Introduction
Atoms are far too small to weigh individually, so chemists needed a clever way to compare their masses. Instead of using actual masses in grams (which would be tiny, awkward numbers), we use relative masses — a scale that compares atoms to a fixed standard. This lesson explains what "relative atomic mass" and "relative molar mass" actually mean, and how to calculate them.
Why we need a relative scale
Early chemists used hydrogen (the lightest atom) as their reference point, giving it a mass of 1. Later, once isotopes were discovered, scientists realised elements aren't made of identical atoms — they're mixtures of isotopes with different masses. In 1961, chemists agreed on a new international standard: carbon-12 (Talbot, p.87).
Relative atomic mass (Ar)
Relative atomic mass is defined as the ratio of the average mass per atom of an element (as it occurs naturally, with all its isotopes) to one-twelfth of the mass of a carbon-12 atom (Talbot, p.46).
In simpler terms:
Ar = (weighted average mass of isotopes of the element) / (1/12 × mass of one ¹²C atom)
Since one-twelfth of a ¹²C atom's mass is defined as exactly 1 (in atomic mass units), Ar is really just the weighted average isotopic mass of the element.
Worked Example 1 — Calculating Ar from isotopic data
Chlorine has two isotopes: ³⁵Cl (75.77% abundance, mass 34.97) and ³⁷Cl (24.23% abundance, mass 36.97).
Ar(Cl) = (34.97 × 0.7577) + (36.97 × 0.2423)
= 26.50 + 8.96
= 35.46
This matches the value on the periodic table (35.45), confirming why chlorine's Ar isn't a whole number — it's an average of two isotopes.
Worked Example 2 — Finding isotopic abundance
Copper has Ar = 63.55, made of ⁶³Cu (mass 62.93) and ⁶⁵Cu (mass 64.93).