# Brownian Motion: Definition & Examples

Instructor: Stephanie Bryan

Stephanie has a master's degree in Physical Chemistry and teaches college level chemistry and physics.

In this lesson, we will look at some basic ideas about how gas and liquid molecules move and how these simple movements give rise to Brownian motion which allows molecules to diffuse and fill a container.

## Brownian Motion

Someone sprays a bottle of perfume across the room and a few seconds later you start to smell the perfume in the air. Have you ever wondered how the perfume molecules traveled to your nose? Or have you put a drop of food coloring in a glass of water? It will spread out without any stirring at all, eventually filling the whole glass with color. Both of these occur because of Brownian motion.

## The Structure of Gases and Liquids

Before explaining Brownian motion, it is important to understand the structure of gases and liquids and how molecules in gases and liquids move. Gases are dilute, meaning their molecules are far apart compared to their small size. Luckily they aren't far apart compared to our size or we would be running around trying to breathe! Gas molecules move in straight lines until they hit another molecule and then they move off in a different direction, again until they hit another molecule. A box of gas molecules is like a box of tiny floating billiard balls colliding in three dimensional space, rather than on a two dimensional table.

Unlike gases, liquids are not dilute. They are much more concentrated and do not take up the entire volume of their container. Liquid molecules move in a similar manner to gas molecules, moving in straight lines until they collide with another molecule. However because they are more condensed and closer together, the liquid molecules don't travel very far before they collide and change direction. For a visualization of this motion, see the figure below.

Figure 1.The blue molecule is moving through a gas or liquid of smaller molecules.

## Brownian Motion

Now that we know how molecules can move in a liquid or gas, we can think about how this motion adds up over time. If we follow the motion of one molecule through a liquid or gas, it goes on a random walk. You can try to simulate this behavior at home. You just need a die. Roll the die and walk the number of steps on the die. This is the molecule traveling in a straight line. Then roll the die again and this time turn 60 degrees clockwise for every number on the die. This is the molecule changing direction due to a collision. Now start the process over and repeat. You are going on a random walk. This is the way a liquid or gas molecule moves and is called Brownian motion. Computers can simulate this motion as well. We can see the results of a computer simulated random walk in figure 2.

Figure 2. Brownian motion of a molecule can be described as a random walk where collisions with other molecules cause random direction changes.

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