Calculating Theoretical, Actual, and Percent Yield
The theoretical yield is the maximum amount of product that a reaction can give according to stoichiometry, the actual yield is the amount actually obtained in an experiment, and the percent yield is (actual yield ÷ theoretical yield) × 100%. In brief: if the calculation shows that 2.61 g of aspirin should form from 2.00 g of salicylic acid, and 2.10 g is collected, the percent yield is 2.10 ÷ 2.61 × 100% = 80.5%.
No real reaction gives a perfect yield. Some product is lost in handling, some reactants form other products, and some reactions do not go to completion. Percent yield measures the efficiency of a reaction and is a key figure in laboratories and industry. This article explains the three kinds of yield, shows how to calculate them, explains why the actual yield is lower than the theoretical yield, covers multi-step syntheses and atom economy, gives tables and worked examples and some history.
What are the three kinds of yield?
- Theoretical yield: the maximum possible amount of product, calculated from the balanced equation and the limiting reactant. It is a calculation, not a measurement.
- Actual yield: the mass (or moles) of product that is actually isolated and measured after the experiment. It is always found by experiment.
- Percent yield: the actual yield as a percentage of the theoretical yield. Actual and theoretical yields must be in the same unit.
How do you calculate each yield?
- Write the balanced equation and identify the limiting reactant.
- Calculate the theoretical yield from the limiting reactant, using the mass-to-mass method.
- Measure the actual yield of the isolated, dry and pure product.
- Calculate the percent yield: percent yield = (actual yield ÷ theoretical yield) × 100%.
The percent yield can be rearranged to find the actual yield (actual = theoretical × percent ÷ 100) or the amount of reactant needed to obtain a desired mass of product (working backward).
Why is the actual yield lower?
- Incomplete reaction: reactions that reach equilibrium do not convert all the reactants. The Haber process gives only about 15% ammonia per pass.
- Side reactions: reactants form other products.
- Loss during separation and purification: product remains on glassware or filter paper, dissolves in the solvent during washing or is lost by transfer.
- Impure reactants: reagents that contain impurities provide less of the reactant than their mass suggests.
- Measurement errors: inaccurate weighing or poor technique.
A percent yield above 100% means that the product contains impurities or is wet (for example, solvent or water has not been completely removed), or that there is an error in the calculation.
Typical yields in practice
| Process | Typical percent yield | Comment |
|---|---|---|
| Precipitation of a salt, carefully done | 90 to 99% | Small losses in filtering and washing |
| Student synthesis of aspirin | 60 to 85% | Losses during recrystallization |
| Industrial ammonia synthesis (per pass) | about 15%, with recycling of unreacted gases to give over 95% overall | Equilibrium limits one pass |
| Multi-step drug synthesis (10 steps at 85% each) | about 20% | Losses compound at each step |
| Combustion of fuels in a good furnace | Nearly 100% of the carbon oxidized | Complete combustion |
Worked examples
- Percent yield of aspirin. Salicylic acid (138.12 g/mol) 2.00 g reacts with excess acetic anhydride to give aspirin (180.16 g/mol). n = 2.00 ÷ 138.12 = 0.01448 mol, so the theoretical yield is 0.01448 × 180.16 = 2.61 g. If 2.10 g is collected, the percent yield is 2.10 ÷ 2.61 × 100% = 80.5%.
- Precipitate. The theoretical yield of AgCl from 5.00 × 10−3 mol of silver ions is 5.00 × 10−3 × 143.32 = 0.717 g. A student collects 0.680 g. Percent yield = 0.680 ÷ 0.717 × 100% = 94.8%.
- Actual yield from the percent yield. A reaction has a theoretical yield of 25.0 g and a percent yield of 72.0%. The actual yield is 25.0 × 0.720 = 18.0 g.
- Reactant needed for a target. A chemist wants 50.0 g of product, and the reaction has an 80.0% yield. The theoretical yield must be 50.0 ÷ 0.800 = 62.5 g. If this corresponds to 0.400 mol of the reactant, the chemist should start with at least that amount (and in practice a little more).
- Limiting reactant first. 5.00 g of Al and 10.0 g of Cl2 give 11.6 g of AlCl3. From the previous article the limiting reactant is Cl2, and the theoretical yield is 12.5 g. Percent yield = 11.6 ÷ 12.5 × 100% = 92.8%.
- Iron production. A blast furnace is fed with 1,000 kg of Fe2O3 and produces 650 kg of iron. The theoretical yield is 699 kg (see the mass-to-mass article). The percent yield is 650 ÷ 699 × 100% = 93.0%.
- Percent yield greater than 100%. A student obtains 3.15 g of a product with a theoretical yield of 2.97 g. The percent yield is 106%, which shows that the product is not dry or has impurities. It should be dried to constant mass and its purity should be tested.
What about reactions with several steps?
In a synthesis with several steps, the overall percent yield is the product of the yields of the individual steps: overall = y1 × y2 × y3 × … For three steps with yields of 90%, 85% and 75%, the overall yield is 0.90 × 0.85 × 0.75 = 0.574, or 57.4%. A synthesis with 10 steps, each with 85% yield, has an overall yield of 0.8510 = 0.197, or about 20%. This is why chemists try to reduce the number of steps and to increase each yield.
What is atom economy?
Percent yield measures how much of the possible product is obtained, but not how much of the reactant mass ends up in the desired product. Atom economy is the molar mass of the desired product divided by the sum of the molar masses of all reactants, multiplied by 100%. In the aspirin synthesis, the reactants are 138.12 + 102.09 = 240.21 g/mol, and the product is 180.16 g/mol: atom economy = 180.16 ÷ 240.21 × 100% = 75.0%. The rest forms acetic acid as a by-product. In “green chemistry” reactions with a high atom economy are preferred, since they produce less waste.
How did the idea develop?
The distinction between calculated and obtained amounts was part of quantitative chemistry from the time of Lavoisier. In the 19th century, chemists such as Justus von Liebig and Friedrich Wöhler reported yields of synthetic compounds, which became standard in the chemical literature. In the 1990s, Barry Trost introduced the concept of atom economy (1991), and Paul Anastas and John Warner formulated the principles of green chemistry (1998), which added new measures of efficiency.
Which mistakes are common?
Mistake 1: Using the excess reactant to calculate the theoretical yield
The theoretical yield is determined by the limiting reactant.
Mistake 2: Mixing units
Actual and theoretical yields must be in the same units (grams or moles).
Mistake 3: Dividing the theoretical yield by the actual yield
Percent yield = actual ÷ theoretical × 100%.
Mistake 4: Averaging step yields instead of multiplying them
The overall yield of a multi-step reaction is the product of the step yields, not their average.