# Boyle's Law

On Earth, matter exists in one of three states: solid, liquid, or gas. Matter in each state exhibits distinct characteristics. Gases, for example, do not have a fixed volume* or shape. As a result, gases respond to pressure changes by changing their volume. In other words, gases are compressible. In contrast, liquids and solids are not compressible: their volume does not change in response to changing pressure. This difference in compressibility is the reason air-filled spaces in our ears “pop” during airplane takeoff and landings while the liquid-filled spaces in our bodies do not.

Boyle's law* describes the relationship between pressure and volume at a constant temperature for a fixed mass* ( i.e., number of molecules) of a gas.

To understand Boyle's law, it helps to visualize the behavior of gas molecules in an enclosed space. In a closed gas-filled container, individual molecules of the gas are constantly bouncing off the container walls. Each time a gas molecule hits a wall, it imparts a force on that wall.1 In a flexible container such as a balloon, the force of the molecules hitting the balloon walls keeps the balloon inflated. The force of each impact is small, but the sheer number of collisions creates enough force to prevent the balloon from collapsing.2

Pressure in a closed container changes if

1. temperature changes
2. number of molecules increases or decreases
3. volume changes
Boyle’s Law deals with number 3; the relationship between volume and pressure when both of the other two factors remain constant.

According to Boyle’s Law, the amount a gas will compress is proportional to the pressure applied. Its mathematical expression is:

P1V1=P2V2

Where, P1 is the pressure of a quantity of gas with a volume of V1 and P2 is the pressure of the same quantity of gas when it has a volume of V2. The formula shows that if nothing else changes, the volume of a given mass of gas is inversely proportional to the pressure applied to it. This relationship is linear, if pressure on a gas doubles, its volume decreases by 1/2. An alternative expression of the law is:

PV = C

The product of the volume (V) and pressure (P) equals a constant (C).

The relationship between pressure and volume results from the influence volume has on the rate at which gas molecules collide with the container walls. If the volume decreases - causing pressure to increase - the molecules encounter the container walls more often. This is true even though the speed (temperature) of the individual molecules has not changed. Conversely, if volume increases, both the rate of collisions and the pressure decreases.

The following illustration shows this relationship with a container of gas with a fixed temperature and number of molecules.

Test your understanding of the concepts with Concept and Calculation practice problems.

Video demonstration:

1This is Newton’s third law of motion which states that when two objects interact, they exert equal and opposite forces on each other. When gas molecules collide with the wall both the wall and the particle experience the force of the impact. 2A typical party balloon has a volume of 10 to 15 liters. Fully inflated it contains approximately 3×1023 molecules of air. At normal* room temperature, these air molecules are moving at about 300 to 500 m/s. At these speeds, each molecule hits the walls of the balloon thousands of times a second.

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