A mole is that number of atoms, ions, molecules, electrons etc which is the same as the number of atoms found in a sample of 12g of the isotope Carbon-12(12C).
This number is 6.022045 x 1023 atoms, which is known as "Avogadro's Number".
So, to obtain exactly one mole of any substance, one would have to weigh out exactly its relative atomic mass / relative molecular mass.
Mole relates to molarity as follows: a one-molar solution (1M) contains one mole of solute, dissolved in one cubic decimetre (1dm3) of solvent.
Anne Evans
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