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

Moles and particles

These moles are not the furry creatures that make holes in the ground. The name comes from molecules (which are apparently too long to write).

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

This is actually a pretty simple experiment. Check it out 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 that water: we know the ratio of the molecules, but we do not know the number. That is why we use moles. It’s basically just a way of counting the innumerable.

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

Constants

Just a quick note: You almost always need some kind 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 is the same as a joule, the unit of energy.

On the right side is the number of moles and the temperature in Kelvin – the two times clearly not to give units of joules. But you *shall* have the same units on both sides of the equation, otherwise it would be like comparing apples and oranges. This is where constant R comes to the rescue. It has units of joules / (mol × Kelvin), so mol × Kelvin cancels and you just get joules. Bom: Now both sides have the same devices.

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

To inflate a balloon

What happens when you blow up a balloon? You are obviously adding air into the system. When you do this, the balloon becomes larger so that its volume increases.

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

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