 So, you know that the mole is defined to be 6.022 x 10 to the 23 things, let's say particles. And apart from investigating issues like what would happen if you had a mole of moles, the mole is usually used in chemistry to think about numbers and ratios of atoms or molecules or ions or things of that kind. The problem here though is that we can't possibly count an actual mole of things. As an exercise, try calculating how long it would take you to count from one to a mole. So to solve this, we need to be able to convert a mole into something that's easy to measure on our human timescale and using human equipment. Well, when a grocer measures out cherries, they don't count out individual cherries, but they'd weigh out a certain mass, say a kilo of cherries. And if you knew how much an average cherry weighed, you could calculate how many cherries were in that kilo. The same principle applies in chemistry. We do know how much atoms weigh, so we can work out how much one mole of those atoms weighs. And we can then convert between the mass of a sample of, say, carbon and how many moles of atoms are in that sample. The quantity that we use to do this is known as molar mass, and it's numerically equivalent to the mass of one mole of a substance. So the molar mass of carbon is the mass of one mole of carbon atoms. If you have one mole of pure carbon-12 isotope, that's 12,000, etc., grams. Remember that's how we defined the mole in the first place. But if you have ordinary carbon, which is a mixture of mostly carbon-12 with a bit of carbon-13 and carbon-14 mixed in, the mass of one mole will be slightly heavier because a small proportion of the atoms are of those heavier isotopes. It will weigh 12.011 grams. Notice that this number is the same number that you've understood as the atomic weight that's listed on the periodic table. A neat and intentional consequence of the way that the atomic mass number and the mole are defined, both using carbon-12 as a standard, is that the numerical value for the atomic weight of an atom is the same as the mass of a mole of those atoms. The only thing that's different is the units. The atomic mass unit, when you're measuring individual atoms, and grams when you're measuring moles of atoms. So for instance, the average atomic weight of iron is 55.85 atomic mass units, and the mass of one mole of iron atoms is 55.85 grams. The average atomic weight of a helium atom is 4.003 atomic mass units, and the mass of one mole of helium, 6.022 times 10 to the 23 helium atoms, is 4.003 grams. Now there's one thing we have to be really careful about when we say that molar mass is the mass of one mole. If you're asked the mass of something, what units would you express it in? Or mass units, grams or kilograms, for moles it's usually grams. But molar mass is not an ordinary mass, it's a ratio. It's the mass per mole of a substance. So its units are grams per mole. This doesn't change the value of the number at all, but it makes a big difference when you're trying to get your units to cancel out nicely in calculations, and it's also an important aspect of proportional thinking. The mass of one mole of something is kind of a one-use number. There's not much you can do with it other than know the value of that mass. But re-expressing it, rebranding it, if you like, as a ratio, the mass per mole means that mathematically we can now apply it to any number of moles to find out what mass they would have. So this is the relationship. The molar mass of a substance in grams per mole equals the mass in grams divided by the moles in mole. You can rearrange this equation to make mass the subject or moles depending on what information you have available to you and what it is that you want to calculate.