Editing Chemical affinity (section)

==Thermodynamics==

The present [[International Union of Pure and Applied Chemistry|IUPAC]] definition is that affinity ''A'' is the negative [[partial derivative]] of [[Gibbs free energy]] ''G'' with respect to [[extent of reaction]] ''ξ'' at constant [[pressure]] and [[temperature]].<ref>{{cite web| url = http://www.IUPAC.org| title = IUPAC Green Book and Gold Book in .pdf}}</ref> That is,
:<math>A = -\left(\frac{\partial G}{\partial \xi}\right)_{P,T}.</math>

It follows that affinity is positive for [[Spontaneous process|spontaneous reactions]].

In 1923, the Belgian mathematician and physicist [[Théophile de Donder]] derived a relation between affinity and the Gibbs free energy of a [[chemical reaction]].  Through a series of derivations, de Donder showed that if we consider a mixture of [[chemical species]] with the possibility of chemical reaction, it can be proven that the following relation holds:

:<math> A = -\Delta_rG. \,</math>

With the writings of [[Théophile de Donder]] as precedent, [[Ilya Prigogine]] and Defay in ''Chemical Thermodynamics'' (1954) defined chemical affinity as the rate of change of the uncompensated [[heat]] of reaction ''Q''' as the [[Stoichiometry|reaction progress variable]] or reaction extent ''ξ'' grows infinitesimally:

:<math>A  = \frac{{\mathrm d}Q'}{{\mathrm d}\xi}. \, </math>

This definition is useful for quantifying the factors responsible both for the state of equilibrium systems (where {{nowrap|1=''A'' = 0}}), and for changes of state of non-equilibrium systems (where ''A'' ≠ 0).