I was looking on the [Wikipedia page](https://en.m.wikipedia.org/wiki/SI_base_unit) for all of the base SI units, and was surprised to see that mole was considered a base unit.
Why is this even a unit? Shouldn’t it be a unit-less quantity? A mole isn’t length, or time, or mass, it’s just a number. Why does it need a unit if it just represents “6×10²³ of something”?
You don’t need units to say “I have 15 pencils,” so why is the mole necessary? It seems like a mole is just a scalar.
In: 10
Because we use moles to turn molecular weight into grams. The molecular weight of hydrogen is ≈1 so 1 mole of hydrogen is 1 gram. When you need to very accurately, count the amount of atoms or molecules in a substance you want to use moles.
Additionally, it’s FAR easier to say you have 1 mole of something than it is to say you have 6.022408 x 10^23.
What if you want to say you have .0081 mol of something? Translate that number to molecules, it’s hard.
All SI units are scalars – they’re just convenient values. We say “meter” because saying “the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second” is long and mostly useless. We could use the Planck length as our “unit” in the same sense, but we’d end up with very large measurements. So instead we picked a useful length more-or-less arbitrarily, called it a meter, and eventually created a very nitpicky science-y value for it.
The mole was picked for the same exact reason – it’s incredibly useful in chemistry for converting between “amount” and “mass,” and using “units” for that calculation is long and unwieldy. It’s not like the SI unit is required to be used in all contexts – nobody’s expecting us to go to the store to get 0.0000000000000000000002 moles of eggs. It’s just defining the unit by something fundamental, so that it can be accurately used in the particular scientific contexts that it’s useful in.
Moles are used for finding out a rough but fairly accurate number of molecules or atoms you have. This can be very useful in chemistry because it allows you to balance reactions etc.
So how does it work? We know that any atom or molecule weighs roughly the weigh of a neutron times how many neutron/protons it has, and if we need more precise methods there’s options for that. That’s called the molar mass. We know that if we have 20 grams of a compound each weighing 20 molar mass, then there will be 1 mole of these molecules. That’s because 1 mole is equal to the amount of atoms with x molar mass in x gram.
Therefore any time we know what something is made of + how much it weighs, we can calculate how many molecules we have.
I guess you could say that, where a gram is a unit if weight and a meter is a unit of length, a mole is a unit of quantity. [A kilogram of steel weighs the same as a kilogram of feathers,](https://youtu.be/-fC2oke5MFg) a meter of road is the same length as a meter of rope, and a mole of hydrogen atoms contains the same number of things as a [mole of moles.](https://what-if.xkcd.com/4/)
Edit: and I would argue that, in your example, “pencil” *is* a unit. Not an SI unit, but a unit. Without it, 15 is just a number. 15 what? 15 joules? 15 lumens? No, 15 pencils.
One can interpret a mole as a scalar, but that is somewhat missing the point. Scalars can be multiplied; amounts of things can not. What is 3 pencils times 4 pencils? It isn’t 12 pencils, it is 12 of the very weird abstract “pencils squared”. But you can multiply 12345 molecules by the abstract scalar number 7 and get again a count of molecules. Same works identically with 3 moles (which is just a lot more molecules than 12345).
The basic SI units form, well, a basis: any mass, any length, any time interval, …, and any amount of particles can be expressed a multiples of them. There is no reason to pick 1 over the mole as the fundamental counting unit, each has advantages and disadvantages. The reason we decided on the latter is that it is in the range of everyday objects and amounts chemistry usually deals with. We could pick one instead, and see mole as a constant like c, G and such; but why having one more constant instead of a unit? It is all choice.
The purpose of the SI units is to provide standardization for quantities that you can’t infer from others. You don’t need to standardize 15 because everybody agrees that it is a natural number following 14. You also don’t need to standardize pi or the euler constant, because there exist mathematically exact and precise ways to define them.
Standardization is required for things that you have to measure. For length or time or mass, it is obvious from everyday life that standardization is necessary. But the relevant distinction of these quantities is not that they have a certain physical dimension but that the have to be measured instead of inferred.
Amount of substance has the same problem, it’s just not obvious on a daily basis unless you work in chemistry. It’s not enough to know the weight of a macroscopic substance in grams, but it is necessary to describe chemical properties at the molecular level. The scale between the two levels is a number, but it is so enormously huge that it is literally like a drop in the ocean (about 10^25 by the way). You cannot simply count or compute this mathematically, nor can you define it based on other SI units. The scale factor is different for every element, for every isotope, for every molecule. Therefore just like for the meter for length, it was necessary to standardize.
Since you mention scalar, you could treat amount of substance as an entirely separate vector. Like you can’t compare a quantity of unit [m*s] with a quantity of unit [s], you cannot compare a quantity of unit [s] with [mol*s]. For most calculations it is best if you treat them just as incompatible until the very end.
Latest Answers