Chemical Affinity

Gibbs Function Or Gibbs Energy

For a "bulk" system they are the last remaining extensive variables. For an unstructured, homogeneous "bulk" system, there are still various extensive composition variables that G depends on, which specify the composition, the amounts of each chemical substances, expressed as the numbers of molecules present or the numbers of moles. 

The expression for dG is especially useful at constant T and P, conditions which are easy to achieve experimentally and which approximates the conditions in living creatures.

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 movement of molecules from one phase to another. We should find a notation which does not seem to imply that the amounts of the components can be changed independently. All the real processes obey conservation of mass, add in addition, conservation of the numbers of atoms of each kind.

Consequently, we introduce an explicit variable to represent the degree of advancement of a process, a progress variable for the extent of reaction and to the use of the partial derivative. The result is an understandable expression for the dependence of dG on chemical reactions.

Where we introduce a concise and historical name for this quantity, the "affinity", symbolized by A, as introduced by Theophile de Donder in 1923. The minus sign comes from the fact the affinity was defined to represent the rule that spontaneous changes will ensure only when the change in the Gibbs free energy of the process is negative, meaning that the chemical species have a positive affinity for each other. The differential for G takes on a simple form which displays its dependence on compositional changes.

A set of reaction coordinates, avoiding the notion that the amounts of the components can be changed independently. The expressions above are equal zero at thermodynamic equilibrium, while in the general case for real systems, they are negative because all chemical reactions proceeding at a finite rate produce entropy. These can be made even more explicit by introducing the reactions rates. For each and every physically independent process.

This is a remarkable result since the chemical potentials are intensive system variables, depending only on the local molecular milieu. They cannot know whether the temperature and pressure 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 fundamentals state functions, but nonetheless is a general criterion for the entropy production from that spontaneous process; or least any part of it that is not captured as external work.

Any decrease in the Gibbs function of a system is the upper limit for any isotherm, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and its surrounding. Or it may go partly toward going external work. 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 one also does. The coupling may occasionally be rigid, but it is often flexible and variable.