Chemical Equation Balancer & Stoichiometry

What it is for

Balancing by trial and error works for H2 + O2 -> H2O but gets painful for redox equations with charges, or for reactions with nine species. This tool balances them the reliable way: it writes down how many atoms of each element (and how much charge) every species carries, and solves for the coefficients that conserve all of them at once. The arithmetic uses exact fractions, so even coefficients in the hundreds come out exact.

Type reactants, an arrow (->, = or →), then products, separated by + . Charges go at the end of an ion (Fe+2, MnO4-, SO4^2-) and electrons are written e-, so half-reactions work too. If you add starting masses, the tool also finds the limiting reagent and the yields.

Balancing tells you nothing about whether a reaction actually happens.

Worked example

Permanganate titrating iron(II) in acid: MnO4- + Fe+2 + H+ -> Mn+2 + Fe+3 + H2O. The result is MnO₄⁻ + 5 Fe²⁺ + 8 H⁺ → Mn²⁺ + 5 Fe³⁺ + 4 H₂O. The balance table confirms it: one manganese, four oxygen, five iron and eight hydrogen on each side, and a charge of 17 on both sides.

Now a yield problem. Burning C3H8 + O2 -> CO2 + H2O balances to C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O. With C3H8 = 44 g, O2 = 100 g as starting amounts, oxygen is the limiting reagent: 100 g is 3.1252 mol, enough for only 0.625039 mol of propane. The theoretical yield of carbon dioxide is 82.522 g, and 16.4377 g of propane is left over. Entering an actual yield of CO2 = 75 g gives a percentage yield of 90.88 %.

Copper with nitric acid, Cu + HNO3 -> Cu(NO3)2 + NO + NO2 + H2O, is different: the tool reports 2 independent reactions. One balanced form is 2 Cu + 6 HNO₃ → 2 Cu(NO₃)₂ + NO + NO₂ + 3 H₂O, but any mix of the two listed basis reactions also conserves every element. That is chemistry, not a bug: the ratio of NO to NO₂ depends on the acid concentration.

How to read the result

Result is one of five outcomes. Balanced means a unique set of smallest whole numbers. Several independent reactions means the coefficients are not unique. Cannot be balanced means no coefficients work — usually a wrong formula. A species does not take part means its coefficient would have to be zero: NaCl -> Na + Cl2 + O2 only balances without the O₂. On the wrong side means a species would need a negative coefficient.

The composition matrix shows the linear algebra behind it: one row per element, one column per species, reactants positive and products negative. The stoichiometry table lists, for each species, what you gave, what reacts or forms, and what is left over.

Tips and common mistakes

• Put spaces around the + between species, so Fe+3 stays a charge and is not read as a separator.
• Coefficients you type are checked: the tool tells you whether they balance, then shows the correct ones.
• State symbols such as (aq) or (g) are accepted and ignored.
• Reactants you leave out of the amounts are treated as being in excess.
• A percentage yield above 100 % almost always means a wet or impure product, or a typo in the amounts.

FAQ

How does it balance redox equations without half-reactions?

The total charge is treated like one more element that must be conserved. Electrons, protons and water are ordinary species, so the same calculation covers redox.

Why does it say several independent reactions?

The species can combine in more than one independent way. The tool lists a basis of these reactions and shows the combination with the smallest positive coefficients.

Can I use moles instead of grams?

Yes. Write amounts such as CO = 2.5 mol or Fe2O3 = 150 mmol; masses in mg and kg work too.

Which atomic weights are used?

The IUPAC standard atomic weights, the same as in the molar mass calculator and the Proofline chemistry cells.