Relative atomic and formula mass

Atoms are far too light to weigh in grams, so chemists compare their masses with an atom of carbon-12. The relative atomic mass, Aᵣ, of an element is the mean mass of its atoms on this scale. Adding up the Aᵣ of every atom in a formula gives the relative formula mass, Mᵣ, and from that you can work out how much of a compound's mass comes from each element.

Key facts

  • Aᵣ is the mean mass of an element's atoms compared with 1/12 of the mass of a carbon-12 atom. It has no units.
  • Aᵣ is a weighted mean of the isotopes, so it need not be a whole number: chlorine is 75% chlorine-35 and 25% chlorine-37, so Aᵣ = 35.5.
  • Aᵣ = (mass of each isotope × its percentage, added up) ÷ 100.
  • Mᵣ is the sum of the Aᵣ of all the atoms in the formula: Mᵣ of H2O = 2 × 1 + 16 = 18.
  • A number after a bracket multiplies everything inside it: Ca(OH)2 has 1 Ca, 2 O and 2 H.
  • Percentage by mass of an element = (Aᵣ × number of its atoms) ÷ Mᵣ × 100.
  • The mass of an element in a sample = mass of sample × (Aᵣ × number of atoms) ÷ Mᵣ.

Worked examples

Example 1

Find the Mᵣ of calcium carbonate, CaCO3. (Aᵣ: Ca = 40, C = 12, O = 16)

  1. Count the atoms: 1 calcium, 1 carbon, 3 oxygen.
  2. Add their relative atomic masses. Mᵣ = 40 + 12 + 3 × 16 = 100

Answer: 100

Example 2

What is the percentage by mass of nitrogen in ammonium nitrate, NH4NO3? (Aᵣ: N = 14, H = 1, O = 16)

  1. Find the Mᵣ: 2 N, 4 H and 3 O. Mᵣ = 2 × 14 + 4 × 1 + 3 × 16 = 80
  2. The nitrogen atoms have a mass of 2 × 14 = 28.
  3. Turn it into a percentage. 28 ÷ 80 × 100 = 35%

Answer: 35%

Example 3

Copper has two isotopes: copper-63 (69%) and copper-65 (31%). Find its relative atomic mass to 1 decimal place.

  1. Multiply each mass by its percentage and add. 63 × 69 + 65 × 31 = 4347 + 2015 = 6362
  2. Divide by 100. 6362 ÷ 100 = 63.62
  3. To 1 decimal place, Aᵣ = 63.6. It is nearer 63 because copper-63 is more common.

Answer: 63.6