Percent Yield Explained: Theoretical vs. Actual Yield

On paper, chemical reactions are perfect. Balance the equation, do the stoichiometry, and you know exactly how many grams of product you’ll get. In the lab, you almost never get that much. The gap between the two is measured by percent yield, and it’s one of the most practical numbers in chemistry — the difference between a profitable industrial process and a failed one.

Three yields

• Theoretical yield — the maximum amount of product possible, calculated from the limiting reagent using a balanced equation.
• Actual yield — the amount you really collect and weigh at the end.
• Percent yield — how close you got:

percent yield = actual yield ÷ theoretical yield × 100

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

Worked example 1

Heating 10.0 g of calcium carbonate produces calcium oxide. A student collects 5.18 g of CaO. What is the percent yield?

Step 1 — balanced equation: CaCO₃ → CaO + CO₂

Step 2 — theoretical yield.

• Moles of CaCO₃: 10.0 g ÷ 100.09 g/mol = 0.09991 mol
• Ratio 1 : 1, so 0.09991 mol CaO
• Mass: 0.09991 mol × 56.08 g/mol = 5.603 g

Step 3 — percent yield: 5.18 ÷ 5.603 × 100 = 92.5%

Worked example 2: with a limiting reagent

5.00 g of aluminium reacts with 15.0 g of chlorine. The actual yield of aluminium chloride is 18.1 g.

2Al + 3Cl₂ → 2AlCl₃

• Al: 5.00 ÷ 26.98 = 0.1853 mol → ÷ 2 = 0.0927
• Cl₂: 15.0 ÷ 70.90 = 0.2116 mol → ÷ 3 = 0.0705

Chlorine is limiting. AlCl₃ formed: 0.0705 × 2 = 0.1410 mol × 133.33 g/mol = 18.81 g theoretical.

Percent yield: 18.1 ÷ 18.81 × 100 = 96.2%

Why yields fall short

Real yields below 100% are normal, and the reasons are worth knowing:

• The reaction doesn’t go to completion. Many reactions reach an equilibrium where reactants and products coexist (see Le Chatelier’s principle).
• Side reactions. Some reactants form unwanted by-products instead.
• Losses during handling. Product sticks to glassware, stays dissolved in the liquid during filtration, or is lost when transferring between containers.
• Purification. Recrystallizing to get a pure product always sacrifices some of it.
• Impure or wet starting materials, which means you had less reactant than you thought.

In multi-step syntheses the losses multiply. Five steps at 80% each give an overall yield of 0.8⁵ = 33%. Twenty steps at 90% give only about 12%. That’s why pharmaceutical chemists work so hard to shorten synthetic routes.

When yield is over 100%

A percent yield above 100% doesn’t mean you’ve made matter from nothing. It means the product you weighed isn’t just the product:

• It’s still wet with solvent or water.
• It contains impurities or unreacted starting material.
• It’s a hydrate that has absorbed water from the air.
• There’s a weighing or calculation error — often the wrong molar mass or the wrong limiting reagent.

Atom economy: a different efficiency

Percent yield tells you how well a reaction worked in practice. Atom economy asks how much of the reactants’ mass could ever end up in the desired product, even at 100% yield:

atom economy = molar mass of desired product ÷ total molar mass of reactants × 100

A reaction that makes a lot of waste by-product has a poor atom economy no matter how skilled the chemist. Green chemistry tries to maximize both numbers.

Quick answers

Is a 70% yield good? It depends entirely on the reaction. For a simple precipitation, 70% is disappointing; for a difficult organic synthesis, it can be excellent.

Do I use grams or moles? Either, as long as actual and theoretical are in the same unit.

Why calculate theoretical yield from the limiting reagent? Because the reaction stops when the limiting reagent runs out. The excess reactant can’t make more product on its own.

Calculate it

The limiting reagent calculator finds the theoretical yield of every product and, if you enter your actual yield, the percent yield.