Stoichiometry Balancer
Balance equations and predict the limiting reagent, theoretical yield, and excess reagent.
How to use this tool
Balance a chemical equation automatically and, if you want, work out which reactant runs out first and how much product you can expect. Pick the tab for the job.
What to enter
- Chemical equation: write species separated by + and the two sides by = or -> (e.g. Fe + O2 = Fe2O3). Case matters: Co (cobalt) ≠ CO (carbon monoxide). Example chips load common reactions.
- Limiting reagent & yield tab: additionally enter the mass available for each reactant (g) and choose the product of interest.
Reading the result
Balance mode shows the balanced equation with a table of coefficients and molar masses. Yield mode flags the limiting reagent and the theoretical mass of product, with the reaction-extent working shown.
Worked example
Fe + O2 = Fe2O3 balances to 4 Fe + 3 O₂ → 2 Fe₂O₃.
Balanced Equation
Balance mode returns the smallest whole-number coefficients and each species' molar mass. Yield mode flags the reactant that runs out first (LIMIT) and the most product it allows, the ceiling the Yield % tool measures a real run against.
Methodology
Balancing solves the homogeneous linear system A·x = 0, where each row of A is an element and each column a species (reactants positive, products negative). The integer null-space vector gives the smallest whole-number coefficients. All arithmetic runs in exact rational form (BigInt fractions) so there is no floating-point drift.
For yield, moles of each reactant are divided by their stoichiometric coefficient; the smallest quotient is the limiting reagent. Theoretical product mass = (limiting moles ÷ its coefficient) × product coefficient × product molar mass.
Sources
- Petrucci, General Chemistry, ch. 4, stoichiometry & limiting reactant.
- Atomic weights: IUPAC 2021 standard atomic weights (as bundled in this site's data).