How to use the limiting reagent and yield calculator
- Enter each reactant with its coefficient from the balanced equation, its molar mass and the grams you have.
- Enter each product with its coefficient and molar mass, and the actual yield in grams if you measured one.
- Read which reactant runs out first and the theoretical yield of each product.
- Check the leftover of each excess reactant and the percent yield.
Formula
Moles = grams / molar mass
Extent = smallest of (moles / coefficient) over the reactants
Product formed = coefficient x extent; theoretical grams = moles formed x molar mass
Leftover = (moles - coefficient x extent) x molar mass; percent yield = actual / theoretical x 100
The limiting reagent is the reactant with the smallest ratio of moles to coefficient. Equation coefficients must come from a balanced equation.
Water, aluminum and methane
2 H2 + O2 -> 2 H2O with 10.0 g of H2 (2.016 g/mol) and 64.0 g of O2 (31.998 g/mol): there are 4.9603 mol of H2, which supports 2.4802 steps of the reaction, and 2.0001 mol of O2, which supports 2.0001 steps. Oxygen is limiting. The theoretical yield of water is 4.0003 mol x 18.015 = 72.065 g, and 1.935 g of hydrogen is left.
Fe2O3 + 2 Al -> Al2O3 + 2 Fe with 50.0 g of Fe2O3 and 20.0 g of Al: Fe2O3 is limiting, the theoretical yield of Al2O3 is 31.924 g, and if 18.0 g was actually made the percent yield is 56.38 percent. 3.104 g of aluminum is left. CH4 + 2 O2 -> CO2 + 2 H2O with 8.0 g of methane and 40.0 g of oxygen: methane is limiting, 21.946 g of carbon dioxide forms and 8.088 g of oxygen is left.
Why the smallest ratio decides
A reaction proceeds in steps in the proportions of the coefficients. The reactant that supplies the fewest steps stops it. Dividing moles by the coefficient puts all the reactants on that common scale, so the smallest result identifies the limiting one, even when it is not the one with the smallest mass or the smallest number of moles.
To balance the equation first use the chemical equation balancer. Convert masses with the moles to grams calculator, dilute solutions with the solution dilution calculator, and when a reaction does not go to completion use the ICE table equilibrium calculator.
Theoretical and percent yield
The theoretical yield is the most product the limiting reagent can make if everything goes as the equation says. The actual yield is what you really collected, and the percent yield compares the two. Yields below 100 percent are normal because of side reactions, losses in transfer and incomplete reactions.
Assumptions and limits
- The coefficients come from a balanced equation that you supply. The tool does not balance equations.
- Molar masses are entered by you, so use values from a reference that match your precision needs.
- The reaction goes to completion in the model, and the limiting reagent is fully consumed.
- Up to five reactants and four products, with coefficients from 1 to 100.
Frequently asked questions
How do I find the limiting reagent?
Convert every reactant to moles, divide each by its coefficient, and pick the smallest result. That reactant is used up first and sets how much product can form.
What is the difference between theoretical and actual yield?
Theoretical yield is the calculated maximum from the limiting reagent. Actual yield is the amount you really get in the lab or factory, usually lower, and their ratio is the percent yield.
What does it mean when the page says exact match?
Two or more reactants run out at the same moment, so they are present in exactly the ratio of the equation and none is left over.
Why is the limiting reagent not always the smallest mass?
Because molar masses and coefficients differ. A small mass of a heavy reactant can be fewer moles than a large mass of a light one, and the coefficients then change the picture again.