Stoichiometry and limiting reactant
n = m / M (mass → amount of substance)
Give the equation (the tool balances it) and the amounts you have, in grams or moles: it identifies the limiting reactant from the smallest “moles ÷ coefficient” ratio, computes the maximum extent. The mass of each product formed and what remains of each excess reactant. A reactant whose amount is left empty is treated as being in excess (the classic “with an excess of…” statement) and the tool says so instead of assuming it silently.
O2
- Balanced equation
- 2 H2 + O2 → 2 H2O
- Maximum extent ξ
- 2.0001 mol
2 H2O: 72.065 g (4.0003 mol)
- M(H2O)
- 18.015 g/mol
H2, in excess: 1.9355 g left (0.96007 mol). O2, limiting: fully consumed (2.0001 mol engaged).
- M(H2)
- 2.016 g/mol
- M(O2)
- 31.998 g/mol
O2 is the limiting reactant: it has the smallest “available moles ÷ coefficient” ratio, and that ratio IS the maximum extent (2.0001 mol). Everything else follows from it.
THEORETICAL amounts: the reaction is assumed complete, with no side reaction and no handling loss. The real yield is always lower.
Some molar masses rest on a conventional atomic weight: for fourteen elements (including H, C, N, O, S and Cl), IUPAC publishes an interval, since isotopic composition varies with the sample’s origin.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasn = m / M (mass → amount of substance)
n = m / M (mass → amount of substance)
ξ = min over reactants of (n / ν), the maximum extent
product formed: n = ν × ξ
reactant left: n − ν × ξ
The limiting reactant is not the one you have least of: it is the one whose “available moles ÷ stoichiometric coefficient” ratio is smallest. That minimum ratio is the maximum extent ξ of the reaction, in moles. And once ξ is known everything follows: each product forms as ν × ξ, each reactant is consumed as ν × ξ, and the leftover is the difference. Balancing uses the same exact engine as the balancer tool: minimal integer coefficients, obtained by linear algebra over exact fractions.
- Limiting reactant
- · the one that runs out first and stops the reaction. Nothing of it remains at the end, the check that lets you verify a result.
- Extent (ξ)
- · the number of “times” the reaction, as written with its coefficients, has occurred. In moles: ξ = 2 means the equation happened twice over.
- Theoretical amount
- · what a complete reaction would give, with no side reaction and no loss. The real yield is the mass actually obtained divided by this theoretical mass.
Validity domainAll product amounts are theoretical: the reaction is assumed complete, with no chemical equilibrium.
All product amounts are theoretical: the reaction is assumed complete, with no chemical equilibrium. No side reaction and no loss. A thermodynamically balanced reaction (esterification, dissociation) never reaches these values. The tool handles neutral species and up to four reactants; redox half-equations and ionic equations, which also require charge conservation, need a different treatment. Molar masses use IUPAC abridged standard atomic weights: terrestrial isotopic averages, fourteen of which are conventional values, flagged when they apply.
Common pitfall: the limiting reactant is not the least abundantWith 10 g of H₂ and 64 g of O₂ in 2 H₂ + O₂ → 2 H₂O, hydrogen is far lighter.
With 10 g of H₂ and 64 g of O₂ in 2 H₂ + O₂ → 2 H₂O, hydrogen is far lighter. Yet oxygen is limiting: 5 mol of H₂ against a coefficient of 2 gives a ratio of 2.5, while 2 mol of O₂ against a coefficient of 1 gives 2.0. Comparing masses, or even moles alone, misleads: only the ratio to the coefficients decides. Another trap: the equation coefficients are not masses, 2 H₂ + O₂ does not mean “two grams of hydrogen”.