Diffusion

One of the things we learn early on in chemistry is the concept of diffusion, or the fact that things tend to mix evenly when possible. For instance, think about a bucket of water with a separator. Half the bucket is salt water, and the other half is sweet water. If we remove (slowly, so as to avoid currents) the separator, we don’t expect the salt to stay on one side. After a while, we expect the salt to be evenly distributed. That’s diffusion.

The thing to get here isn’t that diffusion happens; everyone knows that. It’s to figure out how it happens. After all, salt water is water with a bunch sodium and chorine ions floating around in it. And ions have no sense of self, don’t understand “concentration”, don’t understand “mixing”, or “evenly distributed”, or any of those concepts. So how do they naturally migrate into a state they have no understanding of?

Solutions

Before we tackle that question, let’s remember something about atoms and molecules, which is that they are always moving. Whether in a diamond or in air, atoms and molecules vibrate or whiz about, because they have some amount of energy. The difference between ice, liquid water, and vapor is how much the molecules are moving. In ice, they are vibrating but otherwise stuck to each other in a predefined position. In vapor, they are freely moving at tremendous speeds.

In the case of liquid water, they are still moving around, but don’t have enough energy to escape gravity (or one another, since water tends to attract itself). They bump into each other and generally mill about.

Now suppose we add a sodium ion at one specific point in a glass of water. Like the water molecules, it moves around randomly, buffeted by them. Where would you expect this randomly moving ion to end up in the glass? The answer is nowhere in particular. We have no way, after putting the ion in the water, of knowing where it is; it will keep moving all around the glass.

Okay, that’s one ion. What about a few billion of them? It’s equally impossible to predict where they are going to end up. But they all have to end up somewhere in the glass, and there’s no reason they’ll all end up clumped together—therefore, since there’s a few billion of them, there are likely to be quite a few in any given bit of water. So it’s not that salt knows how to spread itself evenly. It’s that spreading evenly is what happens when things move around randomly.

If you’re having trouble seeing that, imagine a room full of blindfolded people in black, milling around. Add to them a small amount of people in red, also blindfolded. If they walk around talking to each other and don’t know the color of their clothes, there’s no reason for people wearing black to cluster together and people wearing red to cluster together. So over time, you’d expect people in red to be evenly distributed in the room. That’s exactly what happens when something dissolves.

Diffusion

Diffusion is an extension of that. Going back to the room with the blindfolded people, imagine there were two rooms instead: the one we’ve been talking about, and another one with blindfolded people who are only wearing black. Now imagine the wall between the rooms disappears. No one is told this, they just continue chatting. The people that were close to the wall in both rooms are going to start talking to each other, and slowly there will be intermingling. Once again, there’s no reason for the people wearing red to know or care what room they’re in; they’ll just continue mingling. After some time, you’d expect them, once again, to be evenly distributed in the room.

Going back to molecules, that’s what happens when you remove the separator in the bucket. All the molecules continue to bounce around; since there’s more water, there’s more space for the molecules to go, and eventually the water molecules are perfectly mixed. Likewise for the ions: there is no difference between a water molecule from the salt water and one from the unsalted water; the ions just bounce among water molecules. Eventually, they will be evenly distributed because that’s what randomness does.

• • •

So that’s how I got diffusion: really understanding that randomness leads to even distribution. There’s no knowledge required on the part of the molecules. And while it seems fairly obvious, it’s incredibly important to understand, because diffusion underlies a lot of biological processes.

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