Earlier we used boiling points of substances as a way to compare the strengths of attractive forces between molecules (London forces (LDFs), dipole-dipole forces, hydrogen bonds). We now explore that idea in more detail.

When a liquid boils, molecules become much farther apart in the gas phase than they were in the liquid phase. Because of intermolecular attractive forces, the energy of a pair of molecules is lower when the molecules are close together than when they are farther apart. For example, consider argon, which boils at 87.3 K (−185.8 °C). The figure in the activity below shows how the potential energy of two argon atoms varies with distance between their atomic nuclei.

Now think about what happens when argon boils. In the gas phase, nearly all the molecules are much farther apart than 800 pm, so the attractions between them are negligible. In the liquid phase, the molecules are 350–450 pm apart and almost every molecule is surrounded by many other molecules at distances less than 600 pm. Separating two molecules requires that the molecules have at least enough kinetic energy to go from −1.16 kJ/mol on the potential energy curve (distance of 377 pm) to 0 kJ/mol on the curve (distance of >800 pm). For a pair of molecules 377 pm apart, 1.16 kJ/mol (or 1.93 × 10^-21 J per molecule) is required to separate the molecules. At any given instant, each molecule in the liquid is surrounded by about a dozen other molecules at distances ranging between 350 and 450 pm. The situation is more complicated than for just two molecules and the energy required is greater: it takes 6.4 kJ/mol (or 1.06 x 10⁻²⁰ J per molecule) to vaporize a sample of liquid argon.

The energy of all the molecules in 1 mol gaseous argon is 6.4 kJ greater than the energy the molecules had in the liquid phase at the same temperature. This difference is the result of attractive forces (London dispersion forces) that cause the energies of molecules that are close together in the liquid phase to be less than the energies of molecules that are far apart in the gas phase. It follows from the law of conservation of energy (also called the first law of thermodynamics) that, because the energy of the gas-phase molecules is greater than the energy of the liquid-phase molecules, energy must be transferred to the argon from somewhere else as the argon vaporizes.

Distribution of Molecular Energies

As you can see from the simulation of argon gas, molecules are in constant motion. At a given instant, some molecules are moving fast and others are moving slowly. That is, there is a distribution of speeds of the molecules. Because kinetic energy is proportional to the square of molecular speed, there is also a distribution of molecular energies: some molecules have much greater energies than others. The temperature of a sample of matter is proportional to the average energy over all these different molecular energies.

When a sample of liquid argon boils, bubbles of argon gas form within the liquid and rise to the surface. (The same applies to boiling water or any other liquid.) Consider a single argon atom (or a single molecule of any liquid). In both liquid and gas the energy of any individual molecule changes continually as a result of collisions with other molecules: sometimes the molecule’s energy is low, sometimes it is high. If an argon molecule’s energy is equal to or higher than 6.4 kJ/mol, the molecule has enough energy to overcome the attractions toward other molecules that surround it; if the molecule is at the surface of the liquid, then it can transfer from liquid phase to gas phase. However, only those molecules with sufficient energy can escape; that is, only high-energy molecules transfer from liquid to gas phase.

During our discussion of boiling argon, you may have thought, “How did someone find out that it takes 6.4 kJ/mol to separate argon molecules from liquid to gas phase?” Such information is obtained by measurements that involve instruments known as calorimeters. The next section explores such measurements in more detail.