5.3.2.2Amounts of substances in equations (HT only)
AQA GCSE Combined Science (8464), Higher tier · Chemistry › Quantitative chemistry › Use of amount of substance in relation to masses of pure
Practise Amounts of substances in equations (HT only). 14 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
The balancing numbers in an equation tell you the ratio of the numbers of moles that react and form. Using this, you can calculate the mass of a product from the mass of a reactant, or the mass of reactant needed to make a product. This subtopic is Higher tier only.
Grade by grade
What you need to be able to do, from the first marks up to the top grade.
5
Read mole ratios from a balanced equationThe balancing numbers give moles, e.g. 2H2 + O2 → 2H2O means 2 mol of H2 react with 1 mol of O2.
6
Calculate the masses shown in an equationFor each substance, mass = balancing number × Mr, e.g. 2H2O is 36 g.
7
Calculate product mass from reactant massMoles of known substance → mole ratio → moles of wanted substance → mass.
8
Calculate the reactant mass neededStart from the mass of product you want and work back through the mole ratio.
9
Scale reacting masses in kilograms or tonnesMass ratios work in any unit as long as you use the same unit throughout.
Notes
Equations in moles
The balancing numbers in a symbol equation give the ratio of moles of each substance.
Mg + 2HCl → MgCl2 + H2 means 1 mol of Mg reacts with 2 mol of HCl to produce 1 mol of MgCl2 and 1 mol of H2.
A formula with no number in front counts as 1.
Masses in an equation: multiply each Mr by its balancing number. For 2Mg + O2 → 2MgO, 48 g of Mg reacts with 32 g of O2 to make 80 g of MgO.
The three-step method
Step 1: moles of the substance you know = mass ÷ Mr.
Step 2: use the ratio of the balancing numbers to find the moles of the substance you want.
Step 3: mass of the substance you want = moles × Mr.
Worked example: what mass of iron forms from 32.0 g of iron(III) oxide? Fe2O3 + 3CO → 2Fe + 3CO2. Moles of Fe2O3 = 32.0 ÷ 160 = 0.200 mol. The ratio is 1 : 2, so moles of Fe = 0.400 mol. Mass of Fe = 0.400 × 56 = 22.4 g.
The ratio (scaling) method
Work out the masses in the equation (balancing number × Mr), then scale them up or down.
Example: 160 g of Fe2O3 gives 2 × 56 = 112 g of Fe, so 32.0 g gives 112 × 32.0 ÷ 160 = 22.4 g.
This works in any mass unit: 160 tonnes of Fe2O3 gives 112 tonnes of Fe.
Both methods give the same answer. Use the one you find more reliable.
Cheatsheet
Balancing numbers = mole ratio
moles = mass ÷ Mr
moles wanted = moles known × (balancing number of wanted ÷ balancing number of known)
mass = moles × Mr
Masses in an equation = balancing number × Mr
Mass ratios work in g, kg or tonnes if the unit stays the same
How to answer each type of question
Use an equation to find amounts in moles
1 to 2 marks5
Read the balancing numbers as numbers of moles.
Scale the ratio to the amount given.
Example. N2 + 3H2 ⇌ 2NH3 (a) How many moles of hydrogen react with 1 mol of nitrogen? [1 mark] (b) What is the maximum amount of ammonia that can be made from 6 mol of hydrogen and excess nitrogen? [1 mark]
Show the model answer
(a) 3 mol (1) (b) 6 × 2 ÷ 3 = 4 mol (1)
Calculate the mass of a product
3 to 4 marks7
Moles of the known substance = mass ÷ Mr.
Use the balancing numbers to find the moles of the product.
Mass of product = moles × Mr.
Example. Hydrogen peroxide decomposes: 2H2O2 → 2H2O + O2 Calculate the mass of oxygen produced from 3.40 g of hydrogen peroxide. Ar: H = 1; O = 16 [4 marks]
Show the model answer
Mr of H2O2 = 34, so moles = 3.40 ÷ 34 = 0.100 mol (1) ratio 2 : 1, so moles of O2 = 0.0500 mol (1) mass of O2 = 0.0500 × 32 (1) = 1.60 g (1)
Calculate the mass of reactant needed
3 to 4 marks8
Work out the Mr values you need.
Either find the moles of product and work back through the ratio, or scale the equation masses.
Keep the unit the question uses (g, kg or tonnes).
Example. Aluminium is extracted from aluminium oxide by electrolysis. 2Al2O3 → 4Al + 3O2 Calculate the mass of aluminium oxide needed to produce 54 kg of aluminium. Ar: O = 16; Al = 27 [4 marks]
Show the model answer
Mr of Al2O3 = (2 × 27) + (3 × 16) = 102 (1) 2 × 102 = 204 kg of Al2O3 gives 4 × 27 = 108 kg of Al (1) mass needed = 204 × 54 ÷ 108 (1) = 102 kg (1) (Or: moles of Al = 54 000 ÷ 27 = 2000 mol; moles of Al2O3 = 1000 mol; mass = 1000 × 102 = 102 000 g = 102 kg.)
Shortcuts and memory tricks
Mass → moles → ratio → moles → mass. Write the chain at the top of your working.
Ratio check: if the substance you want has the bigger balancing number, it should have more moles.
The scaling method saves converting kg or tonnes into grams.
Check with conservation of mass: the total mass reacting equals the total mass produced.
Where marks are lost
Ignoring the balancing numbers and assuming a 1 : 1 ratio.
Multiplying the Mr by the balancing number AND using the mole ratio, so the ratio is counted twice.
Applying the mole ratio straight to masses in grams, without converting to moles first.
Forgetting to change kg to g when using moles = mass ÷ Mr.
Rounding the moles too early.
Exam technique
Label each line of working (moles of X = ..., moles of Y = ...) so each method mark can be given.
Use Mr values given in the question; they are there to save you time.
If you get stuck on one step, carry on with your value: marks for later steps can still be awarded.
Check that your answer has the unit asked for (g, kg or tonnes) and the right number of significant figures.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
In a reaction represented by the general equation X + 3Y → 2Z, the balancing numbers give the ratio of moles that react and are produced. How many moles of Y react with 6 mol of X?
18 mol
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
Sodium reacts with water: 2Na + 2H2O → 2NaOH + H2
(a) What does the equation show? Tick (✓) one box.[1]
2 g of sodium reacts with 2 g of water.
2 moles of sodium react with 2 moles of water.
2 moles of sodium produce 2 moles of hydrogen.
1 g of hydrogen is produced.
(b) How many moles of sodium hydroxide are produced when 0.4 mol of sodium reacts?[1]
(c) How many moles of hydrogen are produced when 0.4 mol of sodium reacts?[1]
(d) How many moles of water react with 3 mol of sodium?[1]
Show the answer and mark scheme
(a)Answer: 2 moles of sodium react with 2 moles of water.
(b)Answer: 0.4 mol
0.4 (mol)
(c)Answer: 0.2 mol
0.2 (mol)
(d)Answer: 3 mol
3 (mol)
Question 2Medium7 marks
Zinc carbonate decomposes when it is heated: ZnCO3 → ZnO + CO2 Relative atomic masses (Ar): C = 12, O = 16, Zn = 65
(a) Calculate the relative formula mass (Mr) of zinc carbonate.[1]
(b) Calculate the mass of zinc oxide produced when 6.25 g of zinc carbonate decomposes completely.[3]
(c) Calculate the mass of zinc carbonate needed to produce 8.8 g of carbon dioxide.[3]
Show the answer and mark scheme
(a)Answer: 125
125
(b)Answer: 4.05 g
moles of ZnCO3 = 6.25 ÷ 125 = 0.05
moles of ZnO = 0.05 / Mr of ZnO = 81
mass = 0.05 × 81 = 4.05 (g)
(c)Answer: 25 g
moles of CO2 = 8.8 ÷ 44 = 0.2
moles of ZnCO3 = 0.2
mass = 0.2 × 125 = 25 (g)
Question 3Hard6 marks
The thermite reaction is used to weld railway lines together. Aluminium reacts with iron(III) oxide to produce molten iron: Fe2O3 + 2Al → Al2O3 + 2Fe Relative atomic masses (Ar): O = 16, Al = 27, Fe = 56
(a) One weld needs 1.12 kg of iron. Calculate the minimum mass of aluminium needed. Give your answer in kg.[4]
(b) Calculate the mass of iron(III) oxide that reacts to produce 1.12 kg of iron. Give your answer in kg.[2]