London Dispersion Forces
London dispersion forces are weak attractions between all atoms and molecules that arise from temporary, randomly fluctuating dipoles; they grow stronger as the number of electrons and the size of the molecule increase. In brief: the boiling points of the noble gases rise from 4 K for helium to 165 K for xenon because larger atoms are more polarizable and attract each other more strongly.
Dispersion forces are present in every substance, including nonpolar ones. They are the only attraction between noble gas atoms and between nonpolar molecules such as methane, which is why these substances can be liquefied at all. This article explains how they arise, what controls their strength, gives data on noble gases, halogens and alkanes, and shows how they explain the grip of a gecko.
How do London dispersion forces arise?
The electrons in an atom or molecule are in constant motion. At any instant they may be more on one side of the particle than on the other, which creates a tiny temporary dipole. This instantaneous dipole distorts the electron cloud of a neighboring particle, so that a dipole is induced in it with the opposite orientation. The two temporary dipoles attract each other. The dipoles keep changing, but they stay correlated with each other, so there is a net attraction.
The attraction energy falls off very quickly with distance, in proportion to 1/r6. Doubling the distance between two particles reduces the interaction energy by a factor of 64. The forces therefore act only between particles in close contact.
What determines their strength?
- Polarizability: how easily the electron cloud is distorted. Large atoms with many electrons that are far from the nucleus are more polarizable.
- Molar mass and the number of electrons: these usually go with polarizability, so heavier molecules in a series generally attract each other more.
- Surface area and shape: long, straight molecules can touch each other over a larger area than compact, branched ones.
The strength of dispersion forces ranges from under 1 kJ/mol for helium atoms to tens of kilojoules per mole for large molecules, where there are many contacts.
Noble gases and halogens
| Substance | Number of electrons | Boiling point (K) | Boiling point (°C) |
|---|---|---|---|
| He | 2 | 4.2 | −268.9 |
| Ne | 10 | 27.1 | −246.1 |
| Ar | 18 | 87.3 | −185.9 |
| Kr | 36 | 119.9 | −153.3 |
| Xe | 54 | 165.1 | −108.1 |
| F2 | 18 | 85.0 | −188.1 |
| Cl2 | 34 | 239.1 | −34.0 |
| Br2 | 70 | 332.0 | 58.9 |
| I2 | 106 | 457.6 | 184.4 |
The trend within each group is clear: more electrons and larger size mean stronger dispersion forces and higher boiling points. This is why fluorine and chlorine are gases at room temperature, bromine is a liquid and iodine a solid. Fluorine and argon, which have the same number of electrons, boil at very similar temperatures (85.0 K and 87.3 K).
Alkanes and the effect of shape
| Alkane | Formula | Molar mass (g/mol) | Boiling point (°C) |
|---|---|---|---|
| Methane | CH4 | 16.04 | −161.5 |
| Ethane | C2H6 | 30.07 | −88.6 |
| Propane | C3H8 | 44.10 | −42.1 |
| Butane | C4H10 | 58.12 | −0.5 |
| Pentane | C5H12 | 72.15 | 36.1 |
| Hexane | C6H14 | 86.18 | 68.7 |
| Octane | C8H18 | 114.23 | 125.7 |
The three isomers of C5H12 show the effect of shape: straight-chain pentane boils at 36.1 °C, isopentane (2-methylbutane) at 27.8 °C and the almost spherical neopentane (2,2-dimethylpropane) at 9.5 °C. All have the same molar mass, but the more compact molecules have a smaller area of contact.
How do you compare dispersion forces?
Example 1: which substance boils higher, Br2 or Cl2?
Both are nonpolar. Br2 has 70 electrons and Cl2 has 34, so Br2 has stronger dispersion forces and boils higher (58.9 °C compared with −34.0 °C).
Example 2: which isomer boils higher, hexane or 2,2-dimethylbutane?
Both have the formula C6H14. Hexane is a straight chain with more contact area and boils at 68.7 °C, while the branched 2,2-dimethylbutane boils at 49.7 °C.
Example 3: dispersion forces in polar molecules
Dispersion forces are also important in polar molecules. For HCl, HBr and HI, the dipole moments fall from 1.08 D to 0.44 D, while the boiling points rise (−85, −67 and −35 °C), which shows that dispersion forces dominate in the larger molecules.
Where do dispersion forces matter?
- Gecko feet: a gecko clings to walls by means of millions of tiny hair-like structures called setae on its toes, which make such close contact with a surface that dispersion forces alone support its weight. This was shown by Kellar Autumn and colleagues in 2002.
- Liquefaction of gases: natural gas, mainly methane, becomes a liquid only at −162 °C because of its weak dispersion forces.
- Fuels: gasoline, kerosene and diesel contain hydrocarbons of increasing chain length and boiling point, which are separated by distillation.
- Polymers and waxes: long chain molecules such as polyethylene are solid at room temperature because of the large number of contacts along their chains.
Who explained these forces?
Johannes van der Waals proposed in 1873 that attractions between molecules exist, and the weak forces in general are often called van der Waals forces. The origin of the attraction in nonpolar molecules was a puzzle until 1930, when the physicist Fritz London explained it with quantum mechanics as a result of correlated fluctuations of electrons. He called it the dispersion effect because the same property of molecules, their polarizability, also explains the dispersion of light by a substance.
Which mistakes are common?
- Saying that nonpolar molecules have no attractions: they have dispersion forces.
- Thinking that dispersion forces are always weaker than dipole–dipole forces: in large molecules they can be stronger.
- Judging only by molar mass: shape and surface area also matter.
- Confusing intermolecular forces with covalent bonds: boiling does not break the bonds within the molecules.
- Assuming that the forces are limited to nonpolar substances: they act between all particles.