Percentage yield
The theoretical yield is the largest mass of product you could make, worked out from the balanced equation. The actual yield is the mass you really collect.
Percentage yield = actual yield ÷ theoretical yield × 100
The yield is almost always less than 100%, because:
- the reaction may be reversible, so it never fully finishes;
- some reactants make other products (side reactions);
- some product is lost when it is separated, filtered or poured;
- the reactants may be impure.
To find the theoretical yield, use moles: mass of reactant → moles → ratio → moles of product → mass.
Atom economy
Atom economy measures how much of the starting material ends up in the product you want.
Atom economy = Mr of wanted product ÷ sum of Mr of all reactants × 100
Use the numbers in the balanced equation: if the equation has 2Fe, use 2 × 56. Because mass is conserved, the total Mr of reactants equals the total Mr of all products.
Reactions with only one product (like making ethanol from ethene and water) have 100% atom economy. Reactions that make waste products have a lower one.
Why both matter: choosing a reaction route
A high atom economy means fewer waste atoms, less pollution and fewer raw materials used up. This is important for sustainable development. A high yield means less product is lost.
The two are different. A reaction can have a 100% atom economy but a low yield (for example a reversible reaction), or a high yield but a poor atom economy. Chemists choose a route by looking at atom economy, yield, rate of reaction, energy needed, and whether the waste product can be sold or used. For example, the CO₂ from making lime could be captured and used.
Try it: laddoo yield
Next time you help make a snack from a recipe, check what the recipe says it makes (theoretical yield) and count what you really get (actual yield). Work out the percentage yield. Then list why it was less: mixture left in the bowl, broken pieces, tasting along the way! Use the slider in the 3D to see the same idea with mass.
Key formulas and definitions
- Percentage yield = actual yield ÷ theoretical yield × 100
- Atom economy = Mr of wanted product ÷ total Mr of reactants × 100
- Theoretical yield: mass → moles → ratio → moles → mass
- Total Mr of reactants = total Mr of products (mass conserved)
- Addition reactions with one product: atom economy = 100%
Worked examples
1. The theoretical yield is 20 g and the actual yield is 15 g. Find the percentage yield.
15 ÷ 20 × 100 = 75%.
2. Find the atom economy for making CaO: CaCO₃ → CaO + CO₂ (CaCO₃ 100, CaO 56).
56 ÷ 100 × 100 = 56%.
3. Find the atom economy for making iron: Fe₂O₃ + 3CO → 2Fe + 3CO₂ (Fe₂O₃ 160, CO 28, Fe 56).
Reactants: 160 + 3 × 28 = 244. Wanted: 2 × 56 = 112. 112 ÷ 244 × 100 = 45.9%.
4. 50 g of CaCO₃ is heated and 22.4 g of CaO is collected. Find the percentage yield.
n(CaCO₃) = 50 ÷ 100 = 0.5 mol → 0.5 mol CaO → theoretical = 0.5 × 56 = 28 g. Yield = 22.4 ÷ 28 × 100 = 80%.
5. Hydrogen can be made by CH₄ + H₂O → CO + 3H₂. Find the atom economy for hydrogen (CH₄ 16, H₂O 18, H₂ 2).
Reactants: 16 + 18 = 34. Wanted: 3 × 2 = 6. 6 ÷ 34 × 100 = 17.6%.
6. A reaction has an 85% yield. The theoretical yield is 40 g. What mass is collected?
Actual = 85 ÷ 100 × 40 = 34 g.
Common mistakes
- Dividing theoretical by actual. It is actual ÷ theoretical, so the answer is 100% or less.
- Forgetting the big numbers from the equation (use 2 × 56 for 2Fe).
- Thinking atom economy and yield are the same. Atom economy comes from the equation; yield comes from the experiment.
- Including only some reactants in the bottom of the atom economy fraction. Add the Mr of all reactants.