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AQA GCSE Chemistry (8462) · 4.3 Quantitative chemistry
Mini-Lesson

Quantitative Chemistry

This mini-lesson walks you through the whole of AQA Topic 4.3 — Quantitative chemistry: conservation of mass and balanced equations, relative formula mass, the mole, reacting masses, concentration, percentage yield, atom economy, titrations and gas volumes.

reactants total mass products total mass = no atoms made or lost

Work through each screen, answer the questions as you go (lots of calculations) and collect ⭐ stars. HT marks Higher-tier-only content; CO marks Chemistry-only (separate science) content. Press Start when you're ready.

Conservation of mass

No atoms are made or lost

The law of conservation of mass states that during a chemical reaction no atoms are created or destroyed. The atoms are just rearranged, so the total mass of the products equals the total mass of the reactants.

That is why a symbol equation must be balanced — the same number of atoms of each element on both sides:

2Mg + O₂ → 2MgO4 atoms each side: 2 Mg + 2 O on the left, 2 Mg + 2 O on the right
48 g Mg + 32 g O₂ 80 g MgO balanced
The balance stays level: 48 g + 32 g of reactants → 80 g of product. Mass is conserved.

Watch out: multipliers work two ways — a big number in front (the 2 in 2MgO) multiplies the whole formula, while a small subscript (the 2 in O₂) multiplies only the atom before it.

Quick check

Mass that seems to change

?A student burns a piece of magnesium ribbon in an open crucible. The white powder left behind has a greater mass than the ribbon did. Why?
Mass changes with a gas

Why mass can seem to change

In an open (non-enclosed) container, mass can appear to rise or fall — but this is only because a gas entered or escaped and was not weighed:

  • Mass appears to rise when a gas is taken in — e.g. a metal reacting with oxygen: the oxide is heavier than the metal.
  • Mass appears to fall when a gas escapes — e.g. thermal decomposition of a metal carbonate: CO₂ escapes into the air.
CaCO₃ → CaO + CO₂↑the CO₂ gas leaves the open dish, so the solid left behind is lighter

Misconception buster: mass is always conserved. In a sealed flask the reading never changes. Seal the same reaction and weigh everything — including the gas — and reactant mass = product mass exactly.

Sort it

Up, down, or steady?

In each open dish, tap what happens to the reading on the balance.

Relative formula mass

Relative formula mass, Mr

The relative formula mass (Mr) of a compound is the sum of the relative atomic masses (Ar) of all the atoms in its formula.

Mr = sum of all the Ar valuesadd an Ar for every atom shown in the formula
CaCO₃ 1 × Ca = 40 1 × C = 12 3 × O = 48 Mₙ = 40 + 12 + 48 = 100
Ar: Ca = 40, C = 12, O = 16. CaCO₃ has three oxygens, so 3 × 16 = 48.

Misconception buster: Mr is a ratio of masses — it has no units. (Only when you talk about "the mass of one mole" do grams appear.)

Calculate

Your turn — find Mr

1Calculate the relative formula mass (Mr) of calcium hydroxide, Ca(OH)₂. (Ar: Ca = 40, O = 16, H = 1)
(no units)
Hint: the brackets ×2 apply to BOTH the O and the H: 40 + 2×(16 + 1).
Higher tier only

The mole & the Avogadro constant

Chemical amounts are measured in moles (symbol mol). One mole of any substance contains the same number of particles — the Avogadro constant:

N = 6.02 × 10²³ per moleone mole = 6.02 × 10²³ atoms, molecules or ions

The clever part: the mass of one mole of a substance in grams is numerically equal to its relative formula mass. So one mole of carbon (Mr = 12) is 12 g, and one mole of CO₂ (Mr = 44) is 44 g.

moles = mass (g) ÷ Mrand rearranged: mass = moles × Mₙ,  Mₙ = mass ÷ moles
mass (grams) moles Mₙ cover what you want to find
Cover mass → moles × Mr. Cover moles → mass ÷ Mr. Cover Mr → mass ÷ moles.
Worked example

How many moles are in 88 g of carbon dioxide, CO₂? (Mr = 12 + 16 + 16 = 44)

moles = 88 ÷ 44 = 2 mol

Calculate · HT

Your turn — mass to moles

2How many moles are in 120 g of sodium hydroxide, NaOH? (Ar: Na = 23, O = 16, H = 1)
mol
Hint: first Mr = 23 + 16 + 1 = 40, then moles = 120 ÷ 40.
Higher tier only

Reacting masses from an equation

A balanced equation is a recipe in moles. The big numbers give the mole ratio, which lets you work out the mass of product from the mass of a reactant:

2Mg + O₂ → 2MgO2 mol Mg makes 2 mol MgO  (a 1 : 1 ratio)
48 g Mg mass given ÷24 2 mol Mg → 2 mol MgO ×40 80 g MgO answer grams → moles → ratio → moles → grams
Route: mass ÷ Mr → moles, use the equation ratio, then moles × Mr → mass.
Worked example

What mass of MgO forms from 48 g of Mg? (Ar: Mg = 24, Mr MgO = 40)

moles Mg = 48 ÷ 24 = 2 mol → ratio 1:1 → 2 mol MgO

mass MgO = 2 × 40 = 80 g

Calculate · HT

Your turn — reacting masses

3Using 2Mg + O₂ → 2MgO, what mass of magnesium oxide is made from 12 g of magnesium? (Ar: Mg = 24, O = 16)
g
Hint: moles Mg = 12 ÷ 24 = 0.5; ratio 1:1 → 0.5 mol MgO; mass = 0.5 × 40.
Higher tier only

Limiting reactants

When two reactants are mixed, one often runs out first. The reactant that is completely used up is the limiting reactant — it limits how much product can form. The other is in excess (some is left over).

Limiting (all used up) none left Excess (some left over) some remains
The amount of product is decided by the limiting reactant — count its moles, not the excess one's.

Misconception buster: the limiting reactant is the one fully used up — not simply the one with the smaller mass. You must compare moles against the equation's ratio to decide which runs out.

Quick check

Which one runs out?

?In Mg + 2HCl → MgCl₂ + H₂, a student adds 0.10 mol of Mg to 0.10 mol of HCl. Which is the limiting reactant?
Concentration of solutions

Concentration in g/dm³

The concentration of a solution is how much solute is dissolved in a given volume of solution. The first way to measure it is mass per volume:

concentration (g/dm³) = mass (g) ÷ volume (dm³)1 dm³ = 1000 cm³ = 1 litre
25 g in 0.5 dm³ 50 g/dm³ 25 g in 1.0 dm³ 25 g/dm³ vs
Same mass of solute, bigger volume → more dilute (lower concentration).
Worked example

25 g of salt is dissolved to make 0.5 dm³ of solution.

concentration = 25 ÷ 0.5 = 50 g/dm³

Calculate

Your turn — mass of solute

4A solution has a concentration of 30 g/dm³. What mass of solute is dissolved in 2 dm³ of it?
g
Hint: rearrange — mass = concentration × volume = 30 × 2.
Higher tier · Chemistry only

Concentration in mol/dm³

Concentration can also be measured in moles per volume. This links straight to the mole equations:

concentration (mol/dm³) = moles ÷ volume (dm³)so moles = concentration × volume

To go from a g/dm³ concentration to mol/dm³, just divide by the Mr (it is the same "grams → moles" step, per dm³).

Worked example

A sodium chloride solution contains 117 g/dm³ of NaCl. (Mr NaCl = 23 + 35.5 = 58.5)

concentration = 117 ÷ 58.5 = 2 mol/dm³

Misconception buster: g/dm³ and mol/dm³ are different units. They describe the same solution but are not the same number — convert with the Mr, never assume they are equal.

Calculate · HT · CO

Your turn — moles in solution

5How many moles of solute are in 0.5 dm³ of a solution of concentration 2 mol/dm³?
mol
Hint: moles = concentration × volume = 2 × 0.5.
Chemistry only

Percentage yield

You rarely collect all the product you'd predict — some is lost on filtering, the reaction may be reversible, or side-reactions occur. The percentage yield compares what you actually got with the theoretical maximum:

% yield = (actual mass ÷ theoretical mass) × 100always between 0% and 100%
Worked example

A reaction could in theory make 8 g of product, but only 6 g is collected.

% yield = (6 ÷ 8) × 100 = 75%

No atoms are ever lost in the reaction itself — a low yield means product was lost during the process or the reaction didn't go to completion. (Calculating the theoretical mass from a reactant mass is HT.)

Calculate · CO

Your turn — percentage yield

6A student's reaction has a theoretical (maximum) mass of 6 g but they collect 4.8 g of product. Calculate the percentage yield.
%
Hint: (4.8 ÷ 6) × 100.
Chemistry only

Atom economy

The atom economy measures how much of the starting mass ends up as the useful product. High atom economy means less waste — important for sustainability and cost:

% atom economy = (Mr of desired product ÷ sum of Mr of all reactants) × 100use the balanced equation's Mₙ values
Worked example

CaCO₃ → CaO + CO₂, where CaO is the desired product.

Mr CaO = 56; reactant Mr = CaCO₃ = 100

atom economy = (56 ÷ 100) × 100 = 56%

Note the difference: % yield is about how much you actually got; atom economy is a fixed property of the equation — it doesn't depend on the lab at all.

Calculate · CO

Your turn — atom economy

7For N₂ + 3H₂ → 2NH₃, calculate the atom economy of making ammonia (NH₃). (Mr: N₂ = 28, H₂ = 2, NH₃ = 17)
%
Hint: desired = 2×NH₃ = 34; reactants = 28 + 3×2 = 34; (34 ÷ 34) × 100.
Higher tier · Chemistry only

Titration calculations

A titration finds an unknown concentration by reacting two solutions completely. If you know the concentration and volume of one, you can find the other. The key step is moles = concentration × volume:

moles = concentration (mol/dm³) × volume (dm³)convert cm³ to dm³ by dividing by 1000
burette: acid known conc. alkali indicator changes colour at the end-point
Run acid from the burette into a measured volume of alkali until the indicator just changes.
Worked example

How many moles of HCl are in 20.0 cm³ of 0.10 mol/dm³ hydrochloric acid?

volume = 20.0 ÷ 1000 = 0.020 dm³

moles = 0.10 × 0.020 = 0.002 mol

Calculate · HT · CO

Your turn — moles from a titration

8A burette delivers 20.0 cm³ of 0.50 mol/dm³ hydrochloric acid. How many moles of HCl is that?
mol
Hint: 20.0 cm³ = 0.020 dm³; moles = 0.50 × 0.020.
Higher tier · Chemistry only

Volumes of gases

Equal moles of any gas take up equal volumes under the same conditions. At room temperature and pressure (rtp: 20 °C, 1 atm), one mole of any gas occupies 24 dm³:

volume of gas (dm³) = moles × 24and: moles = volume ÷ 24  (only at rtp)
Worked example

What volume does 0.5 mol of CO₂ occupy at rtp?

volume = 0.5 × 24 = 12 dm³

This works for any gas — 1 mol of hydrogen and 1 mol of carbon dioxide both fill 24 dm³ at rtp, even though they have very different masses.

Calculate · HT · CO

Your turn — gas volume

9What volume does 2 mol of hydrogen gas occupy at room temperature and pressure (molar gas volume = 24 dm³)?
dm³
Hint: volume = moles × 24 = 2 × 24.
Sort it

Has units, or not?

Tap a quantity, then tap the box it belongs in.

📏 Has units

🚫 No units (a ratio)

Recap

The equations to know

Conservation of mass: mass of reactants = mass of products

Relative formula mass: Mr = sum of all Ar (no units)

Moles (HT): moles = mass ÷ Mr  (1 mol = 6.02 × 10²³)

Concentration: g/dm³ = mass ÷ volume; mol/dm³ = moles ÷ volume

Percentage yield (CO): (actual ÷ theoretical) × 100

Atom economy (CO): (Mr desired ÷ Σ Mr reactants) × 100

Gas volume (HT, CO): volume (dm³) = moles × 24 at rtp

You've covered the whole of AQA 4.3 — from conservation of mass and Mr through moles, reacting masses, concentration, yield, atom economy, titrations and gas volumes. Press Finish to see your score.

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