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I have some trouble understanding exactly what a mole represents. As I understand, one unit mole is 1/12 of the mass of an atom of carbon-12 (thus it is the mass of one nucleon?). What is a mole, then?

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Wikipedia… – Qmechanic Jul 11 '11 at 17:22
$6.02214179 \cdot 10^{23}$ – Alexander Mar 15 '12 at 9:39
up vote 14 down vote accepted

A mole is nothing more than a countable number of things. Specifically, it is approximated by 6.02 × 1023 number of things. Hence, you can have a mole of argon atoms, a mole of electrons, or a mole of house keys all of which contain approximately 6.02 × 1023 of their respective items. Note that each of these groups of things will have a different mass.

What you are referring to as 1/12 of a 12C atoms is not a mole, but an atomic mass unit.

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+1 ... it's just like you would use the word "dozen" for the number 12. – luksen Jul 11 '11 at 17:57
as Luksen says, it is a short hand, as its easier to say in brief than in full... – Nic Jul 11 '11 at 18:15
The comparison to "dozen" is very apt - it is indeed the same thing, just with a much larger number. (Note that, as Jason alluded to in his answer, we don't know exactly what that number is, but it's something that we could, in principle, figure out if our technology ever gets advanced enough.) – David Z Jul 11 '11 at 18:16
So I never understand how "mole", whose dimension is actually 1, be a fundamental unit in SI. – Siyuan Ren Jul 12 '11 at 2:35
@Karsus: consider it a "fake unit," i.e. a unit whose value is really just a number. Even if it doesn't represent anything other than a number, you can still do with it all the normal things you can do with units. (Same applies for the radian, by the way, which is equal to 1.) – David Z Jul 14 '11 at 6:02

A mole is like saying "a dozen," as Luksen points out in a comment. But why pick $(6.02)(10^{23})$ instead of, say, $(6.07)(10^{24})$? The reason is that the number was strategically picked such that the weight, in grams, of a mole would be numerically exactly the same as its molecular weight. It is a number that was formulated for the convenience of the chemist (just like the "dozen" was created for the convenience of... uh... someone... the baker? No, that was 13...)

So, for instance, if you know you have a mole of a substance, you can weigh that mole, in grams, to find the molecular weight without doing any math (like 18.0 grams is about a mole of water, which has a molecular weight of about 18.0). If, on the other hand, you want a mole of a substance and you know its molecular weight (as you almost always do) you can weigh it out in grams to get exactly a mole.

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The mole is of such great use because of the predictable and unique relationship between the number of atoms (counted in moles) in a sample and the sample's easily measured weight or mass (depending on your unit system).

The mass per mole of a substance is called its molar mass. Since the standard unit for expressing the mass of molecules or atoms (the dalton or atomic mass unit) is defined as 1/12 of the mass of a 12C atom, it follows that the molar mass of a substance, measured in grams per mole, is exactly equal to its mean molecular or atomic mass, measured in daltons; which is to say, to the substance's mean molecular or atomic weight. -Wikipedia

For example: one mole (6.02X10^23 atoms) of Carbon atoms has a mass of 12.011 grams, which is also the atomic weight of Carbon in Daltons (shown in this periodic table). The molar mass of water (2 hydrogen atoms and 1 oxygen atom) = 2*(1.0079) + 1*(15.999) = 18.0148 grams (I am using a lot decimal places for effect despite that being impractical in real life).

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I mole is just a way to represent a number of atoms. Instead of saying 12 eggs we can also say a dozen. Similarly one mole of carbon is the same as saying $6.02\cdot10^{23}$ atoms of carbon.

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