How to Calculate Percent Yield (With Examples)

$$\text{percent yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$$

• Actual yield: the amount of product you really collected. It is usually given in the problem or measured in the lab.
• Theoretical yield: the maximum amount of product the reaction could make, calculated with stoichiometry from the limiting reactant.

Both yields must be in the same units, usually grams.

Quick example: A reaction could make 25.0 g of product, and you collect 21.3 g.

$$\frac{21.3 \text{ g}}{25.0 \text{ g}} \times 100\% = 85.2\%$$

Most problems give you a starting mass of reactant instead of the theoretical yield. Then you need stoichiometry before the percent yield formula.

Problem: Heating 50.0 g of calcium carbonate produces 25.8 g of calcium oxide. What is the percent yield?

$$\mathrm{CaCO_3 \rightarrow CaO + CO_2}$$

Molar masses (g/mol): $\mathrm{CaCO_3}$ 100.09, CaO 56.08.

1. Grams to moles of reactant:

$$50.0 \text{ g} \div 100.09 \text{ g/mol} = 0.4996 \text{ mol CaCO}_3$$

2. Mole ratio: 1 mol $\mathrm{CaCO_3}$ makes 1 mol CaO, so 0.4996 mol CaO is possible.
3. Moles to grams of product (theoretical yield):

$$0.4996 \text{ mol} \times 56.08 \text{ g/mol} = 28.0 \text{ g CaO}$$

4. Percent yield:

$$\frac{25.8}{28.0} \times 100\% = 92.1\%$$

(Using the unrounded theoretical yield of 28.01 g also gives 92.1%. Keep extra digits until the last step.)

When two reactant amounts are given, find the limiting reactant first. Only the limiting reactant sets the theoretical yield.

Problem: A student makes aspirin from 2.00 g of salicylic acid ($\mathrm{C_7H_6O_3}$) and 5.00 g of acetic anhydride ($\mathrm{C_4H_6O_3}$). She collects 2.05 g of aspirin ($\mathrm{C_9H_8O_4}$). Find the percent yield.

$$\mathrm{C_7H_6O_3 + C_4H_6O_3 \rightarrow C_9H_8O_4 + CH_3COOH}$$

Molar masses (g/mol): salicylic acid 138.12, acetic anhydride 102.09, aspirin 180.16.

1. Moles of each reactant:
   • Salicylic acid: $2.00 \div 138.12 = 0.01448$ mol
   • Acetic anhydride: $5.00 \div 102.09 = 0.04898$ mol
2. Limiting reactant: the ratio is 1 to 1, so the smaller number of moles is limiting. That is salicylic acid.
3. Theoretical yield: $0.01448 \text{ mol} \times 180.16 \text{ g/mol} = 2.61$ g of aspirin.
4. Percent yield:

$$\frac{2.05}{2.61} \times 100\% = 78.6\%$$

(With the unrounded theoretical yield, 2.609 g, the answer is still 78.6%.)

Sometimes you know the percent yield and need the actual yield, or the amount you must plan to make. Rearrange the formula:

$$\text{actual} = \text{theoretical} \times \frac{\text{percent yield}}{100} \qquad \text{theoretical} = \frac{\text{actual}}{\text{percent yield} / 100}$$

Example 1: A reaction has a theoretical yield of 40.0 g and typically runs at 75.0% yield. How much product should you expect?

$$40.0 \text{ g} \times 0.750 = 30.0 \text{ g}$$

Example 2: You need 50.0 g of product, and the reaction gives an 80.0% yield. What theoretical yield should you plan for?

$$\frac{50.0 \text{ g}}{0.800} = 62.5 \text{ g}$$

Then use stoichiometry in reverse to find how much starting material produces 62.5 g in theory.

• Below 100%: normal. Product is lost during filtering and transfers, side reactions make other products, or the reaction does not go to completion.
• Exactly 100%: possible on paper but rare in a real lab.
• Above 100%: a warning sign. The product is usually still wet with water or solvent, or it contains impurities. It can also mean the theoretical yield was calculated from the wrong reactant.

If you get more than 100%, recheck the limiting reactant and the molar masses before blaming the lab. Paste it into the VeilGPT solver to check your steps.