Why is water bent?
A water molecule is one oxygen atom bonded to two hydrogen atoms. On paper, the easiest drawing is a straight line: H–O–H. But water is not straight. The two bonds meet at an angle of 104.5°.
The last lecture drew water flat, with the two hydrogens on opposite sides of the oxygen, and warned that the flat drawing was not a shape. Now you need the real shape. It matters: the bend in water is one reason ice floats, water dissolves salt, and your body works at all. So where does 104.5° come from? Not 180°, not 90°, not 120°, but 104.5°?
One idea answers this question for water, and for almost every small molecule you will meet. It is called VSEPR theory, and once you see it, you can predict the shape of a molecule you have never seen.
Electron pairs push each other apart
VSEPR stands for valence shell electron pair repulsion. The idea is in the name. The outer (valence) shell of the central atom holds pairs of electrons. Every pair is negative, so every pair repels every other pair. The pairs therefore move as far apart from each other as they can, and the atoms attached to them follow.
Count the pairs carefully, because the count decides everything. Every bonding pair counts, and so does every lone pair. A double or triple bond counts as one, because all its electrons sit in the same place, between the same two atoms. So the thing to count is an electron region: a single bond, a double bond, a triple bond, or a lone pair. Each is one region.
Think of balloons tied together at their necks. Two balloons point in opposite directions. Three spread out in a flat triangle. Four do not lie flat at all: they point to the corners of a pyramid with a triangular base, called a tetrahedron. Nobody arranges them. Each balloon simply pushes the others away until the pushes balance. Electron regions behave the same way.
The angles follow from sharing space equally. Two regions on opposite sides make a straight line: 180°. Three regions in a flat plane share a full turn of 360°, so each pair is ° apart. Four regions could also lie flat, at 90°, but they can get further apart by leaving the plane. In a tetrahedron every pair is 109.5° apart, which is more than 90°, so this is the arrangement the repulsion chooses.
Electron regions around a central atom (bonds and lone pairs) repel each other and arrange themselves as far apart as possible.
2 regions: linear, 180°. 3 regions: trigonal planar, 120°. 4 regions: tetrahedral, 109.5°.
Lone pairs repel more strongly than bonding pairs, so they squeeze the bond angles smaller.
Methane, CH₄, has four bonds around carbon. Drawn on paper as a cross, the angles are 90°. Why is the real angle 109.5° instead?
Show the answer
Because a molecule is not on paper. On a flat page, four bonds can be at most 90° apart. In three dimensions they can do better. If one bond points up, the other three can point down and outwards, like the legs of a tripod. In this arrangement, the tetrahedron, every pair of bonds is 109.5° apart. That is the largest equal angle that four directions in space can have, so the repulsion is as small as it can be. The flat cross is a drawing habit, not the molecule.
Lone pairs take up more room
Now return to water. Oxygen has two bonding pairs and two lone pairs: four regions. So the four regions point to the corners of a tetrahedron, as in methane. But only two of the corners hold hydrogen atoms. The other two hold lone pairs, which have no atom on the end.
Here is a point that confuses many students. The shape of a molecule describes where its atoms are, not where its electrons are. You cannot see a lone pair in the shape. So water, with its electrons in a tetrahedron, has atoms in a bent line: H, then O, then H at an angle. Its shape is called bent (some books say V-shaped).
Why 104.5° and not the tetrahedral 109.5°? Because lone pairs repel more strongly than bonding pairs. A bonding pair is pulled by two nuclei, so it is stretched out between two atoms. A lone pair is held by one nucleus only. It sits closer to the central atom and spreads out more around it, so it pushes harder on its neighbours. The order of repulsion is:
So each lone pair squeezes the bonds a little closer. Methane has none: 109.5°. Ammonia, NH₃, has one: about 107°. Water has two: 104.5°. Same four regions, fewer bonds, a smaller angle each time. That is it. That is the whole idea. Count the regions to find the arrangement, look only at the atoms to name the shape, and let each lone pair squeeze the angles.
BF₃ and NH₃ both have three atoms around a central atom. A student says they must have the same shape. What has the student missed?
Show the answer
The lone pair. Boron in BF₃ has 3 electron regions, all bonds, so they spread out flat at 120°: trigonal planar. Nitrogen in NH₃ has 4 regions, because it also has a lone pair. Four regions point to a tetrahedron, so the three hydrogens are pushed down below the nitrogen, like the legs of a tripod. The formulas look alike, but the shapes are different. You cannot read a shape from a formula. You must count the regions on the central atom, and that needs the dot-and-cross diagram.
Go back to the explorer of the last lecture, where carbon, nitrogen, oxygen and fluorine each bonded to hydrogen. That explorer drew every molecule flat. Now you can give each one its real shape. All four central atoms have 4 electron regions, so in every case the regions point to a tetrahedron. CH₄ uses all four corners for atoms: tetrahedral. NH₃ uses three: trigonal pyramidal. H₂O uses two: bent. HF uses only one, and a molecule with only two atoms can only be a straight line, whatever its lone pairs do. The same rule gives four different shapes, because the number of lone pairs changes.
Explore all five arrangements below.
Choose the number of electron regions around the central atom, and how many are lone pairs. Watch the shape, its name and its bond angle. Then compare the last three: they all have four regions.
Wedge: a bond coming towards you. Dashes: a bond going away. Green: a lone pair.
The five arrangements of this lecture, from the number of electron regions around the central atom:
| Regions | Lone pairs | Shape | Angle | Example |
|---|---|---|---|---|
| 2 | 0 | linear | 180° | CO₂ |
| 3 | 0 | trigonal planar | 120° | BF₃ |
| 4 | 0 | tetrahedral | 109.5° | CH₄ |
| 4 | 1 | trigonal pyramidal | ≈ 107° | NH₃ |
| 4 | 2 | bent | 104.5° | H₂O |
In the last three rows the electron regions all point to a tetrahedron. Only the atoms are named in the shape, and each lone pair makes the bond angle smaller.
Worked examples
The method for every molecule: draw the dot-and-cross diagram of the central atom, count its electron regions, choose the arrangement, then name the shape from the atoms only.
Nitrogen has 5 outer electrons. Three form N–H bonds, and two form one lone pair. Regions: 3 bonding + 1 lone = 4.
Four regions point to a tetrahedron. The lone pair sits at the top corner, and the three hydrogens form a triangular base below the nitrogen. The atoms make a pyramid, so the shape is trigonal pyramidal. The lone pair squeezes the H–N–H angle to about 107°.
Boron has 3 outer electrons. Each forms a B–F bond, and none are left. Regions: 3 bonding + 0 lone = 3.
Three regions spread out in a flat triangle. The shape is trigonal planar, with F–B–F angles of 120°.
Notice that boron has only 6 electrons around it, not 8. BF₃ is one of the exceptions to the "full outer shell" pattern of the last lecture. VSEPR still works, because it only needs the number of regions, not a full shell.
From the last lecture, carbon forms a double bond to each oxygen and has no lone pairs: O=C=O.
Each double bond is one region. So carbon has 2 regions, and they point in opposite directions. The shape is linear, 180°.
Counting the four pairs as four regions would give a tetrahedron and a wrong answer. The two pairs of a double bond cannot point in different directions: both sit between the same carbon and the same oxygen.
The last lecture found H–C≡N, with no lone pairs on carbon. Around carbon: one single bond and one triple bond, so 2 regions.
Two regions give a linear molecule, 180°. Two regions are two regions, whatever kind of bonds they are.
CO₂ and H₂O both have one central atom and two outer atoms. Compare their shapes.
In CO₂, carbon has 2 regions (two double bonds) and no lone pairs, so the molecule is linear. In H₂O, oxygen has 4 regions (two bonds and two lone pairs), so the molecule is bent.
The formulas have the same pattern, but the central atoms are different. Carbon uses all its outer electrons in bonds. Oxygen keeps four of its six as lone pairs. This one difference makes CO₂ straight and water bent, and two lectures from now it explains why water molecules have positive and negative ends while CO₂ molecules do not.
One more example shows a limit. Beryllium chloride, BeCl₂, has 2 regions around beryllium, so a single BeCl₂ molecule is linear. That is true for BeCl₂ as a gas. Solid beryllium chloride is not made of separate BeCl₂ molecules, so VSEPR describes the gas, not the solid.
Now sort some molecules by shape yourself.
Put each molecule in the box for its shape. Count the electron regions around the central atom first, then look only at the atoms.
Ten molecules sorted by shape, with the count of electron regions around the central atom.
- Linear: CO₂ (2 double bonds, 2 regions); HCN (1 single + 1 triple bond, 2 regions).
- Trigonal planar: BF₃ and BCl₃ (3 bonds, no lone pairs).
- Tetrahedral: CH₄ and CCl₄ (4 bonds, no lone pairs).
- Trigonal pyramidal: NH₃ and PH₃ (3 bonds, 1 lone pair).
- Bent: H₂O and H₂S (2 bonds, 2 lone pairs).
Three classic mistakes
A double or triple bond is one electron region, because all its electrons lie between the same two atoms. CO₂ has 2 regions around carbon, so it is linear, not tetrahedral.
NH₃ has four electron regions arranged in a tetrahedron, but its shape is trigonal pyramidal, because the shape describes the atoms only. In the same way, water's shape is bent, not tetrahedral.
A molecule with four regions is three-dimensional. Drawing CH₄ as a flat cross suggests 90°, but the real angle is 109.5°. Chemists draw the third dimension with a wedge (a bond coming towards you) and a dashed line (a bond going away).
For each, draw the dot-and-cross diagram of the central atom first and count the electron regions.
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Predict the shape and bond angle of silane, SiH₄. Silicon is in the same group as carbon.
Hint 1
Silicon has 4 outer electrons, like carbon.
Hint 2
4 bonds, no lone pairs: the same as methane.
Full answer
Silicon forms 4 Si–H bonds and has no lone pairs: 4 regions, all with atoms. The shape is tetrahedral, with angles of 109.5°.
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Predict the shape of phosphorus trichloride, PCl₃, and say whether its Cl–P–Cl angle is more or less than 109.5°.
Hint 1
Phosphorus has 5 outer electrons. How many does it use in bonds to three chlorines?
Hint 2
3 bonds and 1 lone pair, like NH₃.
Full answer
Phosphorus uses 3 electrons in P–Cl bonds and keeps 2 as a lone pair: 4 regions, 3 with atoms. The shape is trigonal pyramidal. The lone pair repels more strongly than the bonding pairs, so the Cl–P–Cl angle is less than 109.5°.
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Hydrogen sulfide, H₂S, smells of bad eggs. Predict its shape. Then explain why it is not linear, even though it has only three atoms.
Hint 1
Sulfur is in the same group as oxygen.
Hint 2
Count the lone pairs on sulfur, not only the bonds.
Full answer
Sulfur has 6 outer electrons: 2 form S–H bonds and 4 form 2 lone pairs. That makes 4 regions, which point to a tetrahedron. Only 2 of them hold atoms, so the molecule is bent. A three-atom molecule is linear only when the central atom has exactly 2 regions, as in CO₂. Lone pairs, though invisible in the shape, decide it.
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Methanal (formaldehyde), CH₂O, has carbon in the middle, bonded to two hydrogens and to the oxygen. Draw its dot-and-cross diagram, predict its shape, and predict whether the H–C–H angle is a little more or a little less than 120°. Give a reason.
Hint 1
Carbon needs 4 bonds. Two go to the hydrogens. How many are left for the oxygen?
Hint 2
A C=O double bond: carbon then has 3 regions. Which region holds the most electrons?
Full answer
Carbon forms two C–H single bonds and one C=O double bond, and has no lone pairs: 3 regions. Oxygen keeps 2 lone pairs. Three regions give a trigonal planar shape, with angles close to 120°. The double bond holds 4 electrons, more than a single bond, so it repels more strongly. It pushes the two C–H bonds closer together, so the H–C–H angle should be a little less than 120°. This is the same reasoning as for lone pairs: a region with more electrons near the central atom takes up more room.
VSEPR is a simple model with surprising power. The real behaviour of electrons is described by quantum mechanics, which needs long calculations. Yet the simple rule that electron regions repel and spread out predicts the shapes of most small molecules correctly. The idea was first put forward by Nevil Sidgwick and Herbert Powell in 1940 and developed into a fuller theory by Ronald Gillespie and Ronald Nyholm in 1957.
Shape matters because it decides what a molecule can do. A drug works only if its shape fits the site it acts on. Water's bent shape gives it a positive end and a negative end, which explains much of its unusual behaviour. The next two lectures show how: first by looking at how unevenly each bond shares its electrons, then by adding up those bonds using the shapes from this lecture.
- VSEPR theory says that electron regions around a central atom repel each other and spread out as far as possible.
- Each single, double or triple bond, and each lone pair, counts as one electron region.
- Two, three and four regions give linear (180°), trigonal planar (120°) and tetrahedral (109.5°) arrangements.
- The shape of a molecule is named from its atoms only, so four regions with one or two lone pairs give trigonal pyramidal or bent molecules.
- Lone pairs repel more strongly than bonding pairs, so the bond angles fall from 109.5° in CH₄ to about 107° in NH₃ and 104.5° in H₂O.