# What is the ideal gas law?

It may seem like a lot of volume, but it’s not. It’s almost half a liter, so it’s half a bottle of soda.

moles and particles

These moles aren’t the furry creatures that dig holes in the ground. The name comes from molecules (which is apparently too long to write).

Here is an example to help you understand the idea of a mole. Suppose you pass an electric current through water. A water molecule is made up of one oxygen atom and two hydrogen atoms. (It’s H._{2}O.) This electric current breaks the water molecule and you get hydrogen gas (H_{2}) and gaseous oxygen (O_{2}).

It’s actually a pretty simple experiment. Check it here:

Since water has twice as many hydrogen atoms as oxygen, you get twice as many hydrogen molecules. We can see this if we collect the gases from this water: we know the ratio of the molecules, but we don’t know the number. That’s why we use moles. It’s basically just a way of counting the uncountable.

Don’t worry, there is indeed a way to find the number of particles in a mole, but you need Avogadro’s number for that. If you have a liter of air at room temperature and normal pressure (we call this atmospheric pressure), then there will be about 0.04 moles. (That would be n in the ideal gas law.) Using Avogadro’s number, we get 2.4 x 10^{22} particles. You can’t count that high. Nobody can. But that’s N, the number of particles, in the other version of the ideal gas law.

Constants

Just a quick note: you almost always need some sort of constant for an equation with variables representing different things. Just look at the right side of the ideal gas law, where we have pressure multiplied by volume. The units for this left side would be newton meters, which equals one joule, the unit of energy.

On the right side is the number of moles and the temperature in Kelvin – those two clearly don’t multiply to give units of joules. But you *to have to* have the same units on both sides of the equation, otherwise it would be like comparing apples and oranges. This is where the constant R comes to the rescue. It has units of joules/(mol × Kelvin) so the mol × Kelvin cancels out and you just get joules. Boom: Both sides now have the same units.

Now let’s look at some examples of the ideal gas law using an ordinary rubber balloon.

To blow a balloon

What happens when you inflate a balloon? You are clearly adding air to the system. As you do this, the balloon gets bigger, so its volume increases.

What about the temperature and pressure inside? Let’s just assume they are constant.

I will include arrows next to the variables that change. An up arrow means increase and a down arrow means decrease.

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