The relationship between the average atomic mass and the gram requirement for one mole of an element is based on the concept of the mole and the Avogadro's constant.
The mole is a unit used in chemistry to represent an amount of substance. One mole of any substance contains Avogadro's number of particles, which is approximately 6.022 × 10^23 particles per mole. These particles can be atoms, molecules, ions, or any other constituent entities, depending on the substance.
The average atomic mass of an element, expressed in atomic mass units (u), represents the weighted average of the masses of all the naturally occurring isotopes of that element. The atomic mass unit, in turn, is defined relative to the mass of a carbon-12 atom, which is assigned a mass of exactly 12 atomic mass units.
Since one mole of any substance contains Avogadro's number of particles, it follows that one mole of an element contains Avogadro's number of atoms of that element. Therefore, the gram requirement for one mole of an element, known as the molar mass, is numerically equal to the average atomic mass of that element expressed in grams.
For example, the average atomic mass of carbon is approximately 12.01 atomic mass units. Therefore, one mole of carbon atoms has a mass of approximately 12.01 grams. Similarly, one mole of oxygen atoms has a mass of approximately 16.00 grams (the average atomic mass of oxygen).
This relationship allows chemists to easily convert between the mass of a substance and the number of moles of that substance, which is crucial for performing various calculations in chemistry, such as determining reaction stoichiometry, calculating mass percentages, or predicting product yields.