 In this video, I'm going to show you how to calculate how many molecules there are in something. That something might be a cloud of gas, it could be the head of the pin, the Pacific Ocean. But you've got a certain amount of a substance and you want to look at how many molecules are in it. So how do you do this? The basic idea is that the number of molecules in something is equal to the mass of that something divided by the mass of one molecule. So how do you work out what the mass of one molecule is? Well, the mass of a molecule is given by the molecular mass times the atomic mass unit. Now what are these things? We'll come to the molecular mass in a second, but the atomic mass unit is a constant. You can look it up. This is the letter U and it has a value of 1.660539 by 10 to the minus 27 kilograms. It's basically the mass of a neutron or a proton. And the molecular mass is basically telling you how many neutrons and protons there are in one molecule of whatever the substance is. So how do you work out the molecular mass? Well, the molecular mass is equal to the atomic mass of each atom that makes up the molecule times the number of that atom in the molecule. And how do you work this out? Well, the number of that atom in the molecule, you work out from the equation for the molecule. So for example, you have CO2. You've only got one carbon atom because it's got a 2 down here. That must mean it has two oxygen atoms. H2O has two hydrogen atoms and one oxygen atom. The atomic mass, once again, you look that up. So for example, for carbon, the atomic mass is equal to 12. And for hydrogen, it's equal to 1. Oxygen is equal to 16. And this is basically telling you how many protons and neutrons there are in the substance. So hydrogen is just one proton. The electron's kind of irrelevant. It's way so little compared to the proton. Carbon has six protons and six neutrons, so an atomic mass of 12. Oxygen has eight protons and eight neutrons, so an atomic mass of 16. Now, these aren't actually exactly precise. The atomic mass of carbon is actually 12.0107. Oxygen is actually 15.9994. So very close to that. The reason why they are slightly different is partially because you have to factor in the binding energy of the atom. Energy has mass according to E equals MC squared, and that makes things very slightly different. You also have to worry about the difference in mass between neutrons and protons. And also, any real substance is going to be a mix of different isotopes. So for example, carbon will normally be a mix of carbon 12, which has six protons and six neutrons, and carbon 13, which has six protons and seven neutrons. And so a smaller mixture of carbon 13 will make the atomic mass a bit more. We'll come back to all that in the nuclear physics course. But that's what you do. You look at your molecule. You work out how much of each type of atom there is. You look at the atomic mass of each atom. Multiply them together. So for CO2, you're going to have two lots of 12. So one lot of 12 plus two lots of 16. So that's going to be 12 plus 16 plus 16. That's going to be 44. So the molecular mass of carbon dioxide is 44. Therefore, the mass of one molecule is going to be 44 times that. So 44 times 1.66 by 10 to the minus 27. And if you had a certain amount of carbon dioxide, you take the mass of your lump of carbon dioxide and divide by the mass of a molecule you just worked out here.