Relative Mass, Moles and Conservation

Measuring amounts in chemistry

Chemists need to count atoms and molecules, but they're far too small to count directly. Instead we use relative masses and the mole to work with measurable amounts.

Relative atomic and formula mass

• Relative atomic mass (Aᵣ) — the average mass of an atom of an element compared to carbon-12. It's the bigger number for each element in the periodic table.
• Relative formula mass (Mᵣ) — add up the Aᵣ of all the atoms in a formula.

Example: Mᵣ of water (H₂O) = (2 × 1) + 16 = 18.

Example: Mᵣ of calcium carbonate (CaCO₃) = 40 + 12 + (3 × 16) = 100.

Conservation of mass

In a chemical reaction, no atoms are created or destroyed — they're just rearranged. So the total mass of reactants = total mass of products. This is why chemical equations must be balanced (the same number of each atom on both sides).

• If mass appears to change, a gas has been taken in or released (e.g. a metal gaining mass by combining with oxygen, or a reaction losing mass as CO₂ escapes).

The mole

• One mole of any substance contains the same number of particles: Avogadro's number = 6.02 × 10²³.
• The mass of one mole equals the substance's Aᵣ or Mᵣ in grams.

Key formula:

moles = mass (g) ÷ Mᵣ

Rearrange: mass = moles × Mᵣ and Mᵣ = mass ÷ moles.

Concentration of solutions

concentration (g/dm³) = mass of solute (g) ÷ volume (dm³)

(Remember 1 dm³ = 1000 cm³, so divide cm³ by 1000 to get dm³.)

Using moles in equations

The balancing numbers in an equation give the ratio of moles reacting. For example, in 2H₂ + O₂ → 2H₂O, 2 moles of hydrogen react with 1 mole of oxygen to make 2 moles of water. This lets you calculate masses of reactants and products.

Worked example

How many moles are in 36 g of water (Mᵣ = 18)?

moles = mass ÷ Mᵣ = 36 ÷ 18 = 2 moles

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Common mistakes

• Forgetting to multiply by the subscript when finding Mᵣ (e.g. H₂O has two H).
• Not converting cm³ to dm³ (÷1000) in concentration calculations.
• Mixing up the moles formula — moles = mass ÷ Mᵣ (mass on top).

Exam tips

• Always write out the formula (moles = mass ÷ Mᵣ) and substitute clearly — you get method marks.
• Double-check your Mᵣ by counting every atom.
• For "explain a mass change", say whether a gas was gained or lost.

Key facts to remember

• Aᵣ = relative atomic mass; Mᵣ = sum of all atoms' Aᵣ in a formula.
• Conservation of mass: reactant mass = product mass (atoms are rearranged, not lost).
• moles = mass ÷ Mᵣ; one mole = 6.02 × 10²³ particles; concentration (g/dm³) = mass ÷ volume (dm³).