most biological molecules, and it's the foundation for understanding chirality

Trigonal Bipyramidal

• Five electron groups with two distinct positions: axial (90° from equatorial) and equatorial (120° apart from each other)
• Axial positions experience more 90° repulsion than equatorial positions. This matters when predicting where lone pairs go in derived geometries.
• Example: $\text{PCl}_5$. Period 3+ elements can accommodate more than four electron groups around the central atom, which is why you don't see expanded geometries with second-period central atoms like C, N, or O.

Octahedral

• Six electron groups at 90°, all positions equivalent in the ideal geometry
• Highly symmetrical, so molecules with identical substituents are nonpolar (e.g., $\text{SF}_6$)
• Like trigonal bipyramidal, this requires a central atom from Period 3 or below

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Geometries Derived from Tetrahedral: One to Two Lone Pairs

When lone pairs replace bonding pairs in a tetrahedral electron geometry, the molecular shape changes and bond angles compress. Lone pairs occupy more angular space than bonding pairs because they're held closer to the nucleus and spread out more, pushing bonded atoms closer together.

Trigonal Pyramidal

• Three bonding pairs + one lone pair gives a pyramidal shape with bond angles of about 107° (e.g., $\text{NH}_3$)
• The lone pair compresses the ideal 109.5° tetrahedral angle by roughly 2.5°
• Even with three identical substituents, the asymmetry from the lone pair makes this geometry polar

Bent (from Tetrahedral)

• Two bonding pairs + two lone pairs creates a bent shape with bond angles of about 104.5° (e.g., $\text{H}_2\text{O}$)
• Two lone pairs cause greater compression than one, which is why water's angle is smaller than ammonia's
• This shape is responsible for water's polarity and its ability to form hydrogen bonds

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Geometries Derived from Trigonal Bipyramidal: Lone Pairs in Equatorial Positions

When lone pairs appear in a trigonal bipyramidal electron geometry, they always occupy equatorial positions first. An equatorial lone pair has only two 90° interactions (with the axial groups), while an axial lone pair would have three 90° interactions (with all three equatorial groups). Lone pairs minimize repulsion by going where they have fewer close neighbors.

Seesaw

• Four bonding pairs + one lone pair, with the lone pair in an equatorial position (e.g., $\text{SF}_4$)
• The axial-equatorial bond angles compress slightly below 90°, and the equatorial-equatorial angles compress slightly below 120°, both due to lone pair repulsion
• The asymmetrical shape makes this a polar molecule

T-Shaped

• Three bonding pairs + two lone pairs, with both lone pairs occupying equatorial positions (e.g., $\text{ClF}_3$)
• Bond angles of approximately 87.5° (between the axial and equatorial bonding pairs), compressed from 90° by the two equatorial lone pairs
• A good example for demonstrating the equatorial preference rule on an exam

Linear (from Trigonal Bipyramidal)

• Two bonding pairs + three lone pairs, with all three lone pairs filling the equatorial positions (e.g., $\text{XeF}_2$)
• The two bonded atoms sit in axial positions, giving a 180° bond angle
• This is a great example of how electron geometry (trigonal bipyramidal) can differ from molecular geometry (linear)

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Geometries Derived from Octahedral: Symmetric Lone Pair Placement

In octahedral electron geometry, all six positions start out equivalent. When lone pairs are added, they position themselves to maximize distance from each other, going 180° apart when possible.

Square Pyramidal

• Five bonding pairs + one lone pair creates a square base with one atom above it (e.g., $\text{BrF}_5$)
• Bond angles of approximately 85° (between the axial atom and the equatorial atoms), compressed from 90° by the single lone pair
• The asymmetry makes the molecule polar

Square Planar

• Four bonding pairs + two lone pairs, with the lone pairs positioned 180° apart from each other (e.g., $\text{XeF}_4$)
• Bond angles of exactly 90° between adjacent atoms in the square plane
• The lone pairs sit above and below the plane (trans to each other) to minimize their mutual repulsion
• Despite having lone pairs, the symmetric arrangement of both bonds and lone pairs makes $\text{XeF}_4$ nonpolar

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Quick Reference Table

*Nonpolar only when all substituents are identical.

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Self-Check Questions

1. Both $\text{CO}_2$ and $\text{H}_2\text{O}$ have three atoms, yet one is linear and one is bent. Explain how lone pairs account for this difference and predict which molecule is polar.

2. Compare the bond angles in $\text{CH}_4$, $\text{NH}_3$, and $\text{H}_2\text{O}$. What trend do you observe, and what principle explains it?

3. Why do lone pairs in a trigonal bipyramidal electron geometry preferentially occupy equatorial rather than axial positions? Use $\text{SF}_4$ as your example.

4. Both $\text{XeF}_4$ (square planar) and $\text{CH}_4$ (tetrahedral) have four atoms bonded to a central atom. Explain why their geometries and bond angles differ.

5. An FRQ asks you to explain why $\text{BF}_3$ is nonpolar but $\text{NF}_3$ is polar, even though both have three fluorines bonded to a central atom. How would you structure your response using molecular geometry concepts?