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I really can't understand why is the mole a unit of measurement and not just a constant. I mean, we use units to express things that we can measure but that are not countable, that are continuous - and not discrete. However, the number of atoms (or whatever) of something is clearly countable, discrete. It is also a huge number, which would request for a constant, a number to multiply to: Avogadro's constant is that number, like mega or kilo in SI for other units. We could still write 14 mole, where mole is the Avogadro constant (exactly the way it is), but every book I read so far states that the mole is a unit of measurement, official in the S.I., and so does Wikipedia. It just makes no sense to me that it is considered that way, but there is obviously a reason why... What is it?

Michiel
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Luan Nico
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3 Answers3

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I think you are confusing unit of measurement with fundamental unit. A unit of measurement is a definite magnitude of a physical quantity. Consider a very common grouping unit, the dozen which is conceptually the same as a mole and is a little easier for us to grasp since it is a commonly used small number. As far as I know, the only requirements for a unit of measurement to be valid is general consensus. If you and I agree that we will measure distance in units of 'Chemistry Textbook Thickness', then it is a valid unit of measurement.

A fundamendal unit is a part of a particular set of units upon which all other units can be derived. In this case, the mole is related to the fundamental unit of mass and is defined as an amount of items equal to the amount of carbon atoms in 12 grams of $^{12}C$.

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bobthechemist
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    Indeed, I think I meant fudamental unit. It just seems to me that it makes sense that the meter is a fundamental unit: you can't just say the distance between you am me is 20. It requires a unit. The mole, on the other hand, is exactly the opposite: it seems to be a unit to count things that do not require units do be counted, like atoms or potatoes. – Luan Nico Jun 16 '13 at 17:06
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    Yet this does not answer the main question: why not simply consider the mole as a constant? A mole is certainly not a dimensional unit such such as one representing mass or time... It is just a number, somewhat like $pi$ or $10^{24}$. – Oliver May 30 '14 at 06:57
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    Like @Oliver, I'm not sure this answer addresses the actual question. Nobody disputes that you could call a mole a unit, and indeed the SI system does, but the question is why does it? "Chemistry Textbook Thickness" is not comparable to moles or dozens, because that's defining a unit of measurement for a concept (length) that we have no other way of defining. When it comes to a simple discrete number of objects, though, the thing looks to me like it's unitless. It's simply a number, and multiplying it by 6E+23 and saying that's a unit doesn't seem logical. – Stephen Holt Apr 30 '17 at 21:18
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    "The definition of mole was adopted in November 2018 as one of the seven SI base units". So now, the mole is a fundamental unit, and does not depend on mass anymore. Which means the above question still stands, and your answer doesn't apply anymore. – Eric Duminil Oct 27 '21 at 14:44
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Let me add to bobthechemist's answer. The mole counts quantity. The fundamental unit involved is Avogadro's Number, approximately $6\times 10^{23}$. So $6\times 10^{23}$ units of anything is a mole of that thing, whether it is atoms of hydrogen or sand particles.

With this in mind reread bobthechemist's answer.

Paul J. Gans
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When my high school teacher wrote at the end of the exam '1 mole of kisses to you', not only she was very ignorant but she made a large disservice to me and to my class. And when my prep school teacher compared a mole to a dozen, as if they were conceptually the same, he made the same disservice, because mole is not just a number. E.g.

1 dozen eggs = 12 eggs

1 dozen atoms of Fe = 12 atoms of Fe

1 dozen particles = 12 particles

1 mole of Fe = {Nᴀ} particles of Fe

1 mole of some substance = {Nᴀ} particles of that substance

So, if you were to follow the syntax of the definition of a mole, then a mole of kisses is NOT {Nᴀ} kisses. It is actually {Nᴀ} particles of kisses, which makes no sense. You see – the mole has the same physical dimension of the particle – and is not a dimensionless quantity like the dozen.

Note: I am using {Nᴀ} as the numerical part of the Avogadro constant, Nᴀ = {Nᴀ}[Nᴀ] = {Nᴀ} mol⁻¹

Alan Pommer
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  • Note that there is Avogadro number and Avogadro constant, where the former is dimensionless like dozen. – Poutnik Apr 14 '23 at 10:13
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    I'm not sure I see the distinction your are trying to make. A mole–like a dozen–is a number of countable things and meaningless if the thing is not specified. It does not specify the nature of the thing, just that it should be countable. – matt_black Apr 14 '23 at 10:21
  • @matt_black Like the 1st level ever of math abstraction - the concept of natural numbers without explicit countable physical objects. – Poutnik Apr 14 '23 at 10:24
  • @matt_black (i)My point is that we usually don't say a 'A dozen of iron' like we say 'A dozen of eggs'. Because what is 'A dozen of iron'? Is it 'A dozen of atoms of Fe'? On the other hand, we usually do say 'One mole of Fe'. Is that just a figure of speech – an ellipsis – for 'One mole [of atoms] of Fe'? I don’t think so. (ii) – Alan Pommer Apr 15 '23 at 07:51
  • @matt_black (ii)My reasoning behind all of this was to try to understand why the amount of substance is usually regarded as a dimensional quantity with the mole being its SI unit – a dimensional unit – unlike the dozen which is regarded as dimensionless. And that was my answer – if mole is dimensional then it cannot be just "a number to multiply to", quoting the owner of the question. This makes it conceptually very different from the dozen even though both are used for countable things. – Alan Pommer Apr 15 '23 at 07:51
  • Maybe the mole is used to bridge the amount of substance – uncountable – and the number of particles – countable – unlike the dozen that bridges countable things with countable things. – Alan Pommer Apr 15 '23 at 08:04
  • In this regard saying 'One mole of atoms of Fe' would probably be incorrect. – Alan Pommer Apr 15 '23 at 08:06
  • @AlanPommer I think that, in most circumstances, chemists should not say a mole of iron. They should specify the countable thing (though a mole of "Fe" implies the thing is iron atoms). This is important to avoid ambiguity. What, for example, does a mole of oxygen mean? It could be atoms or molecules: it should be specified. – matt_black Apr 15 '23 at 08:41