About this calculator
A balanced chemical equation gives the mole ratio in which substances react. When reactants are not mixed in exactly that ratio, one runs out first: the limiting reagent. It decides how much product can form (the theoretical yield), and the other reactants are left over in excess.
Enter the formula, coefficient and molar mass of every substance in your balanced equation, and the mass or moles of each reactant. The calculator first checks the equation atom by atom: for every element, the number of atoms (coefficient × atoms in the formula) must be the same on both sides. As a second, independent check it compares the total mass on both sides with the molar masses you entered. Then it converts masses to moles, compares n ÷ ν for each reactant, and gives the product and the excess. It does not balance or change your equation: if one element is out of balance, it stops and tells you which one.
Formula syntax
- Supported: element symbols with a capital first letter (all 118 IUPAC symbols, e.g. Na, Cl, Fe), whole-number subscripts as plain digits or as ₂, groups in brackets with a subscript, nested groups, square brackets — e.g.
Ca(OH)2,Al2(SO4)3,Mg3(PO4)2,K4[Fe(CN)6]— and hydrates or adducts joined with · or * — e.g.CuSO4·5H2O,CuSO4*5H2O. - Not supported (the formula is rejected with a message): charges such as Na+ or SO4^2-, state labels such as (aq) or (s), a coefficient written inside the formula (2H2O — use the coefficient field), spaces, decimal subscripts, D or other isotope symbols, lowercase symbols. Square brackets are counted as ordinary groups; the calculator only counts atoms and does not interpret coordination chemistry.
Formula
ni = mi ÷ Mi ξ = min(ni ÷ νi) nproduct = νproduct × ξ mproduct = nproduct × Mproduct
Excess left: ni − νi × ξ Element balance, for every element E: Σ ν × atoms of E (reactants) = Σ ν × atoms of E (products) Mass check: Σ ν M (reactants) = Σ ν M (products)
n = amount (mol), m = mass (g), M = molar mass (g/mol), ν = coefficient in the balanced equation, ξ = extent of reaction (mol). The reactant with the smallest n ÷ ν is the limiting reagent.
Worked example
Ammonia synthesis N₂ + 3 H₂ → 2 NH₃ with 50.0 g N₂ (28.014 g/mol) and 10.0 g H₂ (2.016 g/mol); NH₃ = 17.031 g/mol.
- Element balance: N 1 × 2 = 2 × 1 ✓; H 3 × 2 = 2 × 3 = 6 ✓. Mass check: 28.014 + 3 × 2.016 = 34.062 g/mol = 2 × 17.031 ✓
- n(N₂) = 1.7848 mol, n ÷ ν = 1.7848; n(H₂) = 4.9603 mol, n ÷ ν = 1.6534 → H₂ is limiting, ξ = 1.6534 mol.
- NH₃ = 2 × 1.6534 = 3.3069 mol = 56.32 g; N₂ left = 1.7848 − 1.6534 = 0.1314 mol = 3.68 g.
- H₂ + O₂ → H₂O is refused: O has 2 atoms on the reactant side but 1 on the product side. The balanced form is 2 H₂ + O₂ → 2 H₂O.
Assumptions and limitations
- The equation must already be balanced. It is checked atom by atom from the formulas for every element (exact counts), and also for mass (Σν·M of reactants = products, within 0.05 g/mol per unit of coefficient). Electric charge is not checked, because charged species are not supported.
- The molar masses are not calculated from the formulas; you enter them. The mass check catches a molar mass that does not fit the equation, but not every possible typing error.
- One reaction only; side reactions and equilibrium limits are not included. The result is the theoretical (maximum) amount.
- Molar masses are entered by you (for example from IUPAC standard atomic weights). Use the formula of the substance actually weighed, including water of crystallisation, and correct the mass for purity before entering it.
- A calculation tool only, not chemical handling advice.
References
- IUPAC, Quantities, Units and Symbols in Physical Chemistry (the “Green Book”) — stoichiometric numbers and extent of reaction ξ.
- IUPAC Commission on Isotopic Abundances and Atomic Weights — standard atomic weights for molar masses.