Worked example 1
A reaction has a theoretical yield of 12.5 g of aspirin, and 9.85 g is recovered. What is the percent yield?
Try it first: Estimate first: is the answer nearer 60 %, 80 % or 95 %?
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StoichiometryPercent yieldContent level: Core 20 min
Percent Yield
What you'll be able to do: Compare an actual laboratory yield with the theoretical yield and interpret what the percentage says about the experiment.
Best after: Limiting Reactant and Excess
Introduction
Calculations predict the maximum. Flasks deliver less. Percent yield is the honest comparison between the two, and learning to read it is how a calculation becomes an evaluation of an experiment rather than just an answer.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Distinguish theoretical, actual and percent yield.
- Calculate percent yield from experimental data.
- Work backwards from a percent yield to a predicted actual mass.
- Explain common physical reasons a yield falls below or appears above 100 %.
Lesson
Three yields, three meanings
Theoretical yield is calculated from the limiting reactant and represents perfection. Actual yield is measured on a balance after the product is isolated and dried. Percent yield is the ratio of the two. Only the actual yield is data; the other two are, respectively, a prediction and a judgement about the prediction.
The theoretical yield always comes from the limiting reactant, never from the excess reactant.
The calculation
Divide the actual yield by the theoretical yield and multiply by 100. Both quantities must describe the same product and use the same unit, so if one is in grams and the other in moles, convert first. Because it is a ratio of two masses of the same substance, the units cancel and percent yield is dimensionless.
percent yield = (actual yield / theoretical yield) × 100 %
Why yields fall short
Product is lost when transferring between containers, some stays dissolved in the filtrate, side reactions consume reactants, the reaction may not reach completion, and purification always removes some product along with impurities. None of these is a mistake in the calculation, they are physical facts about doing chemistry.
A good explanation of a low yield names a physical loss, not simply human error.
Yields above 100 %
A percent yield above 100 % is not possible for the pure product, so it is a signal. The usual causes are a product that is still wet with solvent, an impure product containing unreacted starting material, a mis-set limiting reactant, or an unbalanced equation. Treat it as a diagnostic prompt to re-check both the calculation and the drying step.
Above 100 % means something is wrong or something extra was weighed.
Working backwards
If a reaction is known to run at, say, 78 % yield, you can predict the product mass: actual = 0.78 x theoretical. Chemists also invert this to decide how much starting material to buy for a target amount of product, which is the everyday industrial use of this idea.
actual yield = (percent yield / 100) x theoretical yield
Trace an error to the numerator or denominator
A percent yield is actual divided by theoretical, so an error's direction depends on which quantity it changes. A wet or contaminated product raises the measured actual mass and inflates the reported percent. Losing solid during transfer lowers actual mass and the percent. Overestimating the limiting reactant raises the calculated theoretical yield and lowers the percent even if the collected mass is unchanged. Name the affected measurement first, then follow the ratio. A value under 100% alone does not tell you which loss mechanism occurred.
Key ideas
Definition
Theoretical yield
The maximum product mass predicted from the limiting reactant, assuming complete reaction and no losses.
Definition
Actual yield
The mass of purified product actually recovered and weighed.
Definition
Percent yield
Actual divided by theoretical, times 100. Dimensionless.
Rule
Same substance, same units
Both yields must refer to the same product and be expressed in the same unit before dividing.
Assumption
The product is pure and dry
Percent yield only means what it claims if the weighed sample is the isolated product, not product plus solvent.
Equation
Percent yield
percent yield = (actual / theoretical) × 100 %
- actual = measured mass (or moles) of purified product
- theoretical = maximum predicted from the limiting reactant, same units
- use when = an experimental product mass is reported alongside a calculation
- limits = values above 100 % indicate impurity or a calculation error, not a better reaction
Equation
Predicted actual yield
actual = (percent yield / 100) x theoretical
- percent yield = an efficiency known from previous runs
- use when = planning how much product a given amount of reactant will really deliver
- limits = assumes the new run behaves like the previous ones
Worked examples
Worked example 2
Burning 25.0 g of C₃H₈ in excess O₂ gives 68.2 g of CO₂. What is the percent yield? C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O
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Worked example 3
A synthesis reliably runs at 65.0 % yield. If the theoretical yield is 40.0 g, how much product should you expect, and how much would you need theoretically to obtain 40.0 g of product?
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Worked example 4
The theoretical yield is 5.00 g. A collected product weighs 4.60 g while wet and 4.20 g after drying. What are the two apparent percent yields?
Try it first: Use the same theoretical mass with each measured actual mass.
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Common mistakes
Dividing theoretical by actual.
Why it's wrong: That gives a value above 100 % for any normal experiment and reverses the meaning of the number.
Check instead: Actual on top, always. The measured value is the numerator.
Calculating the theoretical yield from the excess reactant.
Why it's wrong: The excess reactant is still present when the reaction stops, so the prediction is too large and the percent yield is falsely low.
Check instead: Identify the limiting reactant before computing any theoretical yield.
Dividing a mass by a mole value.
Why it's wrong: The units do not cancel, so the result is not a percentage.
Check instead: Convert both to the same unit for the same substance first.
Reporting a yield above 100 % as a good result.
Why it's wrong: You cannot recover more pure product than the limiting reactant can supply, so it points to a wet or impure sample or a calculation error.
Check instead: Re-check the limiting reactant, the balanced equation, and whether the product was dried.
Explaining a low yield only as human error.
Why it's wrong: Most losses are inherent to the procedure, such as transfer losses and solubility in the filtrate.
Check instead: Name a specific physical loss step when asked to explain a low yield.
After the lesson · Question bank
Independent practice
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What you should now know
Percent yield is the actual yield divided by the theoretical yield, times 100. The theoretical yield always comes from the limiting reactant. Both masses must be for the same substance and in the same units, and a value above 100 % signals an error or an impure product rather than an unusually good reaction.
- Percent yield = actual / theoretical x 100, with both for the same product in the same units.
- Theoretical yield always comes from the limiting reactant.
- Yields below 100 % are normal and usually reflect transfer, solubility and purification losses.
- A yield above 100 % is a diagnostic signal of impurity, moisture, or a calculation error.
Sources and further reading
- Chemistry 2e, Section 4.4: Reaction YieldsPaul Flowers, Klaus Theopold, Richard Langley, William R. Robinson · OpenStax, Rice University · Chapter 4.4View source
Chemistry 2e, OpenStax, Rice University, licensed CC BY 4.0. License