Chemistry – Stoichiometry - Relative masses of atoms and molecules | e-Consult

Relative atomic mass (A_r) is defined as the weighted average of the masses of all the naturally occurring isotopes of an element. The weighting is based on the relative abundance of each isotope. It is compared to 1/12 the mass of a carbon-12 atom, which is defined as having a mass of exactly 12 atomic mass units (amu). Therefore, A_r is a ratio of the mass of an atom of the element to 12 amu.

This value is not a whole number because isotopes of an element have different masses. Since the relative abundance of each isotope is not necessarily a simple fraction, the weighted average will often result in a decimal value. For example, if an element has two isotopes, one with a mass of 10 amu and a relative abundance of 50%, and another with a mass of 20 amu and a relative abundance of 50%, the A_r would be calculated as: (10 x 0.50) + (20 x 0.50) = 10 + 10 = 20. However, if one isotope had a relative abundance of 60% and the other 40%, the calculation would be: (10 x 0.60) + (20 x 0.40) = 6 + 8 = 14. The weighted average is a more accurate representation of the element's atomic mass than simply averaging the masses of the isotopes.