|An example of Gibbs free energy G as a function of the extent x of a process or reaction with plot (a) showing a generic reaction as it is assumed to occur and (b) showing a hypothetical reaction that is not possible or assumed not to ever occur. |
Mathematically, extent of reaction or ‘extent of process’ refers to the partial differential of a thermodynamic potential, predominantly Gibbs free energy change ∂G, with respect to the partial differential of an extent variable ∂x, such as concentration or time, with specified variables assumed to be held constant, generally temperature T and pressure P, meaning loosely a non-heated open atmospheric reaction:
|With marriage viewed as a human chemical reaction, the factoid of 43% of marriages ending at 15 years, is a measure of the extent of reaction.|
The extent of reaction is essentially the amount of chemical transformations. The extent of reaction also goes by various other names such as reaction coordinate ε or degree of advancement, degree of reaction, and progress variable, all of which characterize the extent or degree to which a reaction has taken place. 
The variable ‘extent’ , symbol ξ, was introduced by Belgian mathematical physicist Théophile de Donder in 1920. 
● Affinity of reaction
1. Extent of reaction – IUPAC Gold Book.
2. Smith, J.M. Van Ness, H.C., and Abbott, M.M. (2005). Introduction to Chemical Engineering Thermodynamics (7th ed.), (pg. 485). New York: McGraw-Hill Book Co. Inc.
3. (a) De Donder, Théophile. (1920). Lecons de Thermodynamique et de Chemie Physique (Lessons of Thermodynamics and Physical Chemistry), (pg. 117, formula 318). Paris: Gauthier-Villars.
(b) De Donder, T. (1936). Thermodynamic Theory of Affinity: A Book of Principles, (pg. 2). Oxford: Oxford University Press.
4. Mortimer, Robert G. (2008). Physical Chemistry (pg. 155). Academic Press.