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This question just popped in my head as I was working with electric force problems involving atoms. Why is the amount in a mole equal to the Avogadro's number? Do atoms/molecules/etc. tend to group in this exact amount? Why do we use this number as a unit of measurement?

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Avogadro articulated the concept that is Avogadro's number, but didn't pick the number. From Wikipedia:

Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules".

https://en.wikipedia.org/wiki/Avogadro%27s_law

The Number is a logical extension of this law: So what is that number in relation to the volume and what is the mass of that amount of material? By agreement, a mole is defined as the mass, in grams, equivalent to the atomic weight of a substance. This was laid out before Avogadro's Number was actually determined. Then it was simply a matter of measuring the mass of a single atom to determine how many atoms were required to have a Mole of a material. Over time, Avogadro's Number has been refined to more and more accuracy.

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