Counting Atoms

Chemistry is bookkeeping. Atoms are never created or destroyed in a reaction, only passed from one partner to another, so every element going in must come out, and the mass of everything going in must equal the mass of everything coming out. Antoine Lavoisier made this the founding rule of modern chemistry in 1789, and wrote that a reaction could be treated “as forming an algebraic equation”.^[1]

The difficulty is that the accounts are kept in atoms and the laboratory works in grams. Nobody can count 10²³ atoms, but anybody can weigh them. The mole is the exchange rate between the two. The three chapters below build the whole subject from that idea: first the exchange rate itself, then the rule that every reaction's accounts must close, then the calculations that a chemist does with both.

How this is made and checked

Every number on this site is computed, and computed exactly. Atomic weights are the IUPAC Commission on Isotopic Abundances and Atomic Weights' abridged table of 2024, copied by program from the Commission's page and tested against a frozen copy of it. Molar masses, balanced equations and yields are worked out in exact fractions, never floating point, and rounded once, for display, to the precision the inputs carry. The balancer solves the equations of atom conservation exactly and reports when an equation cannot be balanced or balances in more than one way, instead of guessing. The engine is tested against textbook worked examples, against PubChem's molecular weights, and against conservation of atoms, charge and mass for every equation it balances; an independent reviewer checks every claim against its source. More about how it is checked.