# Gay-Lussac's Law: Gas Pressure and Temperature Relationship

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• 0:05 Temperature and…
• 1:57 Gay-Lussac's Law
• 3:04 Practice Question 1
• 4:05 Practice Question 2
• 5:49 Lesson Summary

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Lesson Transcript
Instructor: Kristin Born

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

You may know that you aren't supposed to put an aerosol can in a fire because it could explode, but do you know why? In this lesson, we will explain Gay-Lussac's law, which shows the relationship between the temperature and pressure of a gas.

## Temperature and Pressure Relationship

Johnny Dalton is enjoying his day at the beach on Ideal Island, the place where all gases behave ideally. What makes them behave so ideally? Ideal gas particles move rapidly and randomly, they don't lose energy when they collide, and they do not have any intermolecular forces. This means that when two ideal gas particles get near each other, they are not attracted to each other like real gas particles may be.

As he lays his towel out and gets his sunblock out, he notices a warning on the back of the aerosol can: Contents under pressure; do not heat. Why would heating this aerosol can be a cause for warning? Johnny thinks for a minute and then recalls some of the ideas of kinetic molecular theory. He remembers that as the temperature of a gas increases, the gas particles move faster and faster. After all, temperature is really just a measure of the average kinetic energy of the particles. Also, when gas particles are moving quickly, they hit the insides of their container more frequently. Finally, because pressure is just a measure of the force of the particles hitting the inside of the container, the more times it hits the inside of the container, the higher the pressure will be!

Now, the container that is holding these particles may not be able to withstand those high amounts of pressure. If the pressure inside of the container exceeds the limits of the container, an explosion could occur.

If you live in cold climates, you may notice that the pressure in your car's tires decreases as it gets colder. This is because the air particles inside the tires are colder and moving slower. They don't hit the inside walls of the tires as frequently, and the pressure in your car's tires decreases.

## Gay-Lussac's Law

This relationship between temperature and pressure is known as Gay-Lussac's law. It states that if the volume of a container is held constant as the temperature of a gas increases, the pressure inside the container will also increase. As with the other gas laws, this one can be represented in the form of an equation:

P1/T1 = P2/T2

Recall that we use 1s and 2s to indicate the quantities before (1s) and after (2s) a change has taken place. Also, note that the units for pressure do not matter, as long as they are the same throughout the entire equation. The units for temperature must be Kelvins or the equation will not work. This is because the Kelvin scale is an absolute scale - it doesn't go negative. Finally, this equation only works for an ideal gas. Most gases that surround you and me behave very much like ideal gases, so we can use this equation as an approximation for the gases we encounter.

## Practice Question 1

Let's say you are making dinner using a pressure cooker with an initial internal pressure of 1 atmosphere and an internal temperature of 100 degrees Celsius (or 373 K). Assuming the volume does not change and the gas behaves ideally, what will the pressure inside the container be if the temperature is raised to 200 degrees Celsius (or 473 K)?

To solve this, you will need to make sure you are using the Kelvin temperatures. Substituting the numbers into the correct locations in the equation given to us:

1 atm / 373 K = P2 / 473 K

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