In physical chemistry, the extent of reaction is a quantity that measures the extent in which the reaction proceeds. It is usually denoted by the Greek letter ξ. The extent of a reaction has units of amount (moles). It was introduced by the Belgian scientist Théophile de Donder.
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Definition
Consider the reaction
A ⇌ BSuppose an infinitesimal amount dξ of the reactant A that changes into B. The change of the amount of A can be represented by the equation dnA = – dξ and the change of B is dnB = dξ. The extent of reaction is then defined as
where
The extent of a reaction is defined as zero at the beginning of the reaction. Thus the change of ξ is the extent itself.
Relations
The relation between the change in Gibbs reaction energy and Gibbs energy can be defined as the slope of the Gibbs energy plotted against the extent of reaction at constant pressure and temperature.
Analogously, the relation between the change in reaction enthalpy and enthalpy can be defined.
Use
The extent of reaction is a useful quantity in computations with equilibrium reactions. Let us consider the reaction
2A ⇌ B + 3 Cwhere the initial amounts are
Do not forget that the stoichiometric number of reactants is negative. Now when we know the extent, we can rearrange the equation and calculate the equilibrium amounts of B and C.