Boyle's Law Equation, Example & Problems

Ryan Guenthner, Kristin Born
• Author
Ryan Guenthner

Ryan Guenthner holds a BA in physics and has studied chemistry and biology in depth as well. Has has also been a STEM tutor for 8 years.

• Instructor
Kristin Born

Kristin has an M.S. in Chemistry and has taught many at many levels, including introductory and AP Chemistry.

Examine Boyle's Law. Understand the inverse relationship between pressure and volume through Boyle's Law equation. See real-life applications of Boyle's law. Updated: 10/21/2021

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What is Boyle's Law?

Consider an enclosed system filled with an ideal gas, which is held at a constant temperature. Imagine that the size of the box can be freely adjusted without affecting the temperature, or allowing any gas to escape or enter. What happens to the pressure of the gas as the size of the box is adjusted? What would happen to the volume of the box if a pump was used to change the pressure of the gas? The answer to these questions is given by the mathematical relationship known as Boyle's law.

Boyle's law describes the relationship between the pressure and the volume of an ideal gas which is being held at a constant temperature in an enclosed system, meaning the number of gas molecules is constant. It states that the product of the pressure and volume of an ideal gas must be constant, which implies the relationship between pressure and volume is inverse. This means that at a constant temperature if either pressure or volume is increased, the other quantity must decrease, or vice versa.

The relationship between volume and pressure provided by Boyle's law can also be understood through the kinetic molecular theory of gases (KMT). One of the assumptions needed to apply KMT is that all gas particles in a system have the same kinetic energy, whose value is temperature-dependent. This means if the temperature of the system is held constant, then the kinetic energy of the particles is constant as well. Pressure is defined as the force per unit area. The pressure a gas exerts on the walls of a container is due to the gas particles colliding with the walls of the container. Imagine again a freely adjustable box filled with an ideal gas held at a constant temperature. If the volume of the box is reduced, then the distance each molecule must travel to collide with a wall is reduced as well. Each molecule will collide with the container walls more frequently, thereby imparting more pressure overall. Similarly, by increasing the volume of the box, the distance between walls increases, less frequent collisions will occur, and therefore a lower pressure in the system.

Everyday Examples of Boyle's Law

All animals must breathe to survive, and it is Boyle's law that describes how lungs perform this action. Muscles in the body pull on the lungs, causing them to increase in size. This increase in volume causes the pressure in the lungs to decrease below atmospheric pressure (the pressure outside of the body). Since gas molecules move from areas of high pressure to areas of low pressure, this forces air into the lungs. To exhale, the lungs contract which decreases their volume, thus increasing the pressure inside of them and forcing the air back out.

A bladder pump is a device that uses Boyle's law to pump air in a single direction, which can be used to inflate objects or create a vacuum inside a container. A simplistic bladder pump contains a bladder, which is similar to a balloon but has two openings for air to flow through. and is typically housed in a container. Each end of the container has a valve which only opens in one direction and which the openings of the bladder are connected. When the pump is turned on, some kind of mechanical device causes the bladder to rapidly expand and contract. Upon expanding, the increased volume decreases the pressure in the bladder, allowing air to rush in. When the bladder contracts, the volume decreases which expels the air out of the other end of the pump, and the unidirectional valves ensure the air can only move in one direction. An error occurred trying to load this video.

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Coming up next: Charles' Law: Gas Volume and Temperature Relationship

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Boyle's Law Equation

Mathematically, Boyle's law is expressed by the equation:

{eq}k=PV {/eq}

Here, P stands for pressure, V stands for volume, and k is a constant. This equation also provides proof that the relationship between pressure and volume is an inverse one. In order for the product of two variables to always equal the same value, if one variable is changed, then the other must change in the opposite direction. Consider a container filled with an ideal gas at 2 atm, and occupying 2L of space. The k value for this system is then equal to 4. If the volume in the container is doubled to 4L, then Boyle's law tells us the pressure inside must decrease to 1 atm in order for the k value to remain constant.

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Is Boyle's law a direct relationship?

Boyle's law is not a direct relationship. It is an inverse relationship. It tells us that for an ideal gas held at a constant temperature, the product of the pressure and volume must be constant. This means if one quantity is increased or decreased, then the other quantity must decrease or increase, respectively, for the value of the product to remain constant.

What is Boyle's law in simple terms?

Boyle's law tells us that the relationship between pressure and volume is inverse for an ideal gas held in a closed system at a constant temperature. If the pressure increases, the volume must decrease and vice versa.

What two factors are used in Boyle's law?

Two factors used in Boyle's law are pressure and volume. Boyle's law is a special form of the ideal gas law, where the temperature is held constant and therefore not needed in calculations.

What is a good example of Boyle's Law?

An example of Boyle's law is breathing. When the lungs change volume, this creates a difference in pressure inside the body relative to the atmosphere, driving air in and out of the lungs.

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