Introduction
Chemists can't weigh a single atom on a kitchen scale — atoms are far too tiny! Instead, we use relative masses, which compare atomic masses to a fixed standard. This lesson introduces relative atomic mass (Ar), relative formula mass (Mr), and molar mass (M) — three closely linked ideas that let us connect the invisible world of atoms to the measurable world of grams on a balance.
Relative Atomic Mass
The relative atomic mass (Ar) of an element is defined as the weighted average mass of its naturally occurring isotopes, compared to one-twelfth the mass of a carbon-12 atom (Talbot, p.46).
Ar = (weighted average isotopic mass) / (1/12 × mass of one ¹²C atom)
Because carbon-12 is defined as having a mass of exactly 12, this calculation simplifies — Ar is essentially the weighted average isotopic mass itself (Talbot, p.46).
Why carbon-12? Hydrogen was originally used as the reference (it's the lightest element), but once isotopes were discovered, scientists needed a single, universally agreed isotope. In 1961, carbon-12 was chosen as the international standard (Talbot, p.87).
Worked Example 1: Calculating Ar from isotopic data
Chlorine exists as two isotopes: ³⁵Cl (abundance 75.77%, mass 34.97) and ³⁷Cl (abundance 24.23%, mass 36.97).
Ar(Cl) = (34.97 × 0.7577) + (36.97 × 0.2423)
= 26.50 + 8.96
= 35.45
This matches the value found on the periodic table.
Relative Formula Mass
For compounds, we use relative formula mass (Mr) — the sum of the relative atomic masses of every atom in the formula (whether it's a true molecule or an ionic formula unit) (Talbot, p.86).
Worked Example 2: Finding Mr
Find the relative formula mass of CH₄Cl (methyl chloride-type formula used for illustration):
Mr = Ar(C) + 4×Ar(H) + Ar(Cl)
= 14.01 + (4 × 1.01) + 35.45
= 53.50
(Talbot, p.86)
Worked Example 3: Ionic compound
Calculate Mr of calcium carbonate, CaCO₃:
Ar(Ca) = 40.08
Ar(C) = 12.01
Ar(O) = 16.00 × 3 = 48.00
Mr(CaCO₃) = 40.08 + 12.01 + 48.00 = 100.09
Molar Mass
The molar mass (M) is the mass in grams of one mole of a substance — atoms, molecules, ions, or formula units — and shares the same numerical value as Ar or Mr, but with units of grams per mole (g mol⁻¹) (Talbot, p.86).
| Formula | Molar mass / g mol⁻¹ | Particles per mole |
|---|---|---|
| C | 12.01 | 6.02 × 10²³ atoms |
| H₂O | 18.02 | 6.02 × 10²³ molecules |
| CaCO₃ | 100.09 | 6.02 × 10²³ formula units |
(Talbot, p.86)
Worked Example 4: Using molar mass
What is the molar mass of magnesium nitrate, Mg(NO₃)₂?
Ar(Mg) = 24.31
Ar(N) = 14.01 × 2 = 28.02
Ar(O) = 16.00 × 6 = 96.00
M = 24.31 + 28.02 + 96.00 = 148.33 g mol⁻¹
Key Takeaways
- Relative atomic mass (Ar) compares an element's weighted average isotopic mass to 1/12 the mass of a ¹²C atom — it has no units.
- Relative formula mass (Mr) is the sum of all atomic masses in a compound's formula, whether molecular or ionic.
- Molar mass (M) has the same numerical value as Ar or Mr but is expressed in g mol⁻¹, linking atomic-scale mass to measurable mass.
- Carbon-12 is the modern international standard for atomic mass, replacing the earlier hydrogen-based scale.
- Accurate Ar values are determined experimentally using a mass spectrometer.