Gas Laws: Boyle's Law

Core Concepts

In this tutorial, you will learn about Boyle’s law, and how it can be used to determine relationships between changes in pressure and changes in volume in a given closed system.

Topics Covered in Other Articles

Important Things to Consider

The gas law described in this article only applies to ideal gases, which you can read about on our article, The Ideal Gas Law.

Relationship Between Pressure and Volume

Consider a sample of gas in a 1-liter container. From our article, What is Pressure, we know that the pressure exerted on the container from the gas is the sum of the collisions of the particles, divided by the surface area of the container, $F=\frac{\sum F_{col}}{A}$ . We also know that the volume is related to the surface area, and if the volume decreases, the surface area will decrease as well.

From these two relations, we can see that as the volume decreases, the total pressure is going to increase. This leads us to our gas law, $P\propto\frac{1}{V}$ .

We can make a graph of this relationship as follows:

Change in Pressure and Volume

This proportionality can enable us to solve specific problems relating to the changes in pressure and volume in a closed system.

Consider, for example, a piston full of oxygen. From this proportionality, we know that if the piston is compressed, the pressure of the gas will increase.

Example Problem

Here is an example of how you can solve a Boyle’s Law problem.

An ideal gas exerts a pressure of 3 atm in a 2 L container. What will the pressure be if the volume of the container is changed to 1 L at constant temperature?

Solution:

$\begin{align*}P&\propto\frac{1}{V}\\\implies PV&=c\\\implies P_1V_1&=P_2V_2\\\therefore (3\text{ atm})(2\text{ L})&=(x)(1\text{ L})\\x&=\frac{(3\text{ atm})(2\text{ L})}{(1\text{ L})}\\x&=\boxed{6\text{ atm}}\end{align*}$

Gas Laws: Boyle’s Law