The key idea
02 × 10²³ particles. The relative formula mass (M_r) tells you the mass of one mole in grams. Use moles = mass ÷ M_r.
moles = mass ÷ Mr
Use the labels to explain the scientific relationship shown.
The bit that matters
Keep the idea tight, then use the worked example to practise the exact exam wording.
Relative formula mass (M_r)
The relative formula mass of a compound is found by adding up all the relative atomic masses of the atoms in the formula.For example, CaCO₃ has M_r = 40 + 12 + (3 × 16) = 100. Relative formula mass has no units.It tells you the mass in grams of one mole of the substance.
Mole calculations
The mole is the unit used to count particles in chemistry. 02 × 10²³ (the Avogadro constant) particles.The key equation is: moles = mass ÷ M_r. Rearranging gives mass = moles × M_r and M_r = mass ÷ moles.Always check units — mass must be in grams when using M_r.
Reacting masses from equations
A balanced equation shows the mole ratio of reactants and products.To find the mass of a product, find the moles of the given reactant, use the equation's mole ratio to find moles of product, then multiply by M_r.For example, in 2H₂ + O₂ → 2H₂O, two moles of H₂ produce two moles of H₂O.
Percentage yield and atom economy
Percentage yield = (actual yield ÷ theoretical yield) × 100.It is less than 100% due to incomplete reactions, side reactions or product loss.Atom economy = (M_r of desired products ÷ sum of M_r of all products) × 100.A high atom economy means less waste and is preferred for sustainable chemistry.
Definitions to learn
Mole
The amount of substance containing 6.02 × 10²³ particles; the mass in grams equals the M_r.
Relative formula mass (M_r)
The sum of the relative atomic masses of all atoms in a formula.
Avogadro constant
The number of particles in one mole: 6.02 × 10²³ mol⁻¹.
Percentage yield
The actual yield expressed as a percentage of the theoretical yield.
Atom economy
The proportion of the total mass of reactants that ends up in the desired product, expressed as a percentage.
Calculate the mass of 2 moles of calcium carbonate (CaCO₃). (Ca = 40, C = 12, O = 16)
Find M_r: 40 + 12 + (3 × 16) = 40 + 12 + 48 = 100.
Mass = moles × M_r = 2 × 100.
Mass = 200 g.
Mass = 200 g.
Show every step: write the equation, calculate M_r, state the mole ratio, then calculate the mass.Missing one step costs marks.
Do not confuse relative formula mass (no units) with molar mass (g/mol). At GCSE both are numerically the same.
How to score full marks
- 1Always show M_r calculation as a sum — e.g. (2 × 1) + 16 = 18 for H₂O — do not just write '18' with no working.
- 2For reacting masses, write the mole ratio from the balanced equation before calculating — it must match the equation coefficients.
- 3Percentage yield and atom economy are different things: yield is about what you actually made; atom economy is about what the reaction could make with no waste.
Try these yourself
Open each answer only after you have explained the full chemical process.
1State what is meant by the relative atomic mass of an element.[1 mark]
- 1.Link to the carbon-12 scale.
2Calculate the M_r of sulfuric acid (H₂SO₄). (H = 1, S = 32, O = 16)[1 mark]
- 1.Add up all atomic masses.
3Calculate the number of moles in 9.2 g of sodium (Na = 23).[1 mark]
- 1.Use moles = mass ÷ M_r.
4Calculate the mass of 0.5 moles of water (H₂O). (H = 1, O = 16)[2 marks]
- 1.Find M_r, then mass = moles × M_r.
5In the reaction 2H₂ + O₂ → 2H₂O, calculate the mass of water produced from 4 g of hydrogen. (H = 1, O = 16)[3 marks]
- 1.Use the mole ratio from the equation.
- 2.Find moles of H₂, then moles of H₂O, then mass.
6Calculate the percentage yield when 18.5 g of NaCl is produced from a reaction with a theoretical yield of 23.4 g.[2 marks]
- 1.Use % yield = (actual ÷ theoretical) × 100.
7Calculate the atom economy of the reaction: CH₄ + 2O₂ → CO₂ + 2H₂O where the desired product is CO₂. (C = 12, H = 1, O = 16)[2 marks]
- 1.Use atom economy = (M_r of desired products ÷ M_r of all products) × 100.
8Explain why a high atom economy is desirable in industrial processes.[3 marks]
- 1.Link to waste, cost and sustainability.