a mole is the biochemist’s dozen – it just means 6.02 x 10²³ of something – anything. That number might seem random, but it’s Avogadro’s number and it’s defined as the number of atoms in 12 grams of carbon-12 (the main isotope (version) of carbon). But normally we don’t really care about that part… Instead, we use it more for “accounting purposes” so that we can talk in terms of groups of really really tiny things like atoms and molecules. Kinda like when you’re keeping a tally and you make marks in groups of 5) – or how you might talk about 1 dozen bagels instead of “12 bagels” – but we need a much bigger grouping than 5 or 12. Because molecules are really tiny. Like really, really tiny – so you’re usually dealing with tons and tons of them. Abbreviated mol, which I always found kinda funny since it’s only 1 letter shorter and for a while I thought mole and mol were different things but they’re the same!
Some places you’ll see it put to use:
Molarity (M) is a measure of mol per L
molality (m) is a measure of mol per kg
Mole fraction is # mol of something / total # of mol (note that for a gas, you can multiply the mole fraction by the total pressure to get the partial pressure)
molar mass is how much 1 mol of something weighs in g/mol. molecular weight (MW) is how much 1 molecule weighs in daltons (Da). These terms are often used interchangeably, but, technically… Let’s start with MW units: Dalton, unified atomic mass unit (u), and atomic mass unit (amu) are, practically speaking, the same. We usually use Da in biochemistry to talk about the sizes of proteins and stuff. A dalton is 1/12 the weight of carbon-12 and it’s the same as a unified atomic mass unit (u) . But to make things more confusing… an atomic mass unit (amu) is also almost exactly the same thing but it’s based on the weight of oxygen and is 1/16 the weight of oxygen-16. 1 mol of pure carbon-12 weighs 12 grams so a Da used to be, by definition, 1g/mol so molar mass and MW were the exact same number. Then they redefined things a little so they’re a tiny bit different, but that only really matters for physic-y stuff and for the stuff we’re talking about, we can just consider them the same and you’ll often see all these terms interchanged!
Proteins usually have MWs in the tens to hundreds of kDa range (so tens to hundreds of thousands of daltons) which, since 1 Da ~ 1g/mol means that a mol of an average-ish size protein would weigh around 100,000g. When I purify proteins, I’m glad to get 5mg at the end of the process!