The extent of reaction is a concept used in chemical thermodynamics and reaction kinetics to quantify the progress of a chemical reaction. It is often denoted by the symbol \( \xi \) (xi) and represents the amount by which a reaction has proceeded relative to its stoichiometry. Mathematically, the extent of reaction is defined as a variable that describes the change in the number of moles of reactants and products during a reaction.
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For a closed system with one specified chemical reaction, the extent of reaction records progress from through . Here is the amount of substance of species , and the signed stoichiometric vector has negative entries for reactants and positive entries for reaction products. For the water chemical equation in the order , it is . The normalization of depends on the chosen coefficients. See IUPAC Gold Book, extent of reaction.
With particle numbers instead of molar amounts, a molecular extent obeys , and the chemical potentials are measured per particle. At fixed temperature and volume, the Helmholtz free energy then satisfies . An interior chemical equilibrium requires ; the molar convention gives the same relation with chemical potentials per mole.