|Cover of Theophile de Donder's 1936 Thermodynamic Theory of Affinity, a 144-page book on the thermodynamic explanation of chemical affinity. |
where ΔG is the change in the Gibbs free energy for the process or reaction; and for isothermal-isochoric reactions:
where ΔF is the change in the Helmholtz free energy for the process or reaction.
The first theories on this topic of the measure of chemical affinity were those put forward, independently, it seems, by Danish chemist Julius Thomsen (1854) and French chemist Marcellin Berthelot (1864) who argued that the heat of a reaction was the true measure of affinity. This came to be known as the thermal theory of affinity.
In 1882, German physicist Hermann Helmholtz, in his chemical thermodynamics founding paper "On the Thermodynamics of Chemical Processes", showed that the true measure of affinity is not the heat evolved, but rather free energy, being that the second law of thermodynamics, or rather entropy, plays a role in the measurement or actuation of chemical affinity in chemical reactions. This publication overthrew the older "thermal theory of affinity" advocated by Danish chemist Julius Thomsen (1854) and French chemist Marcellin Berthelot (1864).
In 1884, Dutch physical chemist Jacobus Van’t Hoff showed that the maximum external work that obtained when a chemical reaction was carried out reversibly and isothermally could serve as a measure of chemical affinity.
Belgian chemist Theophile de Donder worked for many years on this subject, publishing articles on this topic beginning in 1922, culminating with his 1936 book Thermodynamic Theory of Affinity.  Gianni Astarita argues that, in addition to being one of the first books to discuss the details of the thermodynamics of affinity, de Donder’s Thermodynamic Theory of Affinity was the first to put forward the concept of ‘extent of reaction’:
The 1923 textbook Thermodynamics and the Free Energy of Chemical Substances, by American physical chemists by Gilbert Lewis and Merle Randall, is said to have led to the replacement of the word ‘affinity’ by ‘free energy’ throughout the world.
Human chemical thermodynamics
In 1809, German polymath Johann Goethe published his physical chemistry based novella Elective Affinities, wherein he showed how chemical affinity governs human interactions. In the years following 1882, with the publication of German physicist Hermann Helmholtz's 1882 "On the Thermodynamics of Chemical Processes", wherein he proved that that the true measure of affinity is not the heat evolved, but rather free energy, being that the second law of thermodynamics, or rather entropy, plays a role in the measurement or actuation of chemical affinity in chemical reactions, and more particularly in the decades after the 1923 publication of American physical chemist Gilbert Lewis' famous Thermodynamics and the Free Energy of Chemical Substances, after which the term "free energy" began to be used over that of "affinity", the subject of human chemical thermodynamics, namely the study of the thermodynamics of human chemical reactions (see: theory), the advanced subject of "human free energy" theory began to be discussed and theorized about, using the language of partial differential equations, the recent work of German solid state thermodynamicist and socio-economic physicist Jurgen Mimkes (“A Thermodynamic Formulation of Social Science”, 2007) and American physical chemist Thomas Wallace (“The Fundamentals of Thermodynamics Applied to Socioeconomics”, 2009) being two prime examples. 
The following are related quotes:
“The influential textbook of G.N. Lewis and Merle Randall led to the replacement of the term ‘affinity’ by the term ‘free energy’ throughout the English speaking world.”
— Henry Leicester (1956), The Historical Background of Chemistry 
“The term "affinity" gave way slowly to "work" and to "free energy," with the adoption by chemists of the so-called Gibbs free energy function (F), rather than the expression (A) developed by Helmholtz (1882), van' t Hoff (1884), and Nernst (1887). Like many of the new physical chemists, Ostwald reveled in the new approach. "As long as we sought to measure chemical ‘forces’," he wrote, "the theory of affinity made no progress." Willard Gibbs's method of making calculations at constant pressure and constant temperature was more useful than the free energy derivation by European scientists for constant volume and constant temperature. Thus, for chemists, H (heat of reaction), cp (heat capacity at constant pressure), and F were more generally useful than E, and A. With the standardization of free energies of formation of electrolytes in solution by Lewis and his American colleagues, thermodynamics became an ordinary tool for most chemists. Indeed, Lewis said of this work that it had given him more personal satisfaction than anything else he had done in chemistry.”
1. De Donder, T. (1936). Thermodynamic Theory of Affinity: A Book of Principles. Oxford: Oxford University Press.
2. (a) Van’t Hoff, J.H. (1884). Studies in Chemical Dynamics: Revised and Enlarged 1896 edition by Ernst Cohen (trans. Thomas Ewan). London: Williams & Norgate.
(b) Leicester, Henry. (1956). The Historical Background of Chemistry (pg. 206). Dover.
3. Astarita, Gianni. (1989). Thermodynamics: an Advanced Textbook for Chemical Engineers (pg. 66). Plenum Press.
4. Leicester, Henry. (1956). The Historical Background of Chemistry (pg. 206). Dover.
5. (a) Mimkes, Jurgen. (2007). “A Thermodynamic Formulation of Social Science”, In: Econophysics & Sociophysics: Trends & Perspectives (pgs. 277 – 308). Bikas K. Chakrabarti, Anirban Chakraborti, Arnab Chatterjee (Eds.). WILEY-VCH Verlag, Weinheim, Germany.
(b) Wallace, Thomas P. (2009). Wealth, Energy, and Human Values: the Dynamics of Decaying Civilizations from Ancient Greece to America (Appendix A: The Fundamentals of Thermodynamics Applied to Socioeconomics, pgs. 469-89). AuthorHouse.
● De Donder, T. (1922). “Article”. Bull. Ac. Roy. Belg. (Cl. Sc.) (5) 7: 197-205.
● De Donder, T. (1927). “L’ Affinite”, Paris: Gauthier-Villars.
● De Donder, T. and Van Rysselberghe P. (1936). Affinity. Menlo Park, CA: Stanford University Press.