What Is the Ideal Gas Law?

The air around you is a gas. Understanding how gases behave is useful when dealing with things like air bags and rubber balloons. Let's be transparent. You aren't here for partying. You're probably here because you're in an introductory chemistry class and the ideal gas law is very confusing.

Maybe you're just here for science. It's awesome.

The ideal gas law is something to ponder. It is a relationship between the pressure, volume, temperature, and number of particles for a gas. The equation is similar to this.

The pressure, volume, number of moles, constant, and temperature are all terms. You can't understand gas law if you don't know what each term means.

Physicists like the other version of the equation.

There are two different versions of this. We have N for the total number of gas particles. The Boltzmann constant has a value of 1.38064910 23 joules per kelvin.

Let us explain each term.

There is pressure.

The air around you is made of small balls. The balls are so small that you can't see them. This is what a gas is, it's made of many molecule that are travelling in different directions. There are two nitrogen atoms bound together in the air, but there are also two oxygen atoms. For this model, imagining a ball shape will work.

Some of the balls would hit the walls of the box. There is a diagram of a collision.

We need some physics. You could have a bowling ball. The ball will keep moving if there isn't a force on it. If it changes direction like when it collides with a wall, then there must be a force pushing on it. If the wall pushes on the ball, then the ball needs to push on the wall as well.

The same thing happens with very small objects. The little gas-balls exert a small force on the wall when they collide with the container.

The force per area is defined by us. It looks like this.

The force is F and the area is A. The force from a collision depends on how fast the molecule is. Imagine if you will, that you could throw a golf ball at a very high speed or roll a bowling ball at a slow speed. It is1-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-6556 is1-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-65561-6556

The total force on a wall of a container holding a gas depends on how fast the molecule is and how many of them collide with the wall. The number of hits with the wall depends on two things: the speed of the molecule and the wall's area. The faster the molecule is moving, the more it will collide. A bigger wall area will also happen. The pressure on the wall can be determined by dividing the force by the area. The mass and speed of the molecule are the most important factors in determining the pressure of a gas.

It is easy to understand the idea of pressure when a molecule of gas collides with a container. Even though they aren't contained by anything, they still move and have pressure. The pressure is an attribute of the gas not of the wall.

The temperature.

Everyone knows that the temperature of the air is 100 degrees. What does that mean for the small molecule of a gas? The molecules in hot air move faster than those in cold air.

The temperature of an ideal gas is related to the average energy of the molecule The speed of an object and the mass of it are the two most important factors in determining the amount of energy in the equation. As the temperature of a gas increases, the molecule move around faster.

Molecules of air are moving quickly. Nitrogen and oxygen have different mass in air. An average nitrogen molecule will have the same energy as an oxygen molecule, but they will move at different speeds. The average speed can be calculated using the following equation.

Since air has more nitrogen, I'm going to calculate the speed of that molecule with a mass of around 10 -26 kilograms. Molecules are incredibly small.

The ideal gas law can be used in temperature units of kelvins. The absolute lowest temperature that can be achieved is 0 kelvins, meaning it has zero energy. It is so cold that it is even colder than the planet Hoth.

The temperature is dependent on the energy of the molecule. Mass isn't negative and thevelocity isn't squared, so you can't have negative energy. It shouldn't be possible to have a negative temperature. This problem can be fixed by not using them. You can't go lower than 0. The molecule of a gas would have no energy at all.

The average molecule speed with the Boltzmann constant is 511 meters per second. That's 1,143 miles per hour. Those molecules are moving fast. This is not a 1000-mph wind. Some of the molecule are going slower and some are going faster. They are all moving in different directions. The Molecules are moving in the same direction for wind.

It was volume.

I'm going to explain it even though I think it's easy. I have a big box that is 1 meter on both sides. After filling it with air, I close it. The gas volume is 1 m x 1 m x 1 m

There is a balloon filled with air. Since balloons are not regular shapes, it's more complicated. If it is a completely spherical balloon, it has a radius of 5 centimeters. The amount of the balloon will be determined after that.

It isn't a large volume. That's half a bottle of soda.

There are moles and particles.

The moles are not the furry creatures that make holes. It's too long to write the name.

To understand the idea of a mole, you need to see this example. If you run an electric current through water, what would it look like? One oxygen atom and two hydrogen atoms are used to make a water molecule. That's H2O. The water molecule is broken up by the electric current and you get hydrogen gas and oxygen gas.

This is a fairly easy experiment. You can check it out here.

There is a video on this

Water has more hydrogen atoms than Oxygen, so you get more hydrogen molecule. We know the ratio of the molecule but we don't know the number. The reason we use moles is because of that. A way to count the uncountable.

You need Avogadro's number to find the number of particles in a mole. There will be 0.04 moles if you have a liter of air at room temperature and atmospheric pressure. In the ideal gas law, that would be the case. Avogadro's number gives us a number of particles. It's not possible to count that high. Everyone can't. The ideal gas law has a number of particles.

There are constants.

It is almost always necessary to have a constant for an equation with variables. The ideal gas law is on the right side. Newton-meters are the same as a joule and are used for energy.

The number of moles and the temperature are on the right side of the equation. It would be like comparing apples and oranges if you didn't have the same units on both sides. The constant R comes to the rescue. It has units of joules so that the mol Kelvin doesn't change. Both sides have the same units, boom.

Some examples of the ideal gas law can be found using a rubber balloon.

A balloon is inflating.

When you blow up a balloon, what will happen? The system is getting air into it. The balloon's volume increases as you do this.

The temperature and the pressure inside are important. Assume they are constant.

Next to the variables that change will be arrows. An up and a down arrow are used to indicate increases and decreases.

On the right side of the equation there is an increase in the number of moles. That can be done. The two sides of the equation are equal. Adding air causes the balloon to blow up.

Does the pressure stay constant if the rubber part stretches? Is the temperature always the same?

Let's do it quickly. There is a pressure and temperature sensor here. There is a temperature probe in the balloon. As the balloon is inflated, I can record both values. This is what that looks like.

Here's the data.

The pressure is at the start of the graph. The Pa is a pascal, which is the same as a newton. This is around the normal atmospheric pressure.

There is a spike in the pressure when I blow up the balloon, but then it goes down. That is an increase in pressure, but it isn't very significant.

That's not a big change since the temperature starts at 23.5C and then goes up to 24.2C. The balloon becomes cooler after it is inflated. The hotter object will get cooler when it is in contact with a cooler object. If you put hot muffins on the kitchen counter it will cool them. It seems like it's legit to assume a constant pressure and temperature.

Molecules of air are pushed into a balloon when it is inflated. The air particles in the balloon are the same temperature as the ones that were already there. The rubber material of the balloon gets hit by the air in more ways than one. The pressure would be increased if the balloon was inflexible. It is not inflexible. There is a greater area for the molecule to hit when the rubber in the balloon stretches. You get a bigger volume and a bigger amount of particles.

A balloon is cooled.

We can start the demonstration with an inflated balloon. Air can't leave or enter since it's closed.

Is it possible to decrease the temperature of the air. You can put a balloon in the freezer for a short time. I won't do that. Liquid nitrogen will be poured on it with a temperature of -196C. This is what it appears to be.

The pressure in the balloon doesn't change but the temperature does. The ideal gas law equation can only be valid if the volume decreases.

The liquid nitrogen makes the gas cooler. The molecule are moving at a slower rate. The impact force on the rubber material of the balloon has been reduced by the slower movement of these Molecules. The rubber will not be pushed out as much, so the balloon will get smaller.

The balloon warms up and the volume goes up. The starting size is back to it's previous size.

A balloon is being squeezed.

The amount of air inside a sealed inflated balloon is constant. I'm going to make the balloon bigger.

The balloon's volume decreases. How does the pressure and temperature change? We will look at the data from the sensors.

The temperature goes from 296 K to 300 K, and the pressure goes from 104 to 112 kilo pascals. The temperature doesn't change a lot. I think it's a good idea to approximate this as a constant temperature. There is an increase in pressure and a decrease in volume It looks like this using my equation.

Constant stuff is on the right side of the equation.

The left side of the equation needs to be constant as well. The only way for this to happen is for the volume to go down and the pressure to go up. Even though it's a weirdly shaped balloon, that's what happens.

The balloon gets smaller with the squeeze. The surface area for the molecule to collide into is reduced. There are more accidents because of this. The pressure in the gas goes up with more accidents.

It does not matter if the example is about putting air into a balloon or a bike tire. This is sometimes called "breathing." The ideal gas law can help us understand the changes in pressure, temperature, volume, and amount of gas.

Perhaps it wasn't so confusing after all.