The concept that 1 mole of an element is numerically equal to its relative atomic mass in grams is derived from Avogadro's constant and the definition of a mole.
Avogadro's constant (denoted by "Nₐ") is a fundamental constant in chemistry and physics. Its value is approximately 6.022 × 10^23 particles per mole. This means that there are about 6.022 × 10^23 atoms in one mole of any element.
The relative atomic mass of an element (expressed in atomic mass units, or amu) is a measure of the average mass of an atom of that element compared to 1/12th the mass of a carbon-12 atom. For example, the relative atomic mass of carbon is approximately 12 amu.
Now, since Avogadro's constant tells us that one mole of any element contains approximately 6.022 × 10^23 atoms, it follows that one mole of carbon (or any other element) contains 6.022 × 10^23 carbon atoms.
The key idea behind the concept is that the relative atomic mass of an element in amu is numerically equal to the mass of one mole of that element in grams. This relationship is known as the molar mass. For example, the molar mass of carbon is approximately 12 grams per mole.
This relationship holds true because the relative atomic mass of an element is essentially the average mass of one atom of that element, and one mole of that element contains Avogadro's number of atoms. Therefore, if you take the relative atomic mass in amu and express it in grams, you get the mass of one mole of that element.
This relationship is a fundamental concept in stoichiometry, as it allows us to easily convert between the number of moles of a substance and its mass, which is essential for performing calculations in chemistry.