C. Structure and Properties of Matter · Structure and Properties of MatterVSEPR Theory: Shapes with Two, Three and Four Electron Groups
C2.3 C3.5About 75 minutes
Learning goals- I can explain the main idea of VSEPR theory.
- I can count electron groups and use AXₘEₙ notation.
- I can predict and draw the shapes and bond angles of molecules and ions with two to four electron groups.
- I can explain how lone pairs and multiple bonds change bond angles.
Words to know
VSEPR theory
Valence Shell Electron Pair Repulsion: electron groups around a central atom arrange themselves as far apart as possible.
electron group
A single bond, multiple bond or lone pair around a central atom.
lone pair
A pair of valence electrons not involved in bonding.
bond angle
The angle between two bonds that share an atom.
resonance
When two or more valid Lewis structures can be drawn; the real structure is a blend of them.
Shape is everything
Why does water dissolve salt while carbon dioxide does not? Why does your nose detect some molecules and not others? Why does a medicine fit into one protein and not another? In every case the answer starts with molecular shape.
Remember from Grade 11: in SCH3U you drew Lewis structures and met a few shapes (linear CO₂, bent H₂O, tetrahedral CH₄, trigonal pyramidal NH₃) and were told the theory behind them would come in Grade 12. That theory is VSEPR: Valence Shell Electron Pair Repulsion. It was developed in 1957 by Ronald Gillespie and Ronald Nyholm; Gillespie spent most of his career at McMaster University in Hamilton, Ontario, and VSEPR is now taught in chemistry courses around the world.
The VSEPR idea
Electron groups around a central atom are all negative, so they repel each other and arrange themselves as far apart as possible. An electron group is any of:
- a single bond,
- a double or triple bond (it counts as one group, because all its electrons sit between the same two atoms),
- a lone pair (non-bonding pair) on the central atom.
The method
- Draw the Lewis structure (count valence electrons; add 1 per negative charge, subtract 1 per positive charge).
- Count the electron groups on the central atom.
- Choose the electron-group arrangement (2 → linear, 3 → trigonal planar, 4 → tetrahedral).
- Name the molecular shape from where the atoms are (lone pairs are invisible in the shape name).
Chemists use AXₘEₙ notation: A is the central atom, X a bonded atom, E a lone pair. Water is AX₂E₂.
| Groups | Notation | Bonds | Lone pairs | Molecular shape | Ideal angle | Examples |
|---|
| 2 | AX₂ | 2 | 0 | linear | 180° | CO₂, HCN, BeCl₂ (gas) |
| 3 | AX₃ | 3 | 0 | trigonal planar | 120° | BF₃, CH₂O, NO₃⁻, CO₃²⁻ |
| 3 | AX₂E | 2 | 1 | bent (angular) | less than 120° (about 115° to 119°) | SO₂, O₃, NO₂⁻ |
| 4 | AX₄ | 4 | 0 | tetrahedral | 109.5° | CH₄, NH₄⁺, CCl₄, SO₄²⁻ |
| 4 | AX₃E | 3 | 1 | trigonal pyramidal | about 107° | NH₃, H₃O⁺, PCl₃ |
| 4 | AX₂E₂ | 2 | 2 | bent (angular) | about 104.5° | H₂O, H₂S, OF₂ |
Lone pairs push harder
A lone pair is held by only one nucleus, so it spreads out closer to the central atom and takes up more space than a bonding pair. The order of repulsion is:
lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair
That is why the angle shrinks from 109.5° (CH₄) to about 107° (NH₃) to about 104.5° (H₂O), even though all three have four electron groups arranged tetrahedrally. Double bonds also take up a little more space than single bonds: in methanal (formaldehyde, CH₂O), the H–C–H angle is a little less than 120°.
Resonance
Some ions and molecules need more than one Lewis structure. In the nitrate ion, NO₃⁻, you can draw the N=O double bond to any of the three oxygens. The real ion is a blend (resonance hybrid): all three N–O bonds are identical, between single and double in length. For VSEPR this does not matter: every resonance structure gives 3 electron groups on N, so NO₃⁻ is trigonal planar.
Worked exampleExample 1: Ammonium ion
Predict the shape and bond angle of NH₄⁺.
- Valence electrons: N 5 + 4 H (1 each) − 1 (for the + charge) = 8 electrons = 4 pairs.
- Lewis structure: N in the centre with four N–H single bonds (uses all 8 electrons); no lone pairs.
- 4 electron groups → tetrahedral arrangement. All four are bonds: AX₄.
NH₄⁺ is tetrahedral, with H–N–H angles of 109.5° (written in square brackets with a + charge).
Worked exampleExample 2: Sulfur dioxide
Predict the shape of SO₂ and estimate the O–S–O angle.
- Valence electrons: S 6 + 2 O (6 each) = 18.
- One Lewis structure: O=S–O with one lone pair on S (and resonance with the double bond on the other side). S has 3 electron groups: 2 bonds and 1 lone pair.
- 3 groups → trigonal planar arrangement. With one lone pair: AX₂E.
SO₂ is bent, with an angle a little less than 120° (measured: about 119°).
Worked exampleExample 3: Hydronium and phosphorus trichloride
Give the AXₘEₙ notation and shape for H₃O⁺ and PCl₃.
- H₃O⁺: 6 + 3 − 1 = 8 electrons. O has 3 bonds and 1 lone pair → AX₃E.
- PCl₃: 5 + 3(7) = 26 electrons. P has 3 bonds (6 e⁻), each Cl has 3 lone pairs (18 e⁻), leaving 2 e⁻: one lone pair on P → AX₃E.
Both are AX₃E: trigonal pyramidal (angles a little under 109.5°).
Just for funVSEPR is often pronounced "vesper". So, strictly speaking, a chemistry class can spend a whole afternoon doing vespers.
Hands-on activityBalloon molecules
You need: 6 round balloons of the same size, string or elastic bands. Grown-up note: balloons are a choking hazard for young children; an adult should supervise and dispose of any broken pieces right away. Anyone with a latex allergy should use latex-free balloons.
- Blow up the balloons to about the same size and tie them.
- Twist two balloons together at their knots. Let go: they point in opposite directions (linear, 180°).
- Twist three together at the knots: they form a flat triangle (trigonal planar, 120°).
- Twist four together: they spread into a tetrahedron, not a flat cross. Set it down and notice that one balloon always points straight up.
- Now replace one balloon in the group of four with a slightly larger balloon (a "lone pair"). Notice the other three get pushed slightly closer together.
What to look for: the balloons find the arrangement that keeps them farthest apart without any help, just as electron groups do. The four-balloon model shows why methane is 3-D (109.5°) and not a flat square (90°). The bigger balloon models why lone pairs squeeze bond angles.
Your turn
1How many electron groups are on carbon in HCN? What is its shape?
H–C≡N: 2 groups (single and triple bond) → linear, 180°.
2Predict the shape of BF₃.
B has 3 bonds and no lone pairs (B has only 6 valence electrons around it): trigonal planar, 120°.
3Predict the shape of H₂S and estimate the bond angle.
S has 2 bonds and 2 lone pairs: AX₂E₂, bent, angle a little under 109.5° (measured about 92°, smaller than water's). Accept "bent, less than 109.5°".
4Predict the shape of the carbonate ion, CO₃²⁻.
4 + 18 + 2 = 24 e⁻. C has 3 electron groups (one C=O and two C–O, with resonance), no lone pairs: trigonal planar, 120°.
5Why is the H–N–H angle in NH₃ smaller than 109.5°?
The lone pair on nitrogen repels the bonding pairs more strongly than they repel each other, squeezing the angle to about 107°.
6Give the AXₘEₙ notation and shape for CCl₄.
AX₄, tetrahedral, 109.5°.
7Predict the shape of ozone, O₃.
18 e⁻; central O has 1 double bond, 1 single bond and 1 lone pair: AX₂E, bent, about 117°.
More practice: warm-up
1What does VSEPR stand for?
Valence Shell Electron Pair Repulsion.
2Does a double bond count as one or two electron groups?
3What is the ideal angle for 3 electron groups?
5Who developed VSEPR theory with Ronald Nyholm?
Ronald Gillespie (McMaster University).
More practice: on your own
1Predict the shape of the nitrite ion, NO₂⁻.
5 + 12 + 1 = 18 e⁻. N has one N=O, one N–O and one lone pair: AX₂E, bent, slightly less than 120°.
2Predict the shape of methanal, CH₂O, and state the approximate H–C–H angle.
C has 3 groups (2 C–H, 1 C=O), no lone pairs: trigonal planar; H–C–H slightly less than 120° because the double bond takes up more room.
3Predict the shape of OF₂.
O has 2 bonds and 2 lone pairs: AX₂E₂, bent, angle under 109.5°.
4Explain why CO₂ is linear but SO₂ is bent.
C in CO₂ has 2 electron groups (two double bonds), so they point opposite ways. S in SO₂ has 3 groups (two bonds and a lone pair), so the arrangement is trigonal planar and the atoms form a bent shape.
5Predict the shape around each carbon in ethene, C₂H₄.
Each C has 3 groups (C=C and two C–H): trigonal planar; the whole molecule is flat.
Challenge
1Predict the shape around each central atom in ethanoic (acetic) acid, CH₃COOH: the CH₃ carbon, the COOH carbon and the O of the O–H group.
CH₃ carbon: 4 bonds → tetrahedral. COOH carbon: 3 groups (C–C, C=O, C–O) → trigonal planar. O–H oxygen: 2 bonds + 2 lone pairs → bent.
2The H–O–H angle in H₂O is about 104.5° but the H–S–H angle in H₂S is about 92°. Suggest a reason, using the size and electronegativity of the central atom.
S is larger and less electronegative than O, so the S–H bonding pairs are farther apart and held less tightly near S. They repel each other less, and the lone pairs push them closer together, giving a smaller angle.
3Draw the Lewis structure of the cyanate ion, OCN⁻, and predict its shape.
6 + 4 + 5 + 1 = 16 e⁻. A good structure is [O=C=N]⁻ with two lone pairs on O and two on N (or [O–C≡N]⁻). Carbon has 2 electron groups: linear.
Quiz
1. What is the shape of NH₃?
2. How many electron groups are around carbon in CO₂?
3. Which molecule is trigonal planar?
4. Why is water's bond angle smaller than methane's?
5. What is the AXₘEₙ notation for SO₂?
6. What is the shape of the ammonium ion, NH₄⁺?
Big idea (C2.3): electron groups repel and spread out, so the number of groups around a central atom fixes the geometry, and the number of lone pairs decides the molecular shape. This lesson also introduces Ronald Gillespie, a Canadian contribution to the field (C3.5).
How to help: the balloon activity is worth doing; seeing four balloons snap into a tetrahedron is memorable. Ask your teen to name the shape of molecules you see in recipes or labels (water, carbon dioxide, ammonia).
Common difficulties:
- Counting a double bond as two groups.
- Naming the electron-group arrangement instead of the molecular shape (NH₃ is trigonal pyramidal, not tetrahedral).
- Wrong Lewis structures (especially forgetting the extra electrons for negative ions). Always count electrons first.