# 18.26 Diffusion

In post 16.37, we saw that the molecules in a liquid or a gas are free to move; in a gas they are free to move anywhere, in a liquid they are free to move anywhere below the surface.

Now let’s think about what happens when we add a coloured liquid to a transparent liquid, like water. I am assuming that the two liquids are free to mix and don’t behave like a drop of oil added to water (post 16.48). The colour spontaneously starts to spread and eventually the whole liquid looks the same.

The pictures shows warm water surrounding a tea bag. The colour begins to spread spontaneously out of the bag (A). More spreads out of the bag (B) until all the water is evenly coloured (C).

We call this spontaneous mixing diffusion.

We also know that diffusion occurs in gases – because smells spread in the air.

Spontaneous mixing of molecules in liquids and gases isn’t surprising. Molecules can move randomly in a liquid or a gas. At temperatures above the minimum possible value of 0 K, the liquid or gas has heat energy (post 16.38). Since heat is the kinetic energy of molecules (or atoms), the molecules in a liquid or gas are constantly moving (post 16.35). It is highly improbable the molecules in our coloured liquid will all move together, as explained in post 16.35. This tendency for the coloured molecules to move apart, because it is so unlikely for them to stay together, is equivalent to saying that the entropy of the system is increasing, as explained in post 16.35 and (in more detail) in post 16.38. According to the second law of thermodynamics, spontaneous changes in a closed system occur to increase its entropy (posts 16.34, 16.35 and 16.38). So we can consider diffusion to be a consequence of the second law of thermodynamics.

Can diffusion occur in solids? Remember that the atoms are not free to move anywhere in a solid (post 16.37). But, at temperatures above 0 K, they do have kinetic energy – so they’re not stationary (post 16.38). In a crystalline solid, they vibrate around their positions in the crystal lattice (post 16.37) – they behave like simple harmonic oscillators (posts 18.6 and 18.7), like an object bouncing on a spring (post 18.11). However, diffusion can occur in solids – for example if gold and lead are in contact, gold atoms will slowly diffuse into the lead.

How can one solid diffuse into another? The idea that atoms in a crystal are perfectly arranged in a regular three-dimensional structure (post 16.37) is a model (post 18.6) that helps us to explain the properties of a solid. Simplifying, by ignoring unnecessary complications, is what helps us to explain how real things work (posts 16.42 and 18.6). The trick is to simplify without oversimplifying (post 16.42). For example, the motion of a pendulum can be explained by treating it as a simple harmonic oscillator (posts 18.6 and 18.7). A simple harmonic oscillator never dissipates energy. Of course, a pendulum will eventually dissipate energy, because of the viscosity (post 17.17) of air. But its frequency of oscillation can be explained by the simple harmonic oscillator model until it stops moving.

So, when we try to explain diffusion of gold into lead, we will have to complicate the perfectly regular model for the arrangement of atoms in a crystal. This is the same idea as the process of diminishing deception, used in teaching science (post 17.25). The irregularities in a real crystal structure are called defects. For example, a gap in a crystal structure that we would expect to be filled by an atom is a type of defect called a vacancy. If gold atoms have enough kinetic energy, they can move into vacancies in lead.

In conclusion, atoms and molecules are moving randomly at any temperature above 0 K, the minimum temperature possible (post 16.38). It is so improbable that all these randomly moving molecules will move together, that molecules of different molecules will spontaneously mix together – this mixing is called diffusion. Diffusion can be clearly detected in gases and liquids because of the freedom of movement of their molecules. Diffusion can sometimes be observed in solids.

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