The two percentages
Percentage yield compares what you made with what the equation promised: actual ÷ theoretical × 100 — and it works in moles OR grams, as long as top and bottom match. Percentage error compares your instrument's uncertainty with what you measured: uncertainty ÷ measured value × 100.
The detail examiners test: when a result comes from two readings — a burette titre (final − start), a temperature change (end − start) — the uncertainty doubles, because each reading brings its own.
Percentage yield started at GCSE — the fuller treatment is in C3 — Yield & atom economy.
% yield = actualtheoretical × 100 · % error = uncertaintymeasured value × 100
Worked example — % error on 50.0 cm3 in a ±0.5 cm3 cylinder
- One reading, so the uncertainty stays ±0.5 cm3.
% error = 0.5 ÷ 50.0 × 100 = 1.0%
Practice
Theoretical yield 5.0 g, actual 3.9 g — % yield?
Worked steps
- % yield = actual ÷ theoretical × 100
- 3.9 ÷ 5.0 × 100 = 78%
A reaction should make 0.050 mol of product; 0.040 mol is collected — % yield?
Worked steps
- Yield works in moles too — top and bottom just have to match.
- 0.040 ÷ 0.050 × 100 = 80%
A thermometer reads to ±0.5 °C. Temperature rises from 21.0 °C to 29.0 °C. % error in ΔT?
Worked steps
- ΔT = 29.0 − 21.0 = 8.0 °C
- Two readings → uncertainty = 2 × 0.5 = 1.0 °C
- 1.0 ÷ 8.0 × 100 = 12.5%
A burette reading has uncertainty ±0.05 cm3, and a titre uses two readings. % error on a 25.00 cm3 titre?
Worked steps
- Two readings → uncertainty = 2 × 0.05 = 0.10 cm3
- 0.10 ÷ 25.00 × 100 = 0.4%
You need exactly 25.0 cm3 of solution as accurately as possible. Best apparatus? Tick (✓) one box.
Atom economy
Percentage yield asks “how much of the product did I actually make?” — atom economy asks a different question: “how much of my starting material ends up as the product I want, rather than as waste?” A reaction can have a high yield but a poor atom economy if it also makes a lot of unwanted by-product. It's a Chemistry-only GCSE topic (Triple, not Combined), so it's worth a look before September if you did Combined Science.
% atom economy = Mr of desired productsum of Mr of all reactants × 100
The full GCSE treatment, with more worked examples, is in C3 — Yield & atom economy.
Hydrogen is made from methane and steam: CH4 + 2H2O → 4H2 + CO2. Calculate the atom economy for making hydrogen. Mr: CH4 16.0, H2O 18.0, H2 2.0.
Worked steps
- Desired product = 4H2 = 4 × 2.0 = 8.0
- Sum of reactant Mr = 16.0 + 2 × 18.0 = 52.0
- 8.0 ÷ 52.0 × 100 = 15.4%
How did you do?
Work through the questions above and your score appears here.
Next up is Module 6 — Practical & Data Skills, where this error work meets the vocabulary examiners check word by word. If you've come this far, retake the diagnostic and watch the bars move.
That's fixable before September — I take on a small number of A-Level students each year →