Video: Diffusion

In this video, we will learn about diffusion in gases and liquids, and explain the irregular way that particles move known as Brownian motion.

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Video Transcript

In this video, we will learn about diffusion in gases and liquids and explain the irregular way that particles move around, known as Brownian motion. A drop of ink in water, smoke in air — what do these have in common? They both demonstrate diffusion. Particles of ink will naturally spread out in water until the water is evenly colored, until the mixture is homogeneous. Meanwhile, thick smoke disperses like it has a mind of its own. But what’s really going on?

In order to understand what’s happening, we need to appreciate that ink, water, smoke, and air are made of particles constantly in motion. Before we go any further, it’s important to mention that the way particles behave is very complex. And we often have to simplify things to be able to do the math.

Real particles have fuzzy edges and can have odd shapes and meaningful attractive and repulsive forces between them. To make things easier, we often pretend that particles are hard spheres like billiard balls that behave in simple, predictable ways when they collide. We assume that particles don’t attract or repel one another and only interact when they collide.

Another assumption we make is that there’s no such thing as potential energy, only kinetic energy. Real particles have attractive forces between them, which gives them potential energy. In the ideal scenario, we ignore bonds and vibrations. And the only energy we have is the energy of the particles moving around. And when particles collide, we assume that kinetic energy is always conserved. The total kinetic energy of the particles before a collision is always the same as the kinetic energy after the collision. This type of collision is called an elastic collision.

We know that this model is not 100 percent true. But it’s often close enough to the truth that the model produces excellent results in a much easier fashion. In this video, we’re going to treat every particle like a hard sphere. A gas where all the particles are behaving ideally is an ideal gas. They only interact when they collide, and they collide elastically. While liquids aren’t ideal gases, for the purposes of looking at diffusion, we can think of liquids as very dense ideal gases.

Now let’s have a look at some particle collisions. Here we have two ideal particles, particle A on the left and particle B on the right. Let’s imagine that particle B starts off as stationary, and let’s imagine that particle A is on a collision course with particle B. Particle A slams into particle B. When they collide, some or all of the kinetic energy of particle A is transferred to particle B. So particle B rockets off.

Now let’s imagine we have more of particle A around. In some collisions, particle B may lose energy. Over time, particle B will have an average speed, which we can predict. Now let’s imagine that B is surrounded by lots of particle A. There will be lots of collisions. B will bounce around in all directions, sometimes moving fast, sometimes moving slow. Remember, this will take place in three dimensions, not just the two that I can draw here.

The path that particle B takes is chaotic, sometimes called random. It’s nearly impossible to tell where the particle will be at any one time. But we can predict roughly how it will behave on average over time. When looking at gases or liquids, this chaotic walk has a special name.

Brownian motion, named after Robert Brown, is the chaotic motion of particles suspended in a fluid, a liquid or a gas, because of collisions with other particles. Brownian motion happens with big particles like smoke in air or small particles like molecules of water. If you collect some smoke from a candle and view it under a microscope with some extra light, you might be able to see individual smoke particles, shining like glitter. These particles will look like they’re moving at random. But actually, what’s happening is that there are thousands of collisions going on at an atomic level that moves the particles around chaotically.

On the small scale, Brownian motion may seem pretty boring. Particles move around a bit. So what? On the large scale, Brownian motion is the reason for so much more interesting behavior.

Let’s have a look back at our first example, ink mixed with water. Here we have three situations. The mixture just after the ink is added, a little time later, and a long time later. What’s the difference? Over time, the particles of ink spread out. And eventually, it looks like nothing is going to change. Once the ink is evenly distributed, the color doesn’t change anymore. No matter how long you wait, you won’t see the mixture separate again. Our mixture of ink and water will never spontaneously unmix. You’ll never have that concentrated drop of ink we had at the beginning. This is an example of diffusion.

Diffusion is the overall movement of particles from a region with lots of particles to a region with fewer particles in a gas or a liquid. In areas with a higher concentration of ink, the tendency is for particles to move out into the lower-concentration areas. This is all because of probability. It’s more likely on average for particles to spread out than it is for them to become more concentrated.

For diffusion to occur, there need to be other types of particle to bump into. For smoke particles, there are atoms and molecules in the air that constantly bombard them, forcing them to spread out. For ink in water, there are water molecules doing the same job. It’s important to realize that diffusion is not the same thing as evaporation or condensation.

The last thing we need to look at is what factors affect how quickly diffusion occurs. There’s a very simple rule. The faster the particles are moving overall, the faster they will diffuse. Particles will move faster if they are lighter or they have more energy. So molecules with a higher mass will diffuse more slowly than molecules with a lower mass. And the same particle in the same circumstance will diffuse faster if it gets warmer. This is one of the reasons why you might smell more things on a hot day than a cold day, although evaporation and convection do play a large part.

Now that we’ve looked at what diffusion is and where it comes from, let’s have some practice.

Which of the following statements could describe particles moving with Brownian motion? (A) Vibrating particles suspended in a liquid. (B) Randomly moving particles suspended in a liquid or gas. (C) Randomly moving particles suspended in a solid. (D) Vibrating particles suspended in a liquid or gas. Or (E) vibrating particles suspended in a solid.

Brownian motion is the chaotic or random way a particle moves due to collisions with particles of a liquid or gas. Every time a particle hits another particle, it loses or gains some energy and changes direction and speed. When we model particles and try and understand Brownian motion, we usually have to make them ideal hard spheres because it’s too complicated to do the math if we take their full shape into account. We also assume that there are no internal bonds. We assume just one lump which isn’t vibrating and isn’t rotating.

Since Brownian motion deals with the movement of particles and not vibrations, we can eliminate the options that mention vibrating particles. Option (C) says that we could describe particles moving with Brownian motion as randomly moving particles suspended in a solid. However, Brownian motion only occurs in a fluid, a liquid or a gas. And in solids, particles vibrate on the spot and don’t move overall. So our final answer is that particles moving with Brownian motion are randomly moving particles suspended in a liquid or gas, although you can refer to this as chaotic.

Now let’s have a look at a more practical scenario.

Which of the following statements correctly describes a difference between two diatomic gases, nitrogen N2 and chlorine Cl2? (A) Nitrogen diffuses more slowly than chlorine as its molecular mass is smaller. (B) Nitrogen diffuses more slowly than chlorine as it is less reactive. (C) Nitrogen diffuses more quickly than chlorine as its molecular mass is bigger. (D) Nitrogen and chlorine diffuse at the same speed. Or (E) nitrogen diffuses more quickly than chlorine as its molecular mass is smaller.

The five statements contain references to diffusion, molecular mass, and reactivity. Let’s have a look at what these mean. Diffusion is the overall movement of particles from an area where they’re at high concentration to an area where they’re at low concentration. You can see diffusion happening when you add ink to water. The individual particles of ink spread out until all the water is the same color.

The molecular mass is simply the mass of a single molecule. And it’s usually measured in unified atomic mass units.

And lastly, reactivity is the measure of the potential of substance to react. Reactivity isn’t generally given a number. It usually depends on the context. But there are substances like chlorine which are generally described as more reactive than nitrogen.

So statement (B) suggests that nitrogen diffuses more slowly because of its lower reactivity. Nitrogen is less reactive than chlorine because nitrogen has a strong triple bond. Whereas chlorine has a weaker single bond and it reacts readily to form chloride ions. But the question is, does the lower reactivity of nitrogen make it diffuse more slowly?

We’ll come back to that in a moment. First, let’s have a look at molecular mass. We can see the atomic mass of nitrogen from our periodic table is 14.007 unified atomic mass units. And we can calculate the molecular mass of nitrogen by multiplying that by two, giving us 28.014 unified atomic mass units. Again, going back to our periodic table, we can see the atomic mass of chlorine is 35.45 unified atomic mass units. Therefore, the molecular mass of chlorine, Cl2, is 70.90 unified atomic mass units. We can see from these numbers that the molecular mass of chlorine is much greater than the molecular mass of nitrogen.

Statement (C) says that nitrogen diffuses more quickly than chlorine as its molecular mass is bigger. We can dismiss this option straightaway because we know nitrogen has a smaller molecular mass than chlorine. This just leaves us a simple question. How do molecular mass or reactivity affect diffusion?

Well, diffusion is driven by Brownian motion. Brownian motion is a seemingly random movement of a particle in a sea of other particles. Every time the particle changes direction and speed, it’s because it’s collided with another particle. And it’s very difficult to predict how these collisions will occur and the consequence on the path of the particle. But what we’re talking about is diffusion, not Brownian motion. So what’s the importance of Brownian motion to diffusion?

Well, simply because of probabilities, it’s more likely for particles to spread out than it is for them to come together because of Brownian motion. So if we have two tiny pockets, one of pure nitrogen gas and one of pure chlorine gas, in another gas, we would expect those pockets to expand and for the particles to intermingle with the surrounding gas. The question is, which one would diffuse the fastest?

Well, there’s a simple principle. If a particle is lighter and it has the same amount of kinetic energy, it must be moving faster. If a particle is moving faster overall, it will diffuse more quickly. It will still follow Brownian motion, but it will move between each collision more quickly. From this, under the same conditions, we’d expect a molecule of nitrogen to move faster and diffuse faster than a molecule of chlorine. So we can eliminate option (D) because nitrogen and chlorine will diffuse at different speeds, nitrogen faster than chlorine.

We can also dismiss option (B) because, a, nitrogen diffuses more quickly than chlorine and the reactivity of nitrogen relative to chlorine doesn’t affect how it diffuses. Diffusion is about motion of individual particles, not how they react. Option (A) says that nitrogen diffuses more slowly than chlorine as its molecular mass is smaller. The molecular mass of nitrogen is smaller than chlorine, but that makes it diffuse faster, not more slowly. And what we’re left with is the correct answer. Nitrogen diffuses more quickly than chlorine as its molecular mass is smaller.

Now let’s have a look at the key points. Particles in a liquid or gas are constantly moving and colliding. You might see liquids and gases lumped together in a category called fluids. Particles in a liquid or gas move around in a chaotic way because of all these collisions. Particles in a liquid or solid will naturally move from regions of higher concentration to regions of lower concentration. Diffusion occurs because of Brownian motion. And finally, the rate of diffusion is higher for lighter particles or at higher temperatures.

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