Have you ever wondered how an air powered water gun works? It uses the fantastic properties of gases to make a summer day more enjoyable! In this lesson, we will be discussing Boyle’s Law and the relationship between pressure and volume of a gas.

## Boyle’s Law

Johnny Dalton has a very big day ahead of him. He is vacationing on Ideal Island, where all gases behave ideally. Johnny and his family are going to start off the morning by scuba diving around the island. As we follow Johnny during his dive, we will be paying close attention to the role that gases play in this activity.

More specifically, we will be seeing how **Boyle’s Law** helps us explain and predict some of the behaviors of gases.Johnny puts on his wetsuit and tank and jumps into the water. As he lowers himself under the surface of the water, he feels a little pressure in his ears, so he plugs his nose and swallows to equalize them.

The reason he is feeling that pressure is because the surrounding water is pushing in on his ear. The deeper he gets, the more water pushes on his ears, which causes even more pressure to be put on his ears. As that pressure increases on the outside of his ear, the air inside the ear gets squished and the volume inside decreases. The air doesn’t go anywhere, it just gets squeezed together, which causes that uncomfortable feeling he had before he equalized. When a scuba diver descends, he will need to let some of the air inside the ear out, which reduces this pressure.

This is usually done by pinching your nostrils and trying to blow gently out your nose. If you try it right now, you may hear a little popping sound. That’s the sound of air going in or out of your ear!Another thing Johnny notices as he descends is that his buoyancy compensator (which is just a vest filled with air) is getting smaller and smaller! Even his wetsuit is shrinking! What is causing this? Well, a scientist named Robert Boyle discovered that the pressure on a gas and its volume are inversely proportional to each other. This works for any closed system of gas, such as the inside of your ear, the buoyancy compensator, or even the thousands of tiny bubbles embedded in a neoprene wetsuit. If the temperature is held constant, the pressure of a gas increases as its volume decreases. The reverse is also true; as the pressure of a gas decreases, its volume increases.

This is **Boyle’s Law**.

Now, as Johnny was lowering himself under the water, all of those little ‘containers’ of gas got smaller. The reason they did lies in the **Kinetic Molecular Theory**, which we previously covered.

One thing the kinetic molecular theory states is that gas particles are very far away from each other. This distance allows for the compression of gases. If the particles are far apart, they have room to move closer together.

If the particles are already close together (like they would be in a liquid or solid), there is very little room for compression. Now we also know that gas particles move randomly and rapidly, and each time they collide with the walls of their container, they apply a little bit of pressure. If we keep the same number of particles in a container, all with the same kinetic energy, but we decrease the size of the container, the particles will more frequently hit the walls of that container, causing the pressure to increase.

## Boyle’s Law Examples

Just like in Avogadro’s Law, this can be represented in the form of an equation: **P1 V1 = P2 V2**. We use 1s and 2s to indicate the status before and after a change has taken place. Also, the units for pressure and volume don’t matter as long as they are the same for pressure and the same for volume. So, let’s say you have a 1 liter balloon at sea level (which is 1 atmosphere).

If we were to release the balloon and allow it to float up to an altitude where it only experiences 0.5 atmospheres, what will happen to the volume? Well, we can think about it logically: if the pressure is decreasing by half, the volume will double. Or we can plug numbers into this equation. Our initial pressure is 1 atmosphere, and our initial volume is 1 liter. The final pressure is 0.5 atmospheres. So, if we solve for V2 – the final volume – this gives us 2 liters.

Let’s try another example. If Johnny’s air-filled scuba vest holds 1.43 liters of air at 1.03 atmospheres of pressure, what volume of air will it hold at 10 meters underwater, which is equivalent to about 2.03 atmospheres? To solve this, we will start with our equation.

The initial pressure times the initial volume equals the final pressure times the final volume. Our initial pressure is 1.03 atmospheres and our initial volume is 1.43 liters. Our final pressure is 2.03 atmospheres and our final volume is unknown.

If we isolate V2, we find that it is equal to (1.03 * 1.43) / 2.03, which is equal to 0.

726 liters! That should make sense because the pressure increased, so the volume should decrease.

## Lesson Summary

As Johnny is finishing his scuba diving adventure, he needs to make sure that he does not hold his breath as he ascends. If he doesn’t let some air of his lungs as he swims to the surface, he could damage his lungs. This is because there is less pressure pushing on his lungs as he moves toward the surface. As the pressure on his lungs decreases, the volume of the gas in his lungs increases, which can cause a dangerous situation. All of this applies **Boyle’s Law**, which states that as long as the temperature is held constant, the pressure and volume of a gas are inversely proportional to each other. Meaning, if one increases, the other one decreases.

Often the equation **P1 V1 = P2 V2** is used to make calculations involving Boyle’s Law.

## Learning Outcomes

At the end of this video, you’ll be able to:

- Explain Boyle’s Law
- Apply the Boyle’s Law equation to solve pressure and volume problems