**2. The integration of thermodynamics into chemical grounds: From a qualitative to a quantitative** *affinity*

The new rules of the French Royal Academy of sciences (1699), Wilhelm Homberg's work on the interchangeability of 'average' -now called 'neutral'- salts, the mechanist philosophy influences at the end of the seventeenth century, and as well Paracelsus and the alchemists' traditions, paved the way for the empirical production of affinity tables during the 18th century. From Etienne-François Geoffroy (1718) to Bergman (1775), these tables were multiplied; some chemists, such as Guyton de Morveau (1773), developed the first experimental devices to quantify these affinities (Mi Gyung, 2003; Partington, 1962).

A shift of the explanatory function of the principles – Aristotelian, Paracelsian, or other, which previously accounted for qualities and chemical transmutations, towards the state of union between two chemical substances and the concept of process which implies union and disunion, gradually occurred (Bensaude-Vincent & Stengers, 1996). This major epistemological upheaval led to the attraction between chemical bodies being operationally redefined within the context of salts chemistry. The key question of the force or power which governed the chemical combinations remained rather unclear and mysterious according to Henri Sainte Claire Deville (Deville, 1864) until the chemists integrated knowledge of calorific and thermodynamics into their own practices.

Using a new calorimeter with mercury, J.T. Silbermann and P.A Favre showed for the first time in 1852 that a chemical decomposition could involve a release of heat. At the same time, Julius Thomsen published a paper entitled *Les bases d'un système thermochimique2* in the Annals of Poggendorf which upset the generally accepted ideas. The differentiation between combination and decomposition defended by Claude-Louis Berthollet could not be maintained anymore. A chemical act which produces heat was said to occur spontaneously. The concept of chemical reaction understood as an observable and measurable phenomenon was thus worked out by means of mathematical equations, and new experimental practices related to an innovative thermal instrumentation. Pierre Duhem reported a sentence of Thomsen according to whom: "When the chemical combination occurs, it releases a quantity of heat proportional to the affinity of the two chemical bodies"3 (Duhem, 1893). Thomsen originally argued that the heat of a reaction was the true measure of affinity (Kragh, 1984). The chemical act became a work to refer to the physicists' vocabulary but a work reinterpreted from within the current framework of chemical knowledge and laboratory practices. In 1873, Marcellin Berthelot precisely applied the Principle of maximum work to a chemical reaction (Médoire & Tachoire, 1994). He stated that in the absence of external energy, every chemical change tends towards the production of the greatest quantity of heat (Nye, 1993).

As Thermochemistry began to develop, chemists paid attention to other facts which first appeared foreign from each other. In 1852, Edmond Fremy and Henri Becquerel showed that the production of ozone was an incomplete reaction, a conclusion that Berthelot and Pan de Saint Gilles also reached for the esterification reaction ten years later. The chemical reaction appeared limited and dependent on the time factor, Sainte Claire Deville and his collaborators widened and strengthened those findings thanks to many experiments

<sup>2 &#</sup>x27;The foundations of a thermodynamic system', my translation.

<sup>3</sup> The French original sentence is : '*Lorsque la combinaison se produit, il se dégage une quantité de chaleur proportionnelle à l'affinité des deux corps.*'

The new rules of the French Royal Academy of sciences (1699), Wilhelm Homberg's work on the interchangeability of 'average' -now called 'neutral'- salts, the mechanist philosophy influences at the end of the seventeenth century, and as well Paracelsus and the alchemists' traditions, paved the way for the empirical production of affinity tables during the 18th century. From Etienne-François Geoffroy (1718) to Bergman (1775), these tables were multiplied; some chemists, such as Guyton de Morveau (1773), developed the first

A shift of the explanatory function of the principles – Aristotelian, Paracelsian, or other, which previously accounted for qualities and chemical transmutations, towards the state of union between two chemical substances and the concept of process which implies union and disunion, gradually occurred (Bensaude-Vincent & Stengers, 1996). This major epistemological upheaval led to the attraction between chemical bodies being operationally redefined within the context of salts chemistry. The key question of the force or power which governed the chemical combinations remained rather unclear and mysterious according to Henri Sainte Claire Deville (Deville, 1864) until the chemists integrated

Using a new calorimeter with mercury, J.T. Silbermann and P.A Favre showed for the first time in 1852 that a chemical decomposition could involve a release of heat. At the same time, Julius Thomsen published a paper entitled *Les bases d'un système thermochimique2* in the Annals of Poggendorf which upset the generally accepted ideas. The differentiation between combination and decomposition defended by Claude-Louis Berthollet could not be maintained anymore. A chemical act which produces heat was said to occur spontaneously. The concept of chemical reaction understood as an observable and measurable phenomenon was thus worked out by means of mathematical equations, and new experimental practices related to an innovative thermal instrumentation. Pierre Duhem reported a sentence of Thomsen according to whom: "When the chemical combination occurs, it releases a quantity of heat proportional to the affinity of the two chemical bodies"3 (Duhem, 1893). Thomsen originally argued that the heat of a reaction was the true measure of affinity (Kragh, 1984). The chemical act became a work to refer to the physicists' vocabulary but a work reinterpreted from within the current framework of chemical knowledge and laboratory practices. In 1873, Marcellin Berthelot precisely applied the Principle of maximum work to a chemical reaction (Médoire & Tachoire, 1994). He stated that in the absence of external energy, every chemical change tends towards the production of the greatest quantity of heat

As Thermochemistry began to develop, chemists paid attention to other facts which first appeared foreign from each other. In 1852, Edmond Fremy and Henri Becquerel showed that the production of ozone was an incomplete reaction, a conclusion that Berthelot and Pan de Saint Gilles also reached for the esterification reaction ten years later. The chemical reaction appeared limited and dependent on the time factor, Sainte Claire Deville and his collaborators widened and strengthened those findings thanks to many experiments

3 The French original sentence is : '*Lorsque la combinaison se produit, il se dégage une quantité de chaleur* 

**2. The integration of thermodynamics into chemical grounds: From a** 

experimental devices to quantify these affinities (Mi Gyung, 2003; Partington, 1962).

knowledge of calorific and thermodynamics into their own practices.

2 'The foundations of a thermodynamic system', my translation.

*proportionnelle à l'affinité des deux corps.*'

**qualitative to a quantitative** *affinity* 

(Nye, 1993).

(Daumas, 1946). After many attempts, Maximilian Güldberg and Peter Waage asserted in 1861 that they were able to "find for each element and each chemical combination, numbers which express their relative affinity"4 (Güldberg & Waage, 1867). Güldberg and Waage quickly connected the emerging concept of chemical equilibrium with the notion of affinity so as to designate the chemical force which was supposed to lead to the equilibrium. They then established the crucial chemical law of mass action while studying reaction rates, and the effects of time, temperature and mass factors.

The development of the energy approach in chemistry was the result of a fortuitous combination of independent works proposed by Wilhelm Hortsmann in Germany, by Josiah Willard Gibbs in America and by Bakhuis Roozeboom and J.H. Van't Hoff in Holland. Hortsmann integrated Rudolf Clausius' considerations on isolated systems into chemistry. In so doing, he rediscovered in 1873 the law of mass action by means of calculation without having any idea that it had already been found on other grounds. The same year, Gibbs, published a paper entitled '*On the equilibrium of heterogeneous substances'*, within which he proposed a mathematical description of chemical equilibrium. This work remained mostly unknown by chemists because they didn't have the necessary basic mathematical knowledge to grasp it. In 1882, Hermann von Helmholz rediscovered Gibbs' results -which he totally ignored- using the theory of heat published by J. Clark Maxwell in 1871. All these publications gave rise to new chemical concepts which dealt with energy changes in a chemical system submitted to the action of the various forces that led to an equilibrium. One must have distinguished, according to Helmholtz, between the part of energy which appeared only as heat and the part which could be freely converted into other kinds of work, i.e. the "free energy". Subsequently, the production of a decrease in free energy enabled chemists to explain chemical stability (Kondepudi & Prigogine, 1998). In 1884, Pierre Duhem introduced the notion of internal thermodynamic potential by analogy with classical mechanics (Duhem, 1902).

Applications to experimental chemistry by the Dutch school, for example, Roozeboom had to cope with difficulties in interpreting hydrobromic acid decomposition in the presence of water in the gas phase. His colleague physicist J.D. Van der Waals suggested to him to use Gibbs's work and helped him to put forward the so-called *phases rule*. Van't Hoff established the law of equilibrium variation depending on temperature and gave to the measure of the affinity as the expression of the maximum work that the system must be able to provide under defined conditions. According to Van't Hoff, affinity was the leading force which produced chemical transformation. The change of affinity sign accompanied the change in the direction of the reaction which occurred at the transition point (Kragh & Weininger, 1996). From that time onwards, researchers gradually moved their attention to other factors of equilibrium. In 1888, Henry Le Chatelier proposed a way to predict how a chemical equilibrium moved according to the variation of the factors on which it depended. Chemical affinity became therefore one of the many aspects of the chemical act allowing improved forecasts and performances.

At the beginning of the twentieth century, chemists attempted to know not loner why, but how matter is transformed. Chemical kinetics studied the process of transformation of matter. Swante Arrhenius introduced the concept of energy activation, researches gradually

<sup>4</sup> The French original sentence is : " (…) *trouver pour chaque élément et pour chaque combinaison chimique, des nombres qui expriment leur affinité relative"*

The Role and the Status of Thermodynamics in Quantum Chemistry Calculations 473

described by its form and motion could not account for the world of chemical activities and diversity according to Venel. On the other hand, most chemists considered matter to be heterogeneous and able to act and react (Bensaude-Vincent & Simon, 2008). More often than not, chemists pragmatically used one description or the other according to their laboratory goals. As Bensaude-Vincent and Simon write: 'We prefer to see this duel between the two approaches as a characteristic feature of the history of chemistry. Chemists have always been confronted with this interpretative dichotomy, and, depending on the period, they have opted for a version of atomism or an elementary approach, or else have tried to

Not only did thermodynamics enable chemists to construe a quantitative version of affinity but it also fitted very well into the cultural background that had been framing chemists' activities for a long time. Thermodynamics embodiment within chemical practices was thus at least twofold; it provided chemists with quantitative tools for understanding chemical reaction while recasting old oppositions of matter representations. Along with this perspective, thermodynamics could easily be integrated into the usual chemical way of thinking about matter while reconfiguring it. As Rouse claims (1996, p.157): 'In order to understand how scientific knowledge is situated within practices, we need to take account of how practices are connected to one another, for knowledge will be established only through these interconnections. Scientific knowing is not located in some privileged type of practice, whether it be experimental manipulation, theoretical modeling, or reasoning from

evidence, but in the ways these practices and others become intelligible together.'

Duhem focused his work on the dichotomy between the 'mixt' and the aggregate referring to Aristotle's philosophy (Needham, 1996). Like Sainte-Claire Deville and Berthellot, but not because of the same positivist reasons, he rejected atomism then deeply rooted in structural organic chemistry. According to the structural molecular paradigm, the physical arrangement of the constituent elements accounted for the properties of the whole compound. Since Lavoisier, chemists have been explaining the properties of compounds by reference to the nature, the proportion and, more recently, the bonds of its constitutive parts, be they atoms or elements: a logic that runs from simple to complex frameworks in post-Lavoisian chemistry (Bensaude-Vincent & Simon, 2008). Conversely, the holistic energy approach used compounds to explain the properties of the elements. In this respect, atomism had a weak explanatory power because it could not completely illuminate chemical processes. According to Duhem, chemical formula could make chemists believe that substances remained unchanged when they entered into combinations whereas they only existed potentially within them (Duhem, 1902). Joseph Earley has recently proposed an argument on the same lines. He uses the example of sea water in which salt and water cease to exist in their actual states–because for instance of solvatation- but they can be reproduced by distillation (Earley, 2007). When the 'mixt' ceases to exist, it is made to reproduce its separate constituents as Venel might have asserted. In this respect, water and salt potentially exist in sea water but do not actually exist within it. Duhem then undertook to retranslate Aristotle's concept of power into that of the thermodynamic potential (Duhem, 1902). Measurable properties and mathematics allowed him to describe chemical reaction within

Duhem rejected both the idea of valence taken as an intrinsic atomic property and the concept of atomicity. According to him, the whole components could only give rise to valence information but not the contrary. The opposition between a holistic approach of

reconcile the two.*'* (Bensaude-Vincent & Simon, 2008, p. 128).

the context of thermochemistry.

turned to focus on the question of the energy transfer and the direction of collisions between chemical bodies. Wilhelm Ostwald succeeded in describing chemical equilibrium without making any reference to atoms (Ostwald, 1919). Two antagonistic approaches of matter were at stake. Thermochemistry revolved around energy and denied any reality to atoms whereas chemical kinetics was based on the atomic assumption. Thomsen, for instance, used structural theory to assign heats of formation to specific bond types found in organic molecules. In this respect, he tried to reduce chemical properties to a mere juxtaposition of atomic properties. Others, like F.W. Clarke tried to connect the heat of formation with the one and only number of atomic linkages within the molecule. By doing so, he tried to connect valence with affinity (Weininger, 2001). All the attempts that tried to understand affinity thanks to additive and reductive descriptions failed.

To sum up this first part, I would like to emphasize that the integration of thermodynamics within the frameworks of chemistry was made possible because chemists were looking for a quantitative measure of affinity. The way thermodynamics became thermochemistry depended on the instrumentation and the practices that chemists contrived to tackle the challenge of affinity. As the philosopher Joseph Rouse points out: 'Practices are not just pattern of action, but the meaningful configurations of the world within which actions can take place intelligibly, and thus practices incorporate the objects that they are enacted with and on and the settings in which they are enacted'. (Rouse, 1996, p.135). Thermodynamics was thus integrated into chemical projects and then transformed by such integration because it made chemists goals achievable and intelligible within such new practical backgrounds.

I suggest we should take more distance and consider the whole history of chemistry to analyze the way this integration actually took place. Let us widen the circle to grasp what is at stake behind this integration and how the duel between different conceptions of matter will remain active at the very beginning of quantum chemistry. This study will enable us to understand the role of thermodynamics in the first chemical quantum calculations.
