How to Calculate Percent Yield Step by Step

The percent yield formula is actual yield divided by theoretical yield, multiplied by 100. Suppose a reaction should theoretically produce 20 grams of product, but the experiment produces 16 grams. Divide 16 by 20 to get 0.8, then multiply by 100. The percent yield is 80 percent.

This is the basic method for calculating percent yield, but the two yields must refer to the same product and use compatible units. Do not divide grams by moles or compare the yield of one substance with the predicted amount of another. Convert quantities first if the question gives them in different forms.

In many chemistry questions, theoretical yield is not given directly. You may need to calculate it from the reactants. Start with a balanced chemical equation, convert the available reactant amount to moles, identify the limiting reactant when necessary, and use the equation's mole ratio to predict the number of moles of product.

You can then convert the predicted product into the requested unit, often grams. Only after that should you calculate the percent yield. Keeping the stoichiometry and percent calculation as separate stages makes the problem easier to check. If the theoretical yield is wrong, the final percentage will also be wrong even if the division is performed perfectly.

Real experiments rarely collect every particle of the product predicted by a simple equation. A reaction may not go to completion, competing reactions may occur, or some product may remain in equipment. Material can also be lost during filtering, transferring, drying, or purification. These practical losses often make actual yield smaller than theoretical yield.

When calculating percent yield, a result above 100 percent should make you investigate rather than immediately assume chemistry has broken its own rules. The measured product may contain water, solvent, impurities, or another substance that increases its mass. Measurement errors can also matter. A percent yield calculation is therefore both a mathematical result and a clue about the experiment.

Suppose you burn 12 grams of magnesium in excess oxygen to make magnesium oxide and collect 18 grams of product. First find the theoretical yield. The equation is 2Mg + O2 gives 2MgO, and magnesium's molar mass is about 24 grams per mole, so 12 grams is 0.5 moles. The ratio of Mg to MgO is one to one, so you expect 0.5 moles of MgO. Its molar mass is about 40 grams per mole, so the theoretical yield is 20 grams. Now the percent yield: 18 divided by 20 is 0.9, so 90 percent.

Notice that the chemistry took four steps and the percentage took one. If a question gives 24 grams of product, stop before dividing. A yield of 120 percent means the product was weighed wet or impure, or the mass of the crucible crept into the reading, and saying which is the mark-winning part of the answer.

Making a useful compound, such as a medicine, often takes several reactions in a row, with the product of one step becoming the starting material for the next. The yields then multiply rather than add. If each of five steps gives an 80 percent yield, the overall yield is 0.8 multiplied by itself five times, which is about 33 percent. Ten such steps would leave only about 11 percent. This is why chemists value shorter routes so highly, and why improving one weak step can make a large difference.

Percent yield also differs from atom economy, another measure you may meet. Atom economy compares the mass of the desired product with the total mass of everything produced, according to the balanced equation, so it shows how much of the starting material could ever end up in the useful product. A reaction can have a 95 percent yield and still waste a great deal if it creates heavy by-products, while a reaction with excellent atom economy can still give a poor yield in practice. Green chemistry pays attention to both numbers.

Industrial chemists often accept reactions with surprisingly poor yields, as long as little is wasted. The Haber process for making ammonia is the textbook case. Because the reaction between nitrogen and hydrogen is reversible, it reaches equilibrium before the reactants are used up, and under typical industrial conditions only around 15 percent of the gases are converted into ammonia each time they pass over the iron catalyst. The plant then cools the mixture so that ammonia condenses into a liquid and can be removed, while the unreacted nitrogen and hydrogen are sent back round to try again.

Through repeated recycling, the overall conversion of the starting gases can reach well over 95 percent, even though a single pass looks unimpressive. Industry also splits yield into two parts. Conversion is the fraction of a reactant that reacts at all, and selectivity is the fraction of the reacted material that becomes the product you want rather than by-products. For a simple one to one reaction, yield is conversion multiplied by selectivity. If 60 percent of a reactant reacts and 75 percent of that forms the desired product, the yield is 45 percent. Knowing which of the two numbers is low tells you what to fix.

Making aspirin in the laboratory shows a trade-off that percent yield alone can hide. Aspirin is made by reacting salicylic acid with acetic anhydride, which is used in excess so that salicylic acid is limiting. One mole of salicylic acid, 138 grams, gives one mole of aspirin, 180 grams. Starting from 2.00 grams of salicylic acid, about 0.0145 moles, the theoretical yield is about 2.61 grams. Suppose the dried crude product weighs 2.10 grams, an 80 percent yield. After recrystallising it to remove impurities, perhaps 1.70 grams remain, so the yield of pure aspirin is only about 65 percent.

Recrystallisation loses product deliberately. The crude solid is dissolved in a small amount of hot solvent and allowed to cool, so that aspirin crystallises out while most impurities stay dissolved. Some aspirin always stays dissolved too and is poured away with the leftover liquid. Using too much solvent loses more, while rushing the cooling can trap impurities in the crystals. Chemists then check purity with a melting point. Pure aspirin melts sharply at around 135 degrees Celsius, while an impure sample starts melting lower and over a wider range of temperatures. A high yield of impure material is often worth less than a lower yield of pure product.

Calculating percent yield is straightforward once both yields are known: divide actual yield by theoretical yield and multiply by 100. The harder part is often finding a correct theoretical yield through stoichiometry. Keep units consistent, identify the limiting reactant when needed, and treat unusual percentages as reasons to check your work.