Reaction invariants are quantities that take the same values before, during and after a reaction. We identify a set of reaction invariants that are linear transformations of the species mole numbers. The material balances for chemically reacting mixtures correspond exactly to equating these reaction invariants before and after reaction has taken place. We present a systematic method for determining these reaction invariants from any postulated set of chemical reactions. The strategy presented not only helps in checking the consistency of experimental data, and the reaction chemistry but also greatly simplifies the task of writing material balances for complex reaction chemistries. For examples where the reaction chemistry is not known, we employ Aris and Mah's (Ind. Eng. Chem. Fundam. 2 (1963) 90) classic method to determine a candidate set of chemical equations. Application of reaction invariants in validating proposed reaction chemistry is discussed. One of the important applications of this method is the automation of mole balances in the conceptual design of chemical processes.