Editing Chemical thermodynamics (section)

===Chemical affinity===
{{main|Chemical affinity}}
While this formulation is mathematically defensible, it is not particularly transparent since one does not simply add or remove molecules from a system. There is always a ''process'' involved in changing the composition; e.g., a chemical reaction (or many), or movement of molecules from one phase (liquid) to another (gas or solid). We should find a notation which does not seem to imply that the amounts of the components (&nbsp;''N''<sub>''i''</sub>&nbsp;) can be changed independently. All real processes obey [[conservation of mass]], and in addition, conservation of the numbers of [[atom]]s of each kind.

Consequently, we introduce an explicit variable to represent the degree of advancement of a process, a progress [[Variable (mathematics)|variable]]&nbsp;''ξ'' for the ''[[extent of reaction]]'' (Prigogine & Defay, p.&nbsp;18; Prigogine, pp.&nbsp;4–7; Guggenheim, p.&nbsp;37.62), and to the use of the [[partial derivative]] ∂''G''/∂''ξ'' (in place of the widely used "Δ''G''", since the quantity at issue is not a finite change). The result is an understandable [[expression (mathematics)|expression]] for the dependence of d''G'' on [[chemical reaction]]s (or other processes). If there is just one reaction
<math display="block">(\mathrm{d}G)_{T,P} = \left( \frac{\partial G}{\partial \xi}\right)_{T,P} \, \mathrm{d}\xi.\,</math>

If we introduce the ''[[stoichiometric coefficient]]'' for the ''i''-th component in the reaction

<math display="block">\nu_i = \partial N_i / \partial \xi \,</math>

(negative for reactants), which tells how many molecules of ''i'' are produced or consumed, we obtain an algebraic expression for the partial derivative

<math display="block"> \left( \frac{\partial G}{\partial \xi} \right)_{T,P} = \sum_i \mu_i \nu_i = -\mathbb{A}\,</math>

where we introduce a concise and historical name for this quantity, the "[[chemical affinity|affinity]]", symbolized by '''A''', as introduced by [[Théophile de Donder]] in 1923.(De Donder; Progogine & Defay, p.&nbsp;69; Guggenheim, pp.&nbsp;37,&nbsp;240) The minus sign ensures that in a spontaneous change, when the change in the Gibbs free energy of the process is negative, the chemical species have a positive affinity for each other. The differential of ''G'' takes on a simple form that displays its dependence on composition change

<math display="block">(\mathrm{d}G)_{T,P} = -\mathbb{A}\, d\xi \,.</math>

If there are a number of chemical reactions going on simultaneously, as is usually the case,

<math display="block">(\mathrm{d}G)_{T,P} = -\sum_k\mathbb{A}_k\, d\xi_k  \,.</math>

with a set of reaction coordinates {&nbsp;ξ<sub>''j''</sub>&nbsp;}, avoiding the notion that the amounts of the components (&nbsp;''N''<sub>''i''</sub>&nbsp;) can be changed independently. The expressions above are equal to zero at [[thermodynamic equilibrium]], while they are negative when chemical reactions proceed at a finite rate, producing entropy. This can be made even more explicit by introducing the reaction ''rates'' d''ξ''<sub>''j''</sub>/d''t''. For every <span style="color:maroon;">''physically independent''</span> ''process'' (Prigogine & Defay, p.&nbsp;38; Prigogine, p.&nbsp;24)

<math display="block"> \mathbb{A}\ \dot{\xi} \le 0  \,.</math>

This is a remarkable result since the chemical potentials are intensive system variables, depending only on the local molecular milieu. They cannot "know" whether temperature and pressure (or any other system variables) are going to be held constant over time. It is a purely local criterion and must hold regardless of any such constraints. Of course, it could have been obtained by taking partial derivatives of any of the other fundamental state functions, but nonetheless is a general criterion for (&minus;''T'' times) the entropy production from that spontaneous process; or at least any part of it that is not captured as external work. (See ''Constraints'' below.)

We now relax the requirement of a homogeneous "bulk" system by letting the [[chemical potential]]s and the affinity apply to any locality in which a chemical reaction (or any other process) is occurring. By accounting for the [[entropy production]] due to irreversible processes, the equality for d''G'' is now replaced by

<math display="block"> \mathrm{d}G = - S \, \mathrm{d}T + V \, \mathrm{d}P -\sum_k\mathbb{A}_k\, \mathrm{d}\xi_k  + \mathrm{\delta} W'\,</math>

or

<math display="block"> \mathrm{d}G_{T,P} = -\sum_k\mathbb{A}_k\, \mathrm{d}\xi_k  + \mathrm{\delta} W'.\,</math>

Any decrease in the [[Gibbs function]] of a system is the upper limit for any [[isothermal process|isothermal]], [[isobaric process|isobaric]] work that can be captured in the [[surroundings]], or it may simply be [[dissipation|dissipated]], appearing as ''T'' times a corresponding increase in the entropy of the system and its surrounding. Or it may go partly toward doing external work and partly toward creating entropy. The important point is that the ''[[extent of reaction]]'' for a chemical reaction may be coupled to the displacement of some external mechanical or electrical quantity in such a way that one can advance only if the other also does. The coupling may occasionally be ''rigid'', but it is often flexible and variable.