# Affinity-free energy equation

In equations, affinity-free energy equation (TR:25) refers to any relation that equates the chemical affinities or a reaction or process with the change in the free energy, Gibbs or Helmholtz, of the reaction or process, which depends on the reaction conditions, namely isothermal-isobaric or isothermal-isochoric, respectively.

History
The first to formally state the affinity-free energy relationship in equation form was German physicist Hermann Helmholtz, who in his famous 1882 “On the Thermodynamics of Chemical Processes”, combined the earlier chemical thermodynamics work of American engineer Willard Gibbs with his own electrochemical thermodynamics work and, with the following statement, effectively overthrew the thermal theory of affinity:

“Given the unlimited validity of Clausius' law, it would then be the value of the free energy, not that of the total energy resulting from heat production, which determines in which sense the chemical affinity can be active.”

and gave the following equation formulation for affinity in relation to the direction of reaction changes spontaneously occurring:

where, in modern terms, F is the Helmholtz free energy, and t is time, which states that the affinities will only be active when the system of the chemical process shows a decrease in free energy with time.

In 1936, Belgian physicist Theophile de Donder, in his Thermodynamic Theory of Affinity, head of the so-called "Brussels school of thermodynamics", using a parallel albeit slightly different approach, presented a formulation where the symbol "A" for affinity as the negative partial of the partial of the Gibbs free energy per unit partial of extent of reaction for a change in a isothermal isobaric system: [2]

$A=-\left(\frac{\partial G}{\partial \xi}\right)_{p,T}$

and would go on to discuss this, using coupling theory, in terms of how reactants and chemicals can be made to go, move, or react in a direction contrary to their own affinity, or in an anthropomorphic sense, as Goethe would have seen things, in a direction contrary to their own will. De Donder's approach, according to Indian-born American physical chemist Dilip Kondepudi, of his school, is said to be based on American engineer Willard Gibbs' 1876 concept of chemical potential. [5]

In 2012, the term “Goethe-Helmholtz equation” began to be used, as an Hmolpedia coinage, in reference to the following isothermal-isobaric version of the equation relating affinity to Gibbs free energy change:

$A = - \Delta G \,$

Quotes
The following are related quotes:

Chemical affinity in the chemical battery and in electrolysis, then, is to be identified with free energy or with work, not with heat. As historian Helge Kragh has noted, it was only with Helmholtz's version of the energy/entropy/heat function that its implications for the problem of chemical affinity were clearly understood. It was Helmholtz's version that van't Hoff and Nernst further explored. The importance for chemistry of Helmholtz's work was publicly acknowledged in 1892 when the German Chemical Society elected Helmholtz to honorary membership. In the language of chemistry, the term affinity gave way to the term energy, just as, in the language of physics or natural philosophy, the term force also ceded rhetorical and intellectual space to energy. Physical chemistry became a kind of chemistry focused on energy relations in chemical reactions, thus shelving the problem of the causes of elective affinities of individual atoms for study by a later generation.”
Mary Jo Nye (1999), Before Big Science: the Pursuit of Modern Chemistry and Physics, 1800-1940 (pg. 99)

References
1. De Donder, Theophile. (1936). Thermodynamic Theory of Affinity: A Book of Principles (pg. 2). Oxford University Press.
2. Kondepudi, Dilip and Prigogine, Ilya. (1998). Modern Thermodynamics – from Heat Engines to Dissipative Structures (4.1: Chemical potential and Affinity: the Driving Force of Chemical Reactions, pgs. 103-13). New York: John Wiley & Sons.