Why is the mole considered a base unit of the SI system?

Question

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

Answer 1

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.