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.”
“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)