where ni is the number of moles of species i and N is the total number of moles in the system.
Since the number of moles of a species is directly proportional to the number atoms or molecules of that species through a constant of proportionality, Avogadro's number NA, the mole fraction is really the same as the number fraction for the given species. In other words the mole fraction of species i, refers to the number of atoms or molecules of i divided by the total number of atoms or molecules in the system.
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