Lesson 7 · 30 min

Intermolecular forces

Dispersion, dipole forces and hydrogen bonds decide the temperature at which a substance boils — from the anomalous hydride boiling points to the shallow well of the Lennard-Jones potential.

In this lesson

Tell dispersion forces, dipole–dipole forces and hydrogen bonds apart, and say where each comes from
Explain boiling-point trends of hydrides and noble gases with molecular size (polarisability)
Explain the anomalous boiling points of NH₃, H₂O and HF with hydrogen bonding
Read the strength and range of an intermolecular attraction off the Lennard-Jones potential and compare it with a chemical bond

Water has a molar mass of only 18, yet it boils at 100 °C; hydrogen sulfide is heavier (34) but boils at −60 °C; methane (16) must be chilled to −162 °C to liquefy. If water behaved like its group relatives, it would boil somewhere around minus ninety degrees — and Earth would have no liquid oceans. Boiling points are set not by chemical bonds but by the far weaker attractions between molecules.

Predict first

Following the trend of H₂S, H₂Se and H₂Te backwards, at roughly what temperature “should” water boil?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

About +150 °C About +100 °C About −90 °C About −200 °C

Three kinds of intermolecular force

Dispersion (London) forces: every molecule’s electron cloud fluctuates constantly; a momentary asymmetry creates an instantaneous dipole that induces an aligned dipole in a neighbour, and the two attract. Dispersion acts between all molecules and grows with the number of electrons and with how easily the cloud is distorted (polarisability). That is why the boiling points of the noble gases and the group 14 hydrides climb steadily down the table.
Dipole–dipole forces: the positive end of one polar molecule attracts the negative end of its neighbour, as in HCl. They add to dispersion.
Hydrogen bonds: when H is bonded to strongly electronegative N, O or F, the hydrogen is left almost as a bare proton, strongly attracted to a lone pair on N, O or F of another molecule: X–H···Y. At roughly 10–40 kJ/mol, hydrogen bonds are the strongest intermolecular forces, and they are directional.

With these three forces the hydride chart makes sense: group 14 (CH₄ to SnH₄) has only dispersion and rises smoothly; the heavier hydrides of groups 15–17 are dominated by dispersion too and also rise down each group; only the period-2 compounds NH₃, H₂O and HF can hydrogen-bond, and they leap upward. Water’s excess is the largest because each molecule has two H atoms and two lone pairs and can join up to four hydrogen bonds, knitting a three-dimensional network.

How strong? The Lennard-Jones potential

Two noble-gas atoms feel only dispersion attraction and short-range repulsion. Their potential curve is usually described by the Lennard-Jones potential: an attraction falling off as $r^{-6}$ at long range (the form of the dispersion force) and a steep $r^{-12}$ wall standing in for the repulsion of overlapping clouds. Two parameters describe a gas: the well depth ε and the collision diameter σ.

V(r) = 4\varepsilon\left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right],\qquad r_\text{min} = 2^{1/6}\sigma

The Lennard-Jones 12-6 potential: its minimum lies at

2^{1/6}\sigma

with depth ε.

$\varepsilon$: well depth (argon: ε/k = 119.8 K, about 1.0 kJ/mol)
$\sigma$: distance where V = 0 (argon: 340.5 pm)
$r$: distance between the two molecular centres

Attraction and repulsion between two molecules

Lennard-Jones potential

Well depth ε/k 120 K = 0.996 kJ/mol Collision diameter σ 341 pm

Separation (or click the chart) 460 pm

Total
Repulsion ∝ r⁻¹²
Dispersion ∝ r⁻⁶

Distance: 460 pm
Energy: −0.548 kJ/mol
Force: attractive

Minimum at 2^(1/6)σ: 382 pm
Well depth ε: 0.996 kJ/mol
Thermal energy RT (298 K): 2.48 kJ/mol
Compare: the H–H covalent well: 458 kJ/mol ε is 1/460 of it
Boiling point estimated as T_b ≈ 0.73·ε/k: 88 K
Measured boiling point: 87.3 K

Noble gases: boiling point over ε/k
He	0.41
Ne	0.76
Ar	0.73
Kr	0.70
Xe	0.75

Helium’s zero-point motion rivals its well depth: a quantum exception.

Argon’s well is only 1 kJ/mol deep — less than 1/400 of an H–H covalent bond, and smaller than RT at room temperature (2.5 kJ/mol). Switch to He, Ne, Kr and Xe: the deeper the well, the higher the boiling point, and the ratio T_b / (ε/k) hardly changes (helium excepted). Or drag the sliders to design a “gas” of your own.

Energy scales (kJ/mol)
Interaction	Typical energy
Lattice enthalpy of NaCl	787
H–H covalent bond (D₀)	432
Hydrogen bond (water dimer)	≈ 21
Thermal energy RT (298 K)	2.5
Ar–Ar dispersion (ε)	1.0

Source: Values from this unit’s kernels (Born–Haber cycle, Huber & Herzberg, Hirschfelder–Curtiss–Bird); water-dimer well depth ≈ 5.0 kcal/mol from high-level calculations consistent with B. E. Rocher-Casterline et al., J. Chem. Phys. 134, 211101 (2011).

Worked example

Ranking four boiling points

Without a table, rank Ne, CH₄, HCl and H₂O from lowest to highest boiling point, and justify the order.

Concept check

An F–H···F hydrogen bond is stronger than O–H···O, so why does water (100 °C) boil so much higher than HF (19.5 °C)?

Water has the larger molar mass Water has a much larger dipole moment Each water molecule can join about four hydrogen bonds, an HF molecule only about two HF has no hydrogen bonds at all

Try the calculation

Argon’s Lennard-Jones σ is 340.5 pm. How far apart are two argon atoms at the energy minimum?

Key takeaways

There are three intermolecular forces: dispersion between all molecules, dipole–dipole forces between polar molecules, and hydrogen bonds when H is bonded to N, O or F.
Dispersion grows with the number of electrons and polarisability, so boiling points usually rise down a group.
NH₃, H₂O and HF boil far above their groups’ trends because of hydrogen bonding; water’s network is the most extensive.
Intermolecular attractions are two to three orders of magnitude weaker than chemical bonds: argon’s well is about 1 kJ/mol, the H–H bond about 430 kJ/mol.

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Data and references

W. M. Haynes (ed.), CRC Handbook of Chemistry and Physics, 97th ed., and The Merck Index (via PubChem): boiling points of the hydrides.
J. O. Hirschfelder, C. F. Curtiss, R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, 1954): Lennard-Jones parameters.
F. London, “The general theory of molecular forces”, Trans. Faraday Soc. 33, 8 (1937).
IUPAC Recommendations 2011, “Definition of the hydrogen bond”, Pure Appl. Chem. 83, 1637 (2011).