- How intermolecular forces explain properties
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Water should be a gas
Look at the hydrides of Group 16. Hydrogen sulfide, H₂S, boils at about −60 °C. Going down the group, H₂Se boils at about −41 °C and H₂Te at about −4 °C. That trend makes sense from the last two lectures: bigger molecules have more electrons, so their London forces are stronger, so they boil higher.
Now run the trend backwards to the smallest molecule in the group, water. It has the fewest electrons, so it should boil lowest of all, at roughly −80 °C. Water should be a gas at room temperature, and there should be no oceans, no rain and no life as we know it. In fact water boils at 100 °C, about 180 degrees above the trend.
Water is not alone. Ammonia, NH₃, and hydrogen fluoride, HF, are also far too high. The last lecture left exactly this puzzle open: HF boils at about 20 °C, far above HCl, even though it has fewer electrons. It promised a third and much stronger force between molecules. This lecture is about that force: the hydrogen bond.
What a hydrogen bond is
Look at what NH₃, H₂O and HF have in common. In each, hydrogen is bonded directly to nitrogen, oxygen or fluorine. These are the three most electronegative elements: N 3.04, O 3.44 and F 3.98, against H 2.20. They are also small atoms with lone pairs.
Follow what happens to the hydrogen in an O–H bond. Oxygen pulls the shared electrons strongly towards itself. Hydrogen has only one electron, and it has no inner shells. So when its electron is pulled away, almost nothing is left to cover its nucleus, a single proton. The hydrogen becomes strongly δ+, and it is tiny.
Now bring a second molecule close, with a lone pair on an N, O or F atom. The lone pair is a concentrated region of negative charge. The small, strongly positive hydrogen can get very close to it. Opposite charges, large and close together, attract strongly. That attraction is a hydrogen bond.
A hydrogen bond is an attraction between two molecules. It forms between a hydrogen atom bonded to N, O or F in one molecule and a lone pair on N, O or F in the other.
It needs a donor (an H bonded to N, O or F) and an acceptor (a lone pair on N, O or F). It is drawn as a dotted line.
Why only these three elements? Chlorine has an electronegativity of 3.16, almost as high as nitrogen's 3.04. But a chlorine atom is much larger. Its lone pairs are spread over a bigger region, so the hydrogen cannot get as close to a concentrated negative charge. So the attraction in HCl is an ordinary dipole–dipole force. A hydrogen bond needs high electronegativity and a small atom, and only N, O and F have both.
How strong is it?
Separating two molecules joined by a hydrogen bond typically takes about 10 to 30 kJ/mol. That is roughly ten times the energy needed to overcome ordinary dipole–dipole attraction. For two water molecules, it is about 20 kJ/mol. But a hydrogen bond is still far weaker than the covalent bond inside the molecule. The O–H bond needs 467 kJ/mol to break, more than twenty times as much. So a hydrogen bond is a strong intermolecular force, not a true chemical bond.
When water boils, which bonds break: the O–H covalent bonds, or the hydrogen bonds?
Show the answer
The hydrogen bonds. Steam is still made of H₂O molecules, so the O–H bonds inside each molecule are untouched. Boiling separates whole molecules from each other, which means overcoming the forces between molecules. Breaking O–H bonds would destroy the water itself, and that takes far more energy than boiling does.
Donors and acceptors
To decide whether a substance forms hydrogen bonds between its own molecules, check for both parts. A donor without an acceptor, or an acceptor without a donor, is not enough. The most common trap is a molecule that contains hydrogen and contains N, O or F, but where the hydrogen is bonded to carbon. A C–H hydrogen is only slightly δ+ (carbon 2.55, hydrogen 2.20), so it cannot act as a donor. Sort the molecules below.
For each substance, decide whether its molecules form hydrogen bonds with each other. Look for an H bonded directly to N, O or F, and a lone pair on N, O or F.
Eight substances sorted, each with its reason.
- Hydrogen bonds: water, H₂O (O–H donor, O lone pairs); ammonia, NH₃ (N–H, N lone pair); hydrogen fluoride, HF (F–H, F lone pairs); methanol, CH₃OH (O–H, O lone pairs); methylamine, CH₃NH₂ (N–H, N lone pair).
- No hydrogen bonds: propanone, CH₃COCH₃ (acceptor only: every H is on carbon); fluoromethane, CH₃F (acceptor only: the H atoms are on carbon, not on F); hydrogen chloride, HCl (Cl is too large; dipole–dipole only).
The two hardest cards are fluoromethane and propanone. Both contain an electronegative atom with lone pairs, and both contain hydrogen. Neither has the hydrogen in the right place. The question is never "does it have H and does it have F?" It is "is an H bonded directly to N, O or F?"
Worked examples
Does ethanol, CH₃CH₂OH, form hydrogen bonds? With what?
Ethanol has an O–H group. That hydrogen is bonded to oxygen, so it is a donor. The same oxygen has two lone pairs, so it is an acceptor. Both parts are present, so ethanol molecules form hydrogen bonds with each other: the O–H of one points at the oxygen of another.
Ethanol also forms hydrogen bonds with water, in both directions. Its O–H can donate to a water oxygen, and its oxygen can accept from a water O–H. So ethanol molecules fit into water's network of hydrogen bonds. This is why ethanol and water mix in any proportion.
The last lecture said that propanone, CH₃COCH₃, cannot form hydrogen bonds with itself. Explain this, and explain why it still dissolves well in water.
Propanone has a C=O group, and the oxygen has two lone pairs, so it can accept. But all six hydrogens are bonded to carbon, so propanone has no donor. Two propanone molecules have nothing to make a hydrogen bond with. They attract each other by London and dipole–dipole forces only.
Water, though, has donors to spare. A water O–H can point at propanone's oxygen. So propanone and water form hydrogen bonds with each other, and propanone dissolves well. A molecule that only accepts can still hydrogen-bond, as long as its partner donates.
Methanol, CH₃OH, boils at about 65 °C (338 K). Ethane, C₂H₆, boils at about −89 °C (184 K). Show that this is a fair test of what hydrogen bonding adds.
Count the electrons. Methanol: . Ethane: . The same electron count, and molecules of similar size, so their London forces are about the same.
The difference is the O–H group. Ethane has only C–H bonds, so it is non-polar and has London forces only. Methanol has hydrogen bonds. With London forces matched, a difference of about 150 degrees comes from hydrogen bonding (with a small extra part from methanol's polarity).
Why water beats hydrogen fluoride
Now the graph again. Fluorine is the most electronegative element of all, so each F–H···F hydrogen bond is individually stronger than an O–H···O one. Yet water boils at 100 °C and HF at only about 20 °C. Both molecules have 10 electrons, so their London forces are similar. Make a prediction before reading on.
H₂O and HF both have 10 electrons. Fluorine is more electronegative than oxygen, so a single hydrogen bond in HF is stronger. Yet water boils 80 degrees higher. What is the main reason?
Water forms more hydrogen bonds per molecule. Each H₂O has two donor hydrogens and two lone pairs, so on average each molecule makes two hydrogen bonds. Each HF has only one hydrogen, so although fluorine has three lone pairs, there is only enough hydrogen for one hydrogen bond per molecule on average. More bonds per molecule outweigh slightly stronger individual bonds.
That is it. That is the whole idea behind the three anomalies. Two things decide how strongly a substance is held together by hydrogen bonds: how strong each bond is, and how many bonds each molecule makes. Every hydrogen bond needs one donor hydrogen and one lone pair, so the smaller of the two numbers sets the limit.
Explain the order of boiling points: H₂O (100 °C) > HF (20 °C) > NH₃ (about −33 °C).
| Molecule | Donor H | Lone pairs | H bonds per molecule (average) |
|---|---|---|---|
| H₂O | 2 | 2 | 2 |
| HF | 1 | 3 | 1 |
| NH₃ | 3 | 1 | 1 |
Each hydrogen bond uses one donor H and one lone pair, so the average number per molecule is the smaller of the two counts. Water's numbers are perfectly matched: two of each, so two hydrogen bonds per molecule. HF has spare lone pairs but only one H, so it is limited to one. Ammonia has spare hydrogens but only one lone pair, so it is limited to one as well.
That explains why water is highest. HF and NH₃ both average one bond per molecule, but nitrogen (3.04) is less electronegative than fluorine (3.98). So each N–H···N bond is weaker than an F–H···F bond, and ammonia boils lowest of the three. Check against the graph: all three are far above their groups' trends, and in the order the counting predicts.
Why ice floats
Almost every substance is denser as a solid than as a liquid, because the particles pack closer when they stop moving. Water is a famous exception. Ice has a density of about 0.917 g/cm³, and liquid water at 0 °C about 1.000 g/cm³. So water expands by about 9% when it freezes, and ice floats.
Hydrogen bonds explain this. In ice, each water molecule makes four hydrogen bonds, two as donor and two as acceptor, pointing roughly to the corners of a tetrahedron. To make all four bonds at those angles, the molecules must lock into an open, six-sided lattice, with a lot of empty space inside each ring. When ice melts, some of the hydrogen bonds break, the lattice partly collapses, and the molecules can move into the empty spaces. So liquid water is denser than ice, even though it is warmer.
This matters for life. Ice forms on the top of a lake and floats there, so the water underneath stays liquid and fish can survive the winter. If ice were denser than water, it would sink as it formed, and lakes could freeze solid from the bottom up.
A student says: "Ice floats because it has air bubbles trapped in it." Is that the real reason?
Show the answer
No. Bubbles can make a particular piece of ice float a little higher, but perfectly clear ice with no bubbles at all still floats. The reason is at the molecular level: the hydrogen-bonded lattice of ice holds the molecules further apart, on average, than they are in the liquid. The empty space is part of the crystal structure, not trapped air.
Three classic mistakes
The O–H bond is a covalent bond inside one molecule (467 kJ/mol). The hydrogen bond is an attraction between molecules (about 20 kJ/mol in water). Boiling breaks hydrogen bonds, never O–H bonds.
The H must be bonded directly to N, O or F. In CH₃F and propanone, every H is on carbon, so there is no donor.
For molecules of similar size, yes. But London forces grow with size. Iodine, with only London forces, is a solid at room temperature, while water is a liquid. Always compare like with like.
Use Pauling electronegativities where you need them: H 2.20, C 2.55, N 3.04, O 3.44, F 3.98, Cl 3.16.
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Which of these form hydrogen bonds between their own molecules? Give a reason for each. (a) Dimethyl ether, CH₃OCH₃. (b) Ethanoic acid, CH₃COOH. (c) Hydrazine, H₂N–NH₂. (d) Difluoromethane, CH₂F₂.
Hint 1
Draw out where each hydrogen is attached.
Hint 2
In ethanoic acid, one hydrogen is in the –COOH group, on an oxygen.
Full answer
(a) No. The oxygen has lone pairs (an acceptor), but all six H are on carbon, so there is no donor. (b) Yes. The O–H in the –COOH group is a donor, and both oxygens have lone pairs. (c) Yes. Each nitrogen carries two N–H donors and one lone pair. (d) No. Both F atoms have lone pairs, but the H atoms are bonded to carbon, not to fluorine. Like propanone, (a) and (d) can still accept hydrogen bonds from water.
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HF boils at about 20 °C and HCl at about −85 °C, even though HF has fewer electrons. Explain.
Hint 1
Fewer electrons means weaker London forces. So something else must be stronger in HF.
Hint 2
Which of F and Cl is small and very electronegative?
Full answer
HF has 10 electrons and HCl has 18, so HCl has the stronger London forces. But in HF the hydrogen is bonded to fluorine, which is very electronegative (3.98) and small. So HF molecules form hydrogen bonds: the δ+ H of one molecule is attracted to a lone pair on the F of another. Chlorine is too large to do this, so HCl has only London and dipole–dipole forces. The hydrogen bonds are much stronger, so HF boils about 105 degrees higher.
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Butan-1-ol, CH₃CH₂CH₂CH₂OH, and ethoxyethane, CH₃CH₂OCH₂CH₃, have the same molecular formula, C₄H₁₀O. Predict which has the higher boiling point, and explain.
Hint 1
Same formula means the same number of electrons, so similar London forces.
Hint 2
Which one has an O–H group?
Full answer
Butan-1-ol boils higher. Both have the same electrons, so their London forces are similar. Butan-1-ol has an O–H group, so its molecules hydrogen-bond to each other. In ethoxyethane, the oxygen sits between two carbons, so every hydrogen is on carbon: it can accept but cannot donate, and it cannot hydrogen-bond with itself. (Measured values confirm this: butan-1-ol boils far higher than ethoxyethane.)
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Exactly 1000 g of liquid water at 0 °C (density 1.000 g/cm³) freezes. The density of ice is 0.917 g/cm³. (a) Find the volume of the ice. (b) Explain why water pipes can burst in a hard frost. (c) What fraction of a floating block of ice is below the surface of fresh water?
Hint 1
Volume = mass ÷ density. The mass does not change on freezing.
Hint 2
A floating object sinks until the water it pushes aside has the same mass as the object.
Full answer
(a) cm³, about 9% more than the 1000 cm³ of water. (b) A full pipe has no room for the extra 9% of volume. As the water freezes, the expanding ice pushes on the pipe walls with a very large force, which can split the pipe. (c) The ice sinks until it pushes aside its own mass of water. 1000 g of ice pushes aside 1000 g of water, which is 1000 cm³. That is of the ice's volume, so about 92% is below the surface. The fraction is simply the ratio of the densities, .
Hydrogen bonds are strong enough to hold things in shape, and weak enough to let go. Life depends on that balance. The two strands of DNA are held together by hydrogen bonds between their bases: two between each A–T pair and three between each G–C pair. When a cell reads or copies its genes, enzymes separate the strands by breaking these bonds, then the strands come back together. Covalent bonds would be far too strong to open in this way. Hydrogen bonds are not the only thing holding DNA together (the stacking of the flat bases on top of each other is also important), but they decide which base pairs with which.
The same balance shapes proteins, and it gives water the properties that make it the solvent of life. The next lecture brings all three intermolecular forces together, and uses them to explain the physical properties of many kinds of substances.
- A hydrogen bond is an attraction between an H bonded to N, O or F in one molecule and a lone pair on N, O or F in another.
- It needs a donor and an acceptor; hydrogen bonded to carbon is never a donor, so propanone and CH₃F cannot hydrogen-bond with themselves.
- Hydrogen bonds (about 10–30 kJ/mol) are much stronger than other forces between small molecules, but far weaker than covalent bonds.
- NH₃, H₂O and HF boil far above their group trends; water is highest because it makes two hydrogen bonds per molecule, not one.
- In ice, each molecule makes four hydrogen bonds in an open lattice, so ice is less dense than liquid water and floats.