Balancing a chemical equation
A balanced equation has the same number of atoms of each element on both sides — the law of conservation of mass (Lavoisier). Balancing means finding the smallest whole-number coefficients that make every element balance at once. Formally, this is solving a homogeneous linear system: the coefficients form the null space of the element-count matrix, which is why an algorithm can balance even complex redox equations that are tedious by inspection.
Stoichiometry, moles and molar mass
The balanced coefficients are mole ratios. To turn them into masses you need the molar mass, obtained by summing the standard atomic weights of each element in a formula (values maintained by IUPAC's CIAAW). With molar masses you can convert grams to moles and back, predict how much product a given mass of reactant yields, and identify the limiting reagent — the reactant that runs out first and caps the yield.
How to use the calculator
Enter the reactants and products separated by + and =. The balancer returns the integer coefficients; the stoichiometry panel then reports each species' molar mass and lets you scale from any known amount to all the others.
Note: standard atomic weights are interval or conventional values because isotopic composition varies slightly by source; the tool uses the conventional IUPAC values, which are adequate for stoichiometry to typical laboratory precision.
Frequently asked questions
How do you balance a chemical equation?
Adjust the coefficients so each element has the same number of atoms on both sides, keeping them as the smallest whole numbers. Algorithmically this is solving the null space of the element-count matrix, which this tool does automatically.
What is stoichiometry?
Stoichiometry is the quantitative relationship between reactants and products in a balanced equation. The coefficients give mole ratios, and molar masses convert those ratios into masses.
How do you find the limiting reagent?
Convert each reactant's amount to moles, divide by its coefficient, and the smallest result is the limiting reagent - the one that runs out first and sets the maximum yield. The tool flags it for you.
How do you calculate molar mass?
Sum the standard atomic weight of every atom in the formula. For example, H2O is 2 x 1.008 + 16.00 = 18.02 g/mol. The tool uses IUPAC/CIAAW atomic weights.
References
- International Union of Pure and Applied Chemistry, Quantities, Units and Symbols in Physical Chemistry (the "Green Book"), 3rd ed. (RSC Publishing) — amount of substance, molar mass and stoichiometry.
- IUPAC Commission on Isotopic Abundances and Atomic Weights, standard atomic weights (CIAAW).
- Balancing enforces conservation of mass (A. Lavoisier, 1789) and is equivalent to computing the null space of the reaction's element-count matrix.
- R. H. Petrucci et al., General Chemistry: Principles and Modern Applications, 11th ed. (Pearson).