Chemical Equation Balancer

In short Balancing an equation is not a puzzle to be guessed at — it is a linear algebra problem with a definite answer. Write one row per element, count each species positive on the left and negative on the right, and any set of coefficients the resulting matrix sends to zero is a balanced equation. Solved in exact fractions there is no rounding anywhere, and the smallest whole-number set is the standard form. Propane burning is C3H8 + 5O2 → 3CO2 + 4H2O, and both sides weigh 204.087 g/mol, because conserving every atom conserves the mass automatically. Permanganate and hydrochloric acid gives 2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2. Where the reaction involves ions, charge is conserved as well and becomes one more row in the same matrix: MnO4⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H2O carries a total charge of +17 on each side. Three outcomes are possible and they are genuinely different. Usually there is exactly one balancing. Sometimes there is none, because an element appears on one side only, and no arithmetic can fix that. And occasionally there is a whole family: C + O2 → CO + CO2 is balanced by any mixture of the two products, so the coefficients are decided by how the carbon burns and not by the equation. This tool distinguishes all three and says which one you have, rather than printing one member of a family as though it were the answer.