In thermodynamics, chemical thermodynamics is the energetic and entropic study of physical processes or chemical reactions.  The central aspects of study in chemical thermodynamics are the initial and final states of the process or reaction. If the energy and entropy are known, with respect to appropriate reference points, for all values of pressure, volume, and temperature to be covered in the investigation, then the thermodynamic examination can be a complete one.  In this sense, chemical thermodynamics is the study of energy, entropy, and equilibrium in chemical systems. 
Chemical thermodynamics is generally considered the most intellectually-stimulating and difficult course in all of science. English physical chemist Brian Smith, gives an excellent description on the wondrous yet cautious intrigue many have with their first encounter with chemical thermodynamics: 
“The first time I heard about chemical thermodynamics was when a second-year undergraduate brought me the news early in my freshman year. He told me a spine-chilling story of endless lectures with almost three-hundred numbered equations, all of which, it appeared, had to be committed to memory and reproduced in exactly the same form in subsequent examinations. Not only did these equations contain all the normal algebraic symbols but in addition they were liberally sprinkled with stars, daggers, and circles so as to stretch even the most powerful of minds.”
Chemical thermodynamics, for instance, is commonly considered to be the weeder-course of chemical engineering.
See main: History of chemical thermodynamicsThe "founder of chemical thermodynamics", in the dominant sense of the term, is American engineer Willard Gibbs, who seems to have first been given this epitaph by German physical chemist Wilhelm Ostwald. 
American chemistry historian Mary Jo Nye correctly summarizes the prehistory of chemical thermodynamics in the following quote: 
“The roots of both chemical thermodynamics and contemporary chemical kinetics both lie in the eighteenth-century ideas of chemical ‘affinity’ and ‘force’, transformed into the nineteenth-century conceptions of ‘work’ and ‘energy’.”
German physical chemist August Horstmann was said to have done the first work in chemical thermodynamics. In circa 1865, he began to study the works of Rudolf Clausius for applications in the calculation of equilibriums in chemical systems. His 1869 paper "Dampfspannung und Verdampfungswärme des Salmiaks" (Vapor Pressure and the Heat of Evaporation of Ammonium Chloride) was the first to apply entropy to chemical problems. In October 1873, Horstmann announced the condition for chemical equilibrium to be that of maximum entropy. 
In December of 1873, independent of Horstmann, American mathematical physicist Willard Gibbs, in a footnote, stated that the condition for thermodynamic equilibrium in a chemical system at constant temperature and pressure is that a certain function, now universally known as the thermodynamic potential, should be a minimum.  Gibbs, however, would go on to present a more complete and rigorous treatise on the subject of equilibriums. The following in-context 1996 excerpt gives cogent indication as to the start of chemical thermodynamics: 
“… criticized the thermal theory of chemical affinity and deplored that ‘the chemical bearings on the theory of dissipation … have not hitherto received much attention.’ This was true, but to a lesser degree than imagined by Rayleigh, who knew neither Horstmann’s work nor that of Willard Gibbs, with which chemical thermodynamics can be said to have begun.”
Horstmann aside, the two central founders of the generalized subject of chemical thermodynamics are generally considered to be Gibbs, with the publication of his 1876 On the Equilibrium of Heterogeneous Substances, and German physician and physicist Hermann von Helmholtz (a mentor to Horstmann), with the publication of his 1882 The Thermodynamics of Chemical Processes (Die Thermodynamik Chemischer Vorgänge). 
The year 1876, with the work of Gibbs, however, is the generally agreed upon year in which chemical thermodynamics was born. As Gibbsian biographer Lynde Wheeler tells, the development of the prime or fundamental equation of Gibbs:
or in modern notation:
which is the core equation of Gibbs' Equilibrium treatise, "marks the birth of the theory of chemical thermodynamics". 
In 1913, English chemist James Partington published his Text-book of Thermodynamics with Special Reference to Chemistry, followed by his 1924 updated second edition titled Chemical Thermodynamics. 
The founders of "modern" chemical thermodynamics are American physical chemists Gilbert Lewis and Merle Randall, for the publication of their 1923 Thermodynamics and the Free Energy of Chemical Substances, in which they were the first to apply the principles of Gibbs specifically to chemical processes, and English physical chemist Edward Guggenheim, for his 1933 Modern Thermodynamics by the Methods of Willard Gibbs. Together, the three of them unified the science of chemical thermodynamics into a coherent whole. 
● Chemical thermodynamics (etymology)
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(b) Cahan, David. (1993). Hermann von Helmholtz and the Foundations of Nineteenth-Century Science, (ch. 10: "Between Physics and Chemistry - Helmholtz's Route to a Theory of Chemical Thermodynamics", pg. 403-31). Berkeley: University of California Press.
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7. Horstmann, August F. (1973). “Theorie der Dissociation”, Liebig’s Annalen der Chemie und Pharmacie, Bd. 170 (CLXX), 192-210.
8. (a) Gibbs, Willard. (1873). Trans. Connect. Acad., Dec., II., footnote to pg. 393.
(b) Garrison, Fielding H. (1909). “Josiah Willard Gibbs and his Relation to Modern Science”, Popular Science, pgs. 470-84.
9. Nye, Mary Jo. (1993). From Chemical Philosophy to Theoretical Chemistry: Dynamics of Matter (pg. 117). University of California Press.
10. Wheeler, Lynde Phelps. (1951). Josiah Willard Gibbs: the History of a Great Mind (pg. 77). Ox Bow Press.
11. Pauling, Linus. (1970). “History of Chemical Thermodynamics”, in The Centennial of the Sheffield Scientific School (pgs. 27-32) by Baitsell, George A. and Lawrence, Ernest O. Ayer Publishing.
● Chemical thermodynamics - Wikipedia.
● International Conference on Chemical Thermodynamics - IACT.