The complexity of the chemistry that emerged out of the eighteenth century, especially chemical reactions containing organic compounds, quickly overwhelmed the ability of mechanical theories provided by physics to deal with a large number of bodies involved. These theories had worked well to describe the interactions of objects on our human scale as well as some celestial events, but failed to adequately clarify chemical phenomena. Despite the plausibility of speculation based on atomic principles, efforts to understand chemical processes on these grounds remained largely futile (Farber 1966, pp. 187–188). At the same time, the growing practical and industrial importance of chemical processes meant that an understanding of the physical parameters guiding a chemical reaction was gaining relevance.

It was the concept of the interconvertibility of heat and work which held the seed of the solution. Applied examples existed in the eighteenth century, such as the steam engine and the cannon (Malanima 2009, pp. 53–54, 63–65). While thermal machines made their mark on agriculture and other parts of society, it was the theoretical understanding of heat and work developed in the next century that allowed Rudolf Clausius, William Thomson, and William Rankine to publish the first formulations of thermodynamics in the 1850s. The first law was the conservation of energy: the sum of potential and “actual” (kinetic) energies in the universe remained constant.Footnote 1 It relied on the exact, mathematical formulation of mechanical work and its interconvertibility with kinetic energy (heat). The second law relied on Clausius’ formulation of entropy. The application of these concepts to chemical reactions marked the birth of physical chemistry, enabling the creation of machines that make fertilizer (i.e. Haber-Bosch plants) (Kuhn 1959), (Farber 1966, pp. 150–156), (Girnus 1987), (Laidler 1993, pp. 1–11, 55–121), (Purrington 1993, pp. 80–101, 107–112), (Smith 1998, chapter 7), (Friedrich 2016).

Initially, the description of heat and energy successfully described the behavior of gases. The breakthrough in chemistry came in 1887 when the equation of state for an ideal gas was expanded to describe chemical solutions (Windisch 1892, pp. 476–522), (Ostwald 1927, pp. 16–31), (Partington 1964, pp. 637–662, 663–681). Jacobus Henricus van’t Hoff and Svante Arrhenius were able to equate the pressure of a gas to the osmotic pressure in a solution so that the ideal gas law could be applied in both cases (Arrhenius 1887; van’t Hoff 1887). While this discovery built the foundation of physical chemistry (Ostwald 1927, p. 22), it was another more general thermodynamic concept that was central to Haber’s and Nernst’s work: the free energy.

Until the 1870s, the spontaneity and direction of a chemical reaction was thought to be determined by the principle of maximum work which stated that the specific reaction that occured was the one that released the most heat (and could thus produce the most work) (Nernst 1914), (Partington 1964, pp. 610–620, 684–699), (Farber 1966, pp. 156–157), (Suhling 1972), (Bartel 1989, pp. 71–73), (Smith 1998, pp. 260–263). However, there was evidence, such as endothermic reactions, which contradicted this hypothesis. It was, in fact, a special kind of energy that dictated the behavior of a reaction: the free energy. This was envisioned as an “ordered” energy within the system available to perform work. When the free energy was at a minimum, the reaction stopped and the system was in equilibrium.Footnote 2 There was also a form of “disordered” or “bound” energy, which only manifested itself as heat and did not dictate the course or direction of the reaction (at least at finite temperatures). The total heat released in a reaction was a combination of these two types of energy. Josiah Willard Gibbs and Hermann von Helmholtz independently formulated expressions for the free energy in the 1870s in terms of the state functions of a system: temperature, pressure, volume, entropy, and total energy (Gibbs 1878a,b; von Helmholtz 1882).Footnote 3 With their theories, quantitative predictions could be made about chemical reactions in terms of global variables, which could be represented within a “free energy landscape.” Gibbs also considered pure and mixed-phase systems for which he described the chemical potential, or free energy per species in the reaction.

In terms of the actual application of these ideas to experiment, there was a further necessary development in the 1880s linking the free energy to chemical equilibrium. van’t Hoff, not employing the mathematical rigor of Gibbs or Helmholtz, derived a practical, yet theoretical description of chemical dynamics (Fig. 5.1). The most important quantity was the equilibrium constant which determines how much of each substance is present at equilibrium under specific conditions, which van’t Hoff expressed in terms of the state variables temperature and free energy. The idea of an equilibrium constant had been developed in the 1860s, but it was not until van’t Hoff’s ideas were understood that the dynamic nature of chemical equilibrium could be quantitatively applied to experiment. It had been thought that a chemical reaction was driven by the classical notion of force due to chemical affinity and that at equilibrium the forces for the forward and backward reactions were equal and opposite–a very mechanical approach. Reactions are, however, governed by reaction rates and do not find equilibrium in the mechanical sense. At chemical equilibrium, the forward and backward reaction rates for each substance are equal and there is no net production or dissociation; it is a dynamic equilibrium. The production of a specific substance (driving the reaction in a certain direction) is a matter of finding a set of conditions that favor one side of a chemical equation in equilibrium. This concept clarifies the modern understanding of reversibility in a chemical reaction and how the forward and backward reactions are intimately linked. With this revelation, the role and effect of a catalyst as an accelerator of these reaction rates could be understood.

Fig. 5.1
figure 1

9th Meeting of the German Electrochemical Society in Würzburg, May 8–10, 1902. Several of the architects of the theory of physical chemistry discussed here are pictured. Second Row: Walther Nernst, far left; Wilhelm Ostwald, middle with head turned; Jacobus Henricus van’t Hoff, two to Ostwald’s left; Third row: Guido Bodländer, middle, behind and to Ostwald’s right, Fritz Haber, three to Bodländer’s left. Back row: Heinrich Danneel, behind and just to Haber’s left. Source: Archiv der Berlin-Brandenburgischen Akademie der Wissenschaften, NL Ostwald Nr. 5296

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At the end of the 1880s, the theoretical structure of physical chemistry, having emerged from thermodynamics, included reversibility, dynamic equilibrium, and the free energy. These were consolidated in the expression for the equilibrium constant and enabled a global understanding of a chemical reaction. This was the step beyond mechanical models and the empirical approach of the past century that had been missing. In the case of ammonia, the existence of even the smallest quantities in the presence of hydrogen and nitrogen meant there was a chemical equilibrium, and that ammonia was being actively produced (and dissociated). Once the equilibrium constant was determined, one could identify values of the state functions of the system (temperature, pressure, volume, energy) that would raise the reaction rate of ammonia production.

Due to these developments, the year 1887 can be considered the point at which physical chemistry became a distinct discipline (Ostwald 1927, p. 19). It was also in this year that the journal Zeitschrift für Physikalische Chemie was first published. For ammonia synthesis, only two problems remained at the time: one practical and one theoretical. The solution to the practical problem was the work of Haber, Gabriel van Oordt, and Robert Le Rossignol, and later Carl Bosch and Alwin Mittasch. The theoretical problem was tackled by Walter Nernst, who came out of Wilhelm Ostwald’s renowned Institute for Physical Chemistry in Leipzig. Reminiscent of the Liebig School, generations of internationally recognized chemists were trained under Ostwald; at the time of its founding, also in 1887, his institute was unique in the world as a center for physicochemical research (Ostwald 1927, pp. 16–31). Himself an important figure in the history of physical chemistry, it was at this institute that Ostwald made a decisive step for the chemical industry in general and for ammonia synthesis in particular: he defined the catalyst as an accelerator of chemical reactions. In a talk at the 1901 Meeting of the Society of German Scientists and Doctors Footnote 4 in Hamburg Ostwald stated, “A catalyst is any substance, that, without having an effect on the end product of a chemical reaction, changes its speed [reaction rates] (Ostwald 1902).”Footnote 5

Several years after Ostwald’s initial definition, the role of a catalyst as a promotor was easily measurable. Chemical reactions could be systematically accelerated and became more profitable. The transformation of resources and the transformation of an entire scientific field had become inextricably linked with the transformation of an industry. The chemical industry, at this point consisting largely of the dye manufacturers, was dependent on catalysts for certain processes. An example is the aforementioned contact process that BASF implemented in the late 1890s to produce sulfuric acid. It enabled the production of heretofore unobtainable quantities of acid and, along with synthetic indigo and ammonia synthesis, came to symbolize the birth of the modern chemical industry (Stranges 2000, p. 170), (Marsch 2000, pp. 220–223).

A catalyst, however, could not change the end result of a chemical reaction; only the reaction rates could be manipulated. The free energy was still vital to understanding the direction of a reaction and how far it would proceed. The question was whether the value of the free energy could be calculated rather than determined through a laborious and expensive experimental observation. As mentioned, the free energy is a measure of the maximum amount of work (useful energy) that can be obtained from a chemical system. The spontaneous reaction is the one which minimizes the free energy as it is converted into work during a chemical reaction; at the minimum, the system is in chemical equilibrium. For a prediction or calculation of the free energy a complex, temperature-dependent function of total energy, free energy, and entropy is needed (Müller 2007, p. 148).Footnote 6 Mathematically speaking, one has to solve a differential equation, a difficulty that became one of the central theoretical challenges of physical chemistry at the end of the nineteenth century (Haberditzl 1960; Suhling 1972). In order to obtain a temperature-dependent expression for the free energy, the differential equation must be integrated, a mathematical operation that results in an unknown constant of integration. That means the form of the curve for the change of free energy with temperature was known, but its absolute value was not. In 1900, it was customary to solve this problem by using an empirical measurement of equilibrium quantities to determine the constant. Although this method worked in principle, it burdened an otherwise exact theory with experimental error (Nernst 1914).Footnote 7

Walther Nernst, who habilitated under Wilhelm Ostwald in Leipzig, finally found a solution to this fundamental problem. Nernst was among the first generation of chemists for whom the career choice was considered “acceptable”—such was the state of approval toward scientific professions. Like Liebig, Nernst was a modern chemist, who advocated for basic scientific principles and mathematics in his field, meaning he was (and often still is) considered more of a physicist. In 1887, he joined Ostwald in Leipzig where he quickly became involved in the investigations of the heat developed during chemical reactions and their relationship to chemical equilibria. In 1891, Nernst moved to Göttingen where he became professor in 1894 and head of the new Institute of Physical Chemistry and Electrochemistry the following year. There, his thermochemical studies continued and laid the groundwork for his seminal theoretical contribution to physical chemistry in 1906 when he published his heat theorem in “Ueber die Berechnung chemischer Gleichgewichte aus thermischen Messungen” (On the Calculation of Chemical Equilibria from Thermal Measurements) at the University of Berlin (Nernst 1906), (Bartel 1989, pp. 10–45). The theory allowed Nernst to calculate an expression for the unknown integration constant by introducing a mathematical formulation of the third law of thermodynamics. Neither Nernst nor anyone else made much of the physical significance of his postulate at the time. The third law states that the change in the free energy and of the total energy of a system with temperature will become identical at the absolute zero of temperature. In fact, the change in both energies itself also tends to zero. The new equation enabled Nernst to calculate the integration constant from measurements of heat capacities of the chemicals involved in a reaction (see Appendix B).Footnote 8 The determination of the integration constant became independent of any actual scientific observation of the reaction itself. It depended only on basic characteristics of the pure substances involved which could be measured more simply and exactly than tiny amounts of a chemical yield in equilibrium. Nernst’s method was not only an advancement for academic chemistry, but also for industry as it became more economical to select suitable chemical reactions.

In view of the development of physical chemistry, the problem of ammonia production on the basis of the necessary physicochemical principles could only have been taken up in the 1890s. Although an initial attempt to industrialize ammonia production by Ostwald failed in 1900, it paved the way for the experimental aptitude of Haber and the theoretical insight of Nernst in the new century. The new thermodynamic descriptions were like lines of latitude and longitude on a map—they set up a closely spaced grid to describe the successive steps of a chemical reaction. The state variables defined specific coordinates on the grid and chemical processes could be followed with a precision that ushered in a new era of chemistry and chemical production.