Percentage yield compares the mass of product you actually obtained with the maximum mass the balanced equation predicts. The formula is percentage yield = actual mass ÷ theoretical mass × 100.
It follows on from gas volume and moles inside concentration, gas and yield calculations, because the theoretical mass comes from the same moles-and-ratio chain.
What is the theoretical mass?
The theoretical mass is what you would collect if all of the limiting reactant became product and none was lost. You find it from the equation, not from the experiment.
The chain is: mass of reactant → moles of reactant → moles of product by the equation ratio → mass of product. The actual mass is simply the number the question gives you for what was obtained.
What are the steps?
- Write the balanced equation and underline the reactant you are given.
- Convert its mass to moles using mass ÷ molar mass.
- Use the ratio to find moles of the product.
- Convert to theoretical mass using moles × molar mass.
- Compute actual ÷ theoretical × 100 and check that the answer is below the full theoretical amount.
Worked example
The numbers are invented for practice. Heating 10.0 g of calcium carbonate gives calcium oxide and carbon dioxide: CaCO₃ → CaO + CO₂. A student collects 4.48 g of calcium oxide. Find the percentage yield.
Step 1, moles of CaCO₃: Mᵣ = 40 + 12 + (3 × 16) = 100. Moles = 10.0 ÷ 100 = 0.100 mol.
Step 2, ratio: CaCO₃ : CaO is 1 : 1, so moles of CaO = 0.100 mol.
Step 3, theoretical mass: Mᵣ of CaO = 40 + 16 = 56. Mass = 0.100 × 56 = 5.60 g.
Step 4, percentage yield: 4.48 ÷ 5.60 × 100 = 80.0%.
Check: 80.0% of 5.60 g is 0.800 × 5.60 = 4.48 g. The answer matches the data.
What is the mistake to watch for?
A common slip is to divide the product mass by the mass of reactant instead of the theoretical mass of product.
Mistaken working: percentage yield = 4.48 ÷ 10.0 × 100 = 44.8%
The student compared the mass of calcium oxide with the mass of calcium carbonate, which are different substances with different molar masses.
The correct comparison is always product with product. Find the theoretical mass of the product from the equation first, then compare the measured mass of that same product with it.
Check yourself
Try these, then open the answers.
1. The theoretical mass of a product is 12.5 g and 9.0 g was obtained. Find the percentage yield.
Show answer
9.0 ÷ 12.5 × 100 = 72%.
2. A reaction has a percentage yield of 75%. The mass obtained is 6.0 g. What was the theoretical mass?
Show answer
Theoretical mass = 6.0 ÷ 0.75 = 8.0 g.
3. 4.80 g of magnesium reacts completely: 2Mg + O₂ → 2MgO. A mass of 6.4 g of magnesium oxide is obtained. Find the percentage yield. (Aᵣ: Mg = 24, O = 16.)
Show answer
Moles of Mg = 4.80 ÷ 24 = 0.200 mol. Ratio Mg : MgO is 2 : 2, so MgO = 0.200 mol. Mᵣ of MgO = 40, so the theoretical mass is 0.200 × 40 = 8.0 g. Yield = 6.4 ÷ 8.0 × 100 = 80%.
Where does this lead next?
Yield alone does not say how clean a product is, so continue with yield versus purity. The mole and equation-ratio tutor can confirm the moles step of your theoretical-mass calculation.
If you can follow a worked yield example but freeze on a new one, the gap is usually in choosing the limiting reactant or the ratio. That is something a teacher can isolate in online one-to-one Chemistry tuition.