3.5.7 Working Out the Shapes of Molecules

This topic explains the step-by-step method for determining the shape of a molecule using VSEPR theory.

Definition

Working Out the Shapes of Molecules: The process of using VSEPR theory to predict the three-dimensional arrangement of atoms in a molecule based on the number of electron pairs around the central atom.

Main Idea

• Count the total number of valence electrons around the central atom.
• Divide the total electrons by 2 to get the number of electron pairs.
• Determine the number of bonding pairs and lone pairs.
• Use the VSEPR table to predict the shape and bond angles.

The key formula from the textbook is:

> Add together the number of valence electrons from the central atom, and the number of electrons contributed to bonding by surrounding atoms. Include the ion charge if there is one. Divide the total electrons by 2. This gives the number of electron pairs distributed around the central atom.

Core Concept

The shape of a molecule is determined by the repulsion between electron pairs around the central atom. Electron pairs arrange themselves to be as far apart as possible. The number of bonding pairs and lone pairs determines the molecular geometry.

Detailed Explanation

Step-by-Step Method

• The central atom is usually the least electronegative atom (except hydrogen).
• It is the atom that forms the most bonds.

• Count the valence electrons from the central atom.
• Add the electrons contributed by surrounding atoms (usually 1 electron per bond for each surrounding atom).
• Include the ion charge:
• For a negative ion (anion): Add electrons equal to the charge.
• For a positive ion (cation): Subtract electrons equal to the charge.

• Divide the total number of electrons by 2.
• This gives the total number of electron pairs around the central atom.

• Bonding pairs: Equal to the number of atoms bonded to the central atom.
• Lone pairs: Total electron pairs − Bonding pairs.

Step 5: Determine the Shape - Use the VSEPR table to determine the shape based on the number of bonding pairs and lone pairs.

VSEPR Table

Worked Examples

Example 1: CH₄ (Methane)

• Central atom: Carbon (C)
• Valence electrons of C: 4
• Electrons from 4 H atoms: 4 × 1 = 4
• **Total electrons:** 4 + 4 = 8
• Total electron pairs: 8 ÷ 2 = 4
• Bonding pairs: 4 (four C−H bonds)
• **Lone pairs:** 4 − 4 = 0
• Shape: Tetrahedral
• Bond angle: 109.5°

Example 2: NH₃ (Ammonia)

• Central atom: Nitrogen (N)
• Valence electrons of N: 5
• Electrons from 3 H atoms: 3 × 1 = 3
• **Total electrons:** 5 + 3 = 8
• Total electron pairs: 8 ÷ 2 = 4
• Bonding pairs: 3 (three N−H bonds)
• **Lone pairs:** 4 − 3 = 1
• Shape: Trigonal pyramidal
• Bond angle: < 109.5° (approximately 107°)

Example 3: H₂O (Water)

• Central atom: Oxygen (O)
• Valence electrons of O: 6
• Electrons from 2 H atoms: 2 × 1 = 2
• **Total electrons:** 6 + 2 = 8
• Total electron pairs: 8 ÷ 2 = 4
• Bonding pairs: 2 (two O−H bonds)
• **Lone pairs:** 4 − 2 = 2
• Shape: Bent (V-shaped)
• Bond angle: < 109.5° (approximately 104.5°)

Example 4: CO₂ (Carbon Dioxide)

• Central atom: Carbon (C)
• Valence electrons of C: 4
• Electrons from 2 O atoms: 2 × 2 = 4 (each O contributes 2 electrons for double bonds)
• **Total electrons:** 4 + 4 = 8
• Total electron pairs: 8 ÷ 2 = 4
• Bonding pairs: 2 (two C=O double bonds)
• Lone pairs: 0 (on carbon)
• Shape: Linear
• Bond angle: 180°

Example 5: BF₃ (Boron Trifluoride)

• Central atom: Boron (B)
• Valence electrons of B: 3
• Electrons from 3 F atoms: 3 × 1 = 3
• **Total electrons:** 3 + 3 = 6
• Total electron pairs: 6 ÷ 2 = 3
• Bonding pairs: 3 (three B−F bonds)
• **Lone pairs:** 3 − 3 = 0
• Shape: Trigonal planar
• Bond angle: 120°

Example 6: PCl₅ (Phosphorus Pentachloride)

• Central atom: Phosphorus (P)
• Valence electrons of P: 5
• Electrons from 5 Cl atoms: 5 × 1 = 5
• **Total electrons:** 5 + 5 = 10
• Total electron pairs: 10 ÷ 2 = 5
• Bonding pairs: 5 (five P−Cl bonds)
• **Lone pairs:** 5 − 5 = 0
• Shape: Trigonal bipyramidal
• Bond angles: 90°, 120°

Example 7: SF₆ (Sulfur Hexafluoride)

• Central atom: Sulfur (S)
• Valence electrons of S: 6
• Electrons from 6 F atoms: 6 × 1 = 6
• **Total electrons:** 6 + 6 = 12
• Total electron pairs: 12 ÷ 2 = 6
• Bonding pairs: 6 (six S−F bonds)
• **Lone pairs:** 6 − 6 = 0
• Shape: Octahedral
• Bond angle: 90°

Molecules with Multiple Bonds

• For double bonds, count the bond as one electron pair.
• For triple bonds, count the bond as one electron pair.
• Example: CO₂ has two double bonds, but the carbon atom has 2 electron pairs around it (linear shape).

Ions

• For anions: Add electrons equal to the charge.
• For cations: Subtract electrons equal to the charge.

Example: NH₄⁺ (Ammonium ion)

• Central atom: Nitrogen (N)
• Valence electrons of N: 5
• Electrons from 4 H atoms: 4 × 1 = 4
• Subtract 1 electron for + charge: 5 + 4 − 1 = 8
• Total electron pairs: 8 ÷ 2 = 4
• Bonding pairs: 4
• Lone pairs: 0
• Shape: Tetrahedral
• Bond angle: 109.5°

Example: SO₄²⁻ (Sulfate ion)

• Central atom: Sulfur (S)
• Valence electrons of S: 6
• Electrons from 4 O atoms: 4 × 2 = 8 (double bonds)
• **Add 2 electrons for 2− charge:** 6 + 8 + 2 = 16
• Total electron pairs: 16 ÷ 2 = 8
• But: SO₄²⁻ has 4 bonding pairs and 0 lone pairs on S (expanded octet)
• Shape: Tetrahedral
• Bond angle: 109.5°

Intermediate Level

Steps

• Identify the central atom.
• Count valence electrons from the central atom.
• Add electrons from surrounding atoms (1 per bond).
• Include ion charge (add for anions, subtract for cations).
• Divide by 2 to get total electron pairs.
• Determine bonding pairs (number of bonds).
• Determine lone pairs (total − bonding).
• Use the VSEPR table to find the shape.

Examples

Important Points

• 1. Add valence electrons from the central atom and surrounding atoms.
• 2. Include ion charge (add for anions, subtract for cations).
• 3. Divide total electrons by 2 to get electron pairs.
• 4. Bonding pairs = number of bonds.
• 5. Lone pairs = total pairs − bonding pairs.
• 6. Use the VSEPR table to determine shape.
• 7. Multiple bonds count as one electron pair.
• 8. Examples: CH₄ (tetrahedral), NH₃ (trigonal pyramidal), H₂O (bent), CO₂ (linear), BF₃ (trigonal planar), PCl₅ (trigonal bipyramidal), SF₆ (octahedral).

Remember

• - Step 1: Count valence electrons
• - Step 2: Add electrons from surrounding atoms
• - Step 3: Include ion charge
• - Step 4: Divide by 2 → electron pairs
• - Step 5: Bonding pairs = number of bonds
• - Step 6: Lone pairs = total − bonding
• - Step 7: Use VSEPR table to find shape
• - Multiple bonds: Count as one electron pair

Common Mistakes

• 1. Forgetting to include ion charge: Add for anions, subtract for cations.
• 2. Counting multiple bonds as multiple electron pairs: A double bond is one electron pair.
• 3. Miscounting valence electrons: Double-check the central atom's valence electrons.
• 4. Confusing bonding pairs with total electron pairs: Bonding pairs = number of bonds; total pairs includes lone pairs.
• 5. Forgetting that lone pairs affect shape: Lone pairs reduce bond angles.

Quick Revision

• Add valence electrons from the central atom and surrounding atoms.
• Include ion charge (add for anions, subtract for cations).
• Divide total electrons by 2 to get electron pairs.
• Bonding pairs = number of bonds.
• Lone pairs = total pairs − bonding pairs.
• Use the VSEPR table to determine shape.
• Multiple bonds count as one electron pair.
• Examples: CH₄ (tetrahedral), NH₃ (trigonal pyramidal), H₂O (bent), CO₂ (linear), BF₃ (trigonal planar), PCl₅ (trigonal bipyramidal), SF₆ (octahedral).

60-Second Revision

• Step 1: Count valence electrons
• Step 2: Add electrons from surrounding atoms
• Step 3: Include ion charge
• Step 4: Divide by 2 → electron pairs
• Step 5: Bonding pairs = number of bonds
• Step 6: Lone pairs = total − bonding
• Step 7: Use VSEPR table to find shape
• Multiple bonds: Count as one electron pair

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