The Scientific Publications on Ammonia Synthesis

Abstract

Having set the stage, we now turn to the analysis of Haber’s and Nernst’s published results between 1905 and 1908. A short commentary is in order here—both on style and on the use of theory. In summarizing the articles to emphasize pertinent scientific content, it was not possible to express the tone of the century-old publications and the interested reader is encouraged to review the original sources.

Having set the stage, we now turn to the analysis of Haber’s and Nernst’s published results between 1905 and 1908. A short commentary is in order here—both on style and on the use of theory. In summarizing the articles to emphasize pertinent scientific content, it was not possible to express the tone of the century-old publications and the interested reader is encouraged to review the original sources. As is occasionally mentioned, the number of calculation errors is noticeable as is the obsessiveness with which Haber, Gabriel van Oordt, Robert Le Rossignol, and later Friedrich Jost considered qualitative and quantitative sources of experimental error. The publications are filled with details about uncertainties, insecurities, and checks on sources of inaccuracy that remind today’s reader that these experiments were conducted by human researchers at the limits of then-current science. One characteristic examples is from Haber and Le Rossignol’s 1908 publication (Haber and Rossignol 1908f). During stability tests for the iron catalyst at 30 atm, the nitrogen-hydrogen gas mixture began to run low and further tests had to be performed at 22.35 atm (this lower pressure changed the gas flux and they were concerned with the effect on equilibrium). The results were compared with the help of theoretical corrections and full details were supplied—including the fact that the effect of the gas flux on the catalyst’s effectivity could not be calculated. It was a description of real laboratory difficulty and was not altered to make the study appear more structurally sound than it was. In contrast, today’s publications are often polished in such a way as to fend off attack (also, today one would simply purchase new gas cylinders with the required pressure).

As for theory, the fitting functions found here are key to Haber’s and Nernst’s analyses and extrapolation of the behavior of the ammonia system at temperatures different from their chosen experimental conditions. For those who are interested, the derivation of these functions can be found in Appendix A and a careful examination, along with Appendix B, will provide a deeper understanding of the then-current physicochemical approach to chemical equilibrium, especially with respect to thermal data. The equations are also compared to modern calculations of ammonia equilibrium in Figs. 11.7, 11.8, 11.9, 11.10, and 11.11.¹ Those not inclined to consult the appendices may simply read on!

1 Über die Bildung von Ammoniak aus den Elementen (On the Generation of Ammonia from the Elements) by Fritz Haber and Gabriel van Oordt, 1905

According to physical chemists in 1905, the most promising method for synthesizing fixed nitrogen was expected to be the electric arc, while coking operations would continue to generate meaningful contributions (Ostwald 1903). However, the uncertainty about the effectiveness of these methods meant that the multi-step process and direct synthesis from the elements were simultaneously pursued. In that year alone, Haber himself investigated all three. The production of nitric oxide using the electric arc had become an ongoing project with Adolf König (Haber 1905b, pp. 86–89), (Haber and König 1907d, 1908e; Haber et al. 1910) while with Gabriel van Oordt he published the first accurate, quantitative study on ammonia synthesis from the elements describing their work for the Margulies brothers (Haber and van Oordt 1905b).² The publication also contained the results of their investigation of the multi-step process based on the work of Moissan and Güntz. Several years earlier, these researchers had cycled calcium and barium nitride in H₂ atmosphere to calcium and barium hydride in order to catalytically synthesize ammonia (Güntz 1898; Moissan 1898). Haber and van Oordt used the metals calcium and manganese. With calcium nitride they obtained ammonia only with the reaction Ca₃N₂ + 6H₂ → 3CaH₂ + 2NH₃; cycling back to nitride via the reaction 3CaH₂ + 2N₂ → Ca₃N₂ + 2NH₃ had no result, as expected. According to theory, ammonia yields by this process should remain below the detection limit. Reactions with manganese were similar although the minimum working temperature was lower. Nevertheless, the reaction rates were too small to be of interest, and the cycling experiments were abandoned. Although today the results for direct ammonia synthesis are considered to be the scientifically and historically significant parts of this publication, at the time, the multi-step process was prominent and took up the entire introduction of the article (Fig. 11.1).

Fig. 11.1

The first page of Fritz Haber and Gabriel van Oordt’s 1905 Publication (and English translation) (Haber and van Oordt 1905b)

Fig. 11.2

Walther Nernst circa 1906. Source: A digital copy of this photo was obtained from the Archive of the Max Planck Society, Berlin-Dahlem–its origin is unknown

Fig. 11.3

Portrait of Nernst in 1914 by David Vandermeulen from Fritz Haber: Les Héros (Vandermeulen 2007); ⒸDavid Vandermeulen/Guy Delcourt Productions

Fig. 11.4

Members of Haber’s staff at the Institute for Physical Chemistry and Electrochemistry at the Technical University of Karlsruhe in 1909. Above: laboratory assistant (Laboratoriumsdiener) Adolf; Below: Friedrich Kirchenbauer. Source: Archive of the Max Planck Society, Berlin-Dahlem, Jaenicke and Krassa Collections, Picture Numbers VII/9 and VII/11

Fig. 11.5

Above: H.J. Hodsman; Below: Setsuru Tamaru. The photos also show the state of the laboratories and machinery around the time of the breakthrough of ammonia synthesis. Source: Archive of the Max Planck Society, Berlin-Dahlem, Jaenicke and Krassa Collections, Picture Numbers VII/12 and VII/16

Fig. 11.6

Haber and staff at the Institute for Physical Chemistry and Electrochemistry at the Technical University of Karlsruhe during the summer semester of 1908. Robert Le Rossignol sits behind and to Haber’s right, in front of him is Friedrich Kirchenbauer, J.E. Coates stands in the middle row at left, to his left is H.J. Hodsman, and Paul Krassa sits in the front row, third from left. Source: Archive of the Max Planck Society, Berlin-Dahlem, Jaenicke Collection, Picture Number VII/2

After the multistep process, Haber and van Oordt described their results for the direct production of ammonia from the elements. It is important to keep in mind that for this reaction, there had not yet been any accurate determination of equilibrium. Haber and van Oordt assumed though “that the generated yield will be very small.”³ They proceeded carefully by determining the equilibrium “from both sides” (2 NH₃ → 2 N₂ + 3H₂ and 2 N₂ + 3H₂ → 2 NH₃) using a novel apparatus with two heated, ceramic pipes containing iron and nickel catalysts.⁴ Dry ammonia gas was dissociated in the first pipe, and the resulting nitrogen and hydrogen gases were passed through a known volume of sulfuric acid to remove and determine the remaining quantity of ammonia. The gases were redried and fed into the second ceramic pipe, which was held at the same temperature as the first. Here, ammonia was generated and the reacted gas again passed through a known volume of sulfuric acid. By comparing the ammonia yields in the two pipes, Haber and van Oordt hoped to rule out (or identify) any influence of the apparatus or of differing reaction rates on the formation or dissociation processes. If, as in Ostwald’s experiments, nitrogen contained in the catalyst had altered the measured equilibrium position in one reaction, the two ammonia yields would have differed. Agreement in both pipes was strong evidence equilibrium had been reached. The experiments were carried out at one atmosphere as the experimental conditions were demanding enough. “Practical reasons,” Haber wrote, “which need not be discussed here, caused us to work not at high pressures, but at normal pressures.”⁵

A series of seven measurements (Table 11.1 and the black squares in Fig. 11.7) with the porcelain pipes, an iron catalyst, and a 1:3 N₂:H₂ gas mixture led to the determination that the equilibrium partial pressure of NH₃ at 1293 K was $p_{NH_3}=$ 0.12×10⁻³ atm (0.012 Vol.-%) and is shown as the gray hexagon in Fig. 11.7. This corresponded to an equilibrium constant of

$$\displaystyle \begin{aligned} K_p=\frac{(p_{N_2})^{1/2}(p_{H_2})^{3/2}}{(p_{NH_3})}=\frac{0.25^{1/2}0.75^{3/2}}{0.12\times10^{-3}}=2706 {} \end{aligned} $$

(11.1)

which will be used below together with Eq. A.23 from Appendix A.

Table 11.1 Values given by Haber and van Oordt for ammonia formation/dissociation experiments over iron and a 1:3 N₂:H₂ gas mixture. Experiments VIII* and IX* are shown for later reference and were not included in the table in 1905. The values appear as black squares in Fig. 11.7

Experiments I and II were carried out in a different oven than experiments III–VII and used a different iron catalyst (iron asbestos). The amount of ammonia in both pipes in these experiments was notably higher than in the later determinations and indicated that equilibrium had been reached but with a systematic shift, attributed to a possible irreversible change in the iron. Haber wrote, “we therefore give little weight to the results of the second and mainly the first experiments when calculating a mean value [for $p_{NH_3}$] (Haber and van Oordt 1905b).”⁶ Haber and van Oordt had assessed the time dependence of the catalyst’s activity and had found none. However, later experiments confirmed the fresh iron catalyst had caused a short term excess of ammonia, underscoring that the overall effect of the catalyst was still not completely understood (Haber 1920). It was concluded that out of 1000 ammonia molecules 999.76 would be dissociated at equilibrium with 0.24 remaining, a number higher than any result in experiments III through VII except pipe 2 in experiment III but far below the values in experiments I and II.

Experiments VIII and IX were made using a nickel catalyst (nickel nitrate reduced with hydrogen) but were not originally considered accurate assessments of equilibrium and were not included in the consideration of the final equilibrium value. They were performed in the same apparatus as experiments III through VII, but in both cases the amount of ammonia found in pipe 1 (dissociation) was more than in pipe 2 (generation). This was due, wrote Haber, “to the low catalytic activity [of nickel] compared to iron so that equilibrium was only just reached.”⁷ We will return to these measurements later.

To graph the results of the iron experiments, Haber and van Oordt used Eq. A.23 for the free energy. They chose a heat of formation for ammonia of 12000 cal/mol at standard temperature and constant pressure, so that the value at 0 K would be 10329 cal/mol. It was a difficult determination according to Haber because the mean specific heat for ammonia was still uncertain. Eq. A.23 became

$$\displaystyle \begin{aligned} A=10329 - 14.21\ T\ (log\ T -1.35) + 0.0014\ T^2 + 4.56\ T\ log\ \frac{(p_{N_2})^{1/2}(p_{H_2})^{3/2}}{p_{NH_3}} {} \end{aligned} $$

(11.2)

where the final term was the experimentally determined fraction of the partial pressures, or equilibrium constant K _p = 2706, from Eq. 11.1. By setting A = 0 Haber could determine the thermodynamic equilibrium of a mixture of N₂, H₂, and NH₃ at any temperature and calculated the numbers in Table 11.2 (Fig. 11.7, solid line).

Table 11.2 Calculated values from Eq. 11.2 given by Haber and van Oordt in 1905 for the thermodynamic equilibrium of a mixture of N₂, H₂, and NH₃ at 1 atm, and at different temperatures. Only the point at 1020^∘C was measured.

However, Haber made a mistake. If the values in Table 11.2 had been calculated with Eq. 11.2 using the integration constant determined with the measured value at 1293 K, this point would lie exactly on the curve, but it does not. The rest of the points from 27^∘C to 927 ^∘C do; it was a mathematical error and the volume of ammonia in equilibrium was actually lower than that calculated with Eq. 11.2.⁸ The correct function is shown as the dashed line in Fig. 11.7.

After these first measurements, Haber was convinced his results were of sufficient accuracy, but that they were not promising for industry. His skepticism was tied not only to the unfavorable equilibrium position, but also to the efficacy of the catalyst (Haber and van Oordt 1905b):

It follows further from our table [Table 11.2] that from the beginning of red heat onward, no catalyst can produce more than traces of ammonia at normal pressure with the most favorable gas mixture. Even with much increased pressure, the equilibrium position remains unfavorable.⁹

It was the obdurate di-nitrogen which was the problem. “This peculiar inertness of nitrogen,” he wrote in his 1905 textbook (Haber 1905b, pp. 189–190),

will always pose economical difficulties for a technical production of ammonia from the elements especially because nature offers us huge quantities of organically bound nitrogen in coal that is easily converted to ammonia.¹⁰

In addition to their main publication (definitive Mitteilung) just discussed (Haber and van Oordt 1905b), Haber and van Oordt also published a preliminary letter (vorläufige Mitteilung) (Haber and van Oordt 1905d) earlier in 1905, after becoming aware of Edgar Perman’s work from the previous year (Perman 1904a; Perman and Atkinson 1904a,b). Perman’s research consisted of a series of dissociation experiments in a porcelain container, described as being a continuation of the work of Ramsay and Young (it was William Ramsay himself who read the paper before the Royal Society in London). However, despite knowledge of Ostwald’s ideas, Perman’s approach was empirically based, and he made no attempt to use modern physicochemical concepts. This point was emphasized by the initial referee William Cecil Whethan who did not recommend the paper for publication (Whetham 1904).

“We have confirmed,” wrote Perman, for example,

the observations of Ramsay and Young that the decomposition is never absolutely complete, but after heating at a temperature of 1100 ^∘ for a short time the amount of ammonia remaining is so small that it can be neglected for practical purposes.

Perman believed the generation of ammonia to be reversible but decomposition to be irreversible. That is, there was “no indication whatever of any…equilibrium.”

Haber and van Oordt’s preliminary letter was a summary of the data and discussion contained in their main publication—establishing them in the field of ammonia synthesis—and though at odds with their own, they did not consider Perman’s results or methodology beyond a simple acknowledgment. In 1905, Perman published again with increased attention to synthesis reactions, including the electric arc and multi-step processes (Perman 1905). The paper also required revisions before publication but was received more warmly than the previous one (Scott 1905). However, apart from a more detailed look at ammonia generation with various catalyst materials, it continued Perman’s empirical approach and disregard of the principles of physical chemistry (Perman 1904a, 1905; Perman and Atkinson 1904a; Perman and Davies 1906). Traces of ammonia were only found after heating a mixture of nitrogen and hydrogen with an iron catalyst in the presence of moisture. “The proportion of ammonia [in Haber and van Oordt’s experiments],” Perman wrote,

…was about 0.2 to 1000…which is considerably less than obtained by me […] Moreover, the part played by the iron is not yet completely understood. My experiments show that the quantity of ammonia formed depends on the amount of moisture present, but Haber and van Oordt appear to have overlooked this point and simply say that their gases were dry.

In their response, Haber and van Oordt now took a position in regard to Perman’s work (Haber and van Oordt 1905f). They defended their conclusions and drew attention to Perman’s inconsistencies—especially in relation to the role of moisture and his apparent lack of understanding of physical chemistry. “We hope,” wrote Haber, “that Herr Perman, by giving some attention to the application of thermodynamics to chemical equilibrium, will come to a different consideration.”¹¹ Despite some experimental uncertainty, Haber was confident in his use of these principles and the order of magnitude of the results he had obtained with van Oordt. Further evidence is contained in a letter to Richard Lorentz, editor of Zeitschrift für Elektrochemie, signaling the impending response to Perman’s 1905 article (Haber 1905a):

Two pages will be sent to you from van Oordt, which I request to be included in your journal. I am sorry that this time I am only sending a defense against an unneeded attack. Indeed, I promise something better for next month.¹²

It is the first mention of ammonia synthesis in Haber’s surviving correspondence and he supplied no further scientific detail on the subject. Instead, he turned to the success he had had in his ongoing study of the carbon element (Haber and Moser 1905c; Haber and Bruner 1904g). This lack of comment to his colleagues on the ammonia system was in stark contrast to other topics such as dilute solutions.

The exchange in literature with Perman was not unique for Haber and illustrates the circumstances surrounding the equilibrium of ammonia in 1905. While there was widespread agreement that the effect of the catalyst was not fully understood, the state of application of physicochemical principles was more ambiguous. Despite their demonstrated success, the existence of equilibrium and the reversibility of chemical reactions were not universally accepted. Discrepancies even existed amongst close colleagues and renowned researchers (Le Rossignol, for example, had worked with Ramsay in England and joined Haber by 1906 (Jaenicke 1959)). Haber and van Oordt’s experimental skill and intuition also become evident here. While Ramsay and Young, Ostwald, and Perman were not prepared (or able) to consistently measure (or seriously consider) such minute quantities of ammonia (see Figs. 9.3, 9.4, and 9.5), Haber and van Oordt did so on the first attempt in a way that was remarkably accurate for the tools at hand: compare the modern theoretical curve to Haber’s data points in Fig. 11.7 while remembering that Nernst’s calculations were not yet available. Up until this point, no one knew–not even to an order of magnitude–how much ammonia would be in equilibrium with nitrogen and hydrogen.

At the time, however, the theoretical confirmation of Haber’s measurements was underway. It was a result that would unequivocally establish the authority of physical chemistry in solving the mystery of ammonia synthesis.

1.1 Über die Berechnung chemischer Gleichgewichte aus thermischen Messungen (On the Calculation of Chemical Equilibrium from Thermal Measurements) by Walther Nernst, 1906

Walther Nernst’s initial publication on the subject of ammonia synthesis grew out of theoretical work from the second half of the nineteenth century, which investigated the nature of the heat released during chemical reactions—work that established the existence and role of the free energy in chemical dynamics (Figs. 11.2 and 11.3). At the beginning of the twentieth century, this theoretical framework, while having provided pivotal information on the nature of a chemical reaction, was not able to give a complete quantitative picture. A complementary experimental measurement was needed to calculate the equilibrium of chemical systems, including ammonia. Finding a complete and general theoretical treatment had become one of the central problems in physical chemistry. While Haber and others developed methods for employing the experimental solution (see Appendix A), Nernst continued to consider the theoretical approach. He began with the work of Hermann von Helmholtz and, using a mathematical equation that would later be called the third law of thermodynamics, found a solution that allowed the calculation of thermodynamic equilibria using only the results of thermal data from vapor pressure measurements. At first, however, it was much less dramatic: Nernst saw his new equation as little more than a mathematical tool obtained from a hunch after reviewing experimental data. This development is outlined in more detail in Chap. 13 and Nernst’s full derivation can be found in Appendix B.

Fig. 11.7

Fritz Haber and Gabriel van Oordt ’s 1905 results

Fig. 11.8

Walther Nernst’s 1906 results

Here we concentrate on the sections of Nernst’s work devoted to the calculation of the ammonia system as it related to Haber’s research.

In the second section of his paper (the first section is the derivation of his heat theorem found in Appendix B), Nernst focused on empirical and theoretical methods of obtaining and evaluating vapor pressure curves with which he determined the unknown constant of integration. While this section contained physicochemical considerations, for example, the numerical values and role of molar specific heats in calculations, it was mainly an assessment of the inadequate state of vapor pressure data–ammonia being an important exception (Dieterici 1904). He also gave a table of chemical constants, including those needed to calculate the equilibrium of ammonia, which became central to the interaction with Haber: H₂ had a value of 2.2, N₂ had the value of 2.6, and NH₃ had the value 3.3. Added together they gave the value of the integration constant, equal to the term Σνi in Eq. B.32.

In the third section of his paper, Nernst applied these data and his heat theorem to several examples. For the N ₂ + 3 H ₂ ↔ 2 NH ₃ system, he obtained the following expression for the logarithm of the equilibrium constant K:

$$\displaystyle \begin{aligned} log\ K=log\,\frac{{p_{H_2}}^3\cdot p_{N_2}}{{p_{NH_3}}^2}=log\, \frac{0.75^3\cdot0.25}{x^2} =-\frac{24000}{4.571\ T}+3.5\ log\ T+6,6+2,6-6,6 {} \end{aligned} $$

(11.3)

where the factor 4.571 is obtained as in Eq. A.27 and the three factors at the end of the equation are the chemical constants for H₂ (2.2), N₂ (2.6), and NH₃ (3.3)–there are three moles of molecular hydrogen and one mole of molecular nitrogen in two moles of ammonia.¹³ When referring to “thermal data” later, it will be in reference to these numbers along with the specific heat and the heat of formation of ammonia.

Equation 11.3 reduced to:

$$\displaystyle \begin{aligned} log\,\frac{0.325}{x}=-\frac{2625}{T}+1.75\ log\ T+1.3 {} \end{aligned} $$

(11.4)

and is shown as the solid line in Fig. 11.8.

Using Haber and van Oordt’s value for the partial pressure of ammonia from 1905 (Haber and van Oordt 1905b), x = 0.12 ⋅ 10⁻³, Nernst calculated a corresponding absolute temperature of 893 K, whereas Haber and van Oordt had reported a temperature of 1293 K–a difference of 400 degrees (Fig. 11.8, black squares).¹⁴ Nernst made no further comment at the time. Instead, he offered a final thought on his calculations for homogeneous gas phase systems. Although he felt the numerical results of his theory spoke for themselves, he hoped it would not be the only useful aspect of his work. “Of greater importance,” Nernst wrote,

is the fact that the general character of the relationship between chemical energy and heat seems, after a long search, to unveil itself from the fundamental theorem in harmonic simplicity.¹⁵

The third law delivered information not contained in the first and second laws and allowed Nernst to move beyond Helmholtz. He was able to determine the constant of integration which was tantamount to disentangling the total energy from the entropy, bound together by their mutual definition (Eq. B.3). It was also the last step to a full theoretical formulation of classical thermodynamics (see Chap. 13) (Haberditzl 1960; Suhling 1972), (Müller 2007, pp. 171–172).

1.2 Über das Ammoniak-Gleichgewicht (On Ammonia Equilibrium) by Fritz Haber and Robert Le Rossignol, 1907

In connection with the results from his heat theorem and supporting experiments, Walther Nernst wrote a letter to Fritz Haber in the fall of 1906 concerning Haber’s 1905 publication. Working at lower temperatures and higher pressures, Nernst, together with Karl Jellinek, had found ammonia yields three to four times smaller than expected from Haber’s extrapolations. Haber’s determination of the equilibrium was apparently incorrect. Although Haber was skeptical that Nernst had actually measured the equilibrium state (according to Haber, Nernst had only performed ammonia generation experiments, which would result in lower yields if complete equilibrium had not been reached), he began new experiments to verify his 1905 results, this time with Robert Le Rossignol. The results were published in 1907 (Haber and Rossignol 1907e). The apparatus remained largely the same, with several improvements including a more accurate temperature assessment at the exact site of the reaction¹⁶. During their work, Walther Nernst published his heat theorem, which, along with the earlier letter, changed Haber’s perspective and approach to ammonia synthesis. It was in 1906 and early 1907 (and not at the Bunsen Society meeting in May 1907) that Haber began to entertain the idea of a range of values resulting from his 1905 experiments and that one of these—in fact one of the lower values he had not yet considered—was correct and could provide the necessary response to Nernst’s criticism. For Haber, his determination of the order of magnitude using a weighted average near the upper bound of his earlier results had originally been sufficient—and it had been no small achievement. It was the first determination of the equilibrium of ammonia that could be viewed as a rigorous and dependable establishment of an approximate value, albeit one that indicated little promise for industrial application. But after Nernst’s reaction, Haber decided to take another look (Jost 1908a). In the context of his new experiments with Le Rossignol, he repackaged his earlier results to draw attention to any agreement between the 1905 and 1907 data sets as well as to the improvements in experimental accuracy.

Fig. 11.9

Fritz Haber and Robert Le Rossignol’s 1907 results

Fig. 11.10

Friedrich Jost’s 1908 results

Fig. 11.11

Fritz Haber and Robert Le Rossignol’s 1908 results

Referring to the ammonia yields in pipes 1 and 2 in the 1905 experiments (Table 11.1), Haber described the way in which measurements I and II, and now measurement IX with nickel (a measurement excluded in 1905) had been incorporated:

They were given weight in such a way that rather than a mean value from the results of the six¹⁷ other experiments, a value of 2.4 mols [per 10,000 or 0.012 Vol.-% at 1293 K] close to their upper limit was seen as correct and used for subsequent calculations.¹⁸

This statement may be compared to the quote in 1905 on page 4 on how the average was obtained. Not only did Haber now consider the nickel experiments (VIII and IX in Table 11.1) to be significant, he also began to refer to an upper limit within a range of values. By including the nickel experiments he was able to substantiate the value of 0.24 mols/1000 chosen in 1905, which lay close to the upper limit of the data. Perhaps more importantly though, experiment VIII provided him with a new low value which corresponded precisely with his 1907 measurements. The upper and lower limits, stressed later at the 1907 Bunsen Society meeting (Nernst 1907), were 0.013 and 0.0055 Vol.-%, respectively, and are shown in Fig. 11.7 by the gray triangles.¹⁹

Haber then turned to the 1905 iron stability tests in which large volumes of gas were passed over the catalyst. It had been an effort to show the reliability of experiments III–VII in Table 11.1 because some fluctuation with time had been observed. The stability experiments showed no catalyst degradation although the equilibrium yields were less than half of those found in experiments III–VII. In light of the fact that the stability tests were performed with high gas fluxes, Haber had found the deviation in 1905 to be “not very significant,”²⁰—important was that the order of magnitude was the same. He reacted differently in 1907 (Haber and Rossignol 1907e):

The results of a longer [stability] experiment…were taken to show the ammonia yield stayed well below equilibrium due to the quick flow of the gases over the [iron] catalyst. Our new experiments have shown us that the ammonia generation in that stability test was only slightly lower than the [real] equilibrium value, which was not at the upper, but rather at the lower limit of the range in which the results of the six main experiments [III–VII and now VIII]…were found.²¹

The stability test equilibrium value is given in Fig. 11.7 as a gray star along with Eq. 11.2, recalculated using this point to determine the integration constant (dotted line).

Instead of a range of values, Haber and van Oordt had chosen originally and in less than transparent fashion to represent all of the 1905 experiments with a single value close to the “upper limit.” The true equilibrium value was indeed contained in those results–it was only a matter of recasting them as a range instead of a weighted average. Haber attributed the remaining deviation reported in Nernst’s letter to an old problem: the limited knowledge of the specific heat of ammonia at high temperatures.

In 1907, Haber still found the equilibrium position of ammonia unfavorable for industrial synthesis but “at lower temperatures, it was not so badly shifted as it had seemed after the older calculations [from 1905].”^{22 , 23} As for Edgar Perman’s claim that there was no equilibrium state at all that contained ammonia, Haber now dismissed it altogether. Confidence in the accuracy and interpretation of his 1907 measurements was clearly expressed in the publication.

Haber and Le Rossignol presented the results of at least 49 individual determinations of equilibrium with iron, nickel, chromium, and manganese catalysts, and a 1:3 N₂:H₂ mixture along with a table (Table 11.3) containing the mean values for $K_{p}=\frac {p_{NH_3}}{{p_{N_2}}^{1/2}\ {p_{H_2}}^{3/2}}$, the reciprocal value of that given in 1905 (Fig. 11.9, black squares). There was a shift compared to the 1905 curve in the direction Nernst had expected: the value at ∼1000 ^∘C (∼1273 K) was reduced from $p_{NH_3}=$0.012 Vol.-% to 0.0048 Vol.-% (compare Figs. 11.7 and 11.9).

Table 11.3 Average values given by Haber and Le Rossignol for the equilibrium constant K _p with a mixture of N₂, H₂, and NH₃ (N₂:H₂ = 1:3) at the given temperatures and iron, nickel, chromium, and manganese catalysts (Fig. 11.9, black squares). The corresponding values for volume percent have been added for comparison with the 1905 results

Haber followed his results by renewed theoretical considerations. Applying the approximation from Eq. A.27, he used the function:

$$\displaystyle \begin{aligned} logK_p=\frac{12000}{4.57\ T}-5.89 {} \end{aligned} $$

(11.5)

to fit his data (Fig. 11.9, solid line). 12000 was the heat of formation for one mole of ammonia and, according to Haber, was a reliable value responsible for the quality of the fit. “A complete thermodynamic treatment,”²⁴ however, was not possible because the heat of formation deviated from this value at higher temperatures and reliable numbers had not yet been obtained. In this context, Haber also consulted Nernst’s heat theorem and fit his data with the equation used by Nernst for the ammonia system in 1906 (Eq. 11.4). He had to modify the original expression through the addition of the linear term + 0.000651 T and reformulated it for one mole of ammonia (Fig. 11.9, dashed line):²⁵

$$\displaystyle \begin{aligned} logK_p=\frac{12000}{4.571\ T}-1.75\ log\ T-1.3 +0.000651\ T \end{aligned} $$

(11.6)

Although the resulting curve matched Haber’s data, the term linear in T implied a heat of formation for ammonia (see the expression for Q _p,T, Eq. A.22) that rose more quickly with temperature than had been determined experimentally. Haber did not comment further on the heat theorem. Criticism of Nernst’s work came only after Haber received more information at the 14th Meeting of the Bunsen Society in what was a pivotal act in the scientific development of ammonia synthesis from the elements.

1.3 Über das Ammoniakgleichgewicht (On Ammonia Equilibrium) by Walther Nernst with Experiments from Friedrich Jost, 1907

Nernst’s 1907 published response to Haber and van Oordt’s 1905 study (their 1907 contribution appeared too late for Nernst’s consideration) was from a lecture at the 14th Meeting of the Bunsen Society from May 9–12 in Hamburg (Nernst 1907). In it, he recapped his results from his heat theorem (Nernst 1906), including the discrepancy in the temperature between Haber’s measurements and his own theoretical determination. At the equilibrium concentration of $p_{NH_3}$=0.12× 10⁻³ atm (or 0.012 vol.-%), Nernst had calculated a temperature of 893 K while Haber had reported 1293 K (compare Figs. 11.7 and 11.8). According to Nernst, the ammonia yields reported by Haber in 1905 were unreliable because they had been measured at atmospheric pressure and were too small to provide accurate results.

In order to improve accuracy, Nernst and Friedrich Jost, citing the law of mass action, obtained higher yields using an electric pressure oven during the winter of 1906–1907. The higher pressure would also increase reaction rates and bring the system into equilibrium more quickly. They used a platinum wire catalyst and, like Haber and van Oordt, H₂SO₄ to extract and assess the amount of ammonia in equilibrium with nitrogen and hydrogen. In the publication, only ammonia formation experiments were reported, as Haber had previously noted after receiving Nernst’s letter. Dissociation was not discussed. Despite lacking these complementary measurements, the independence of the results from gas flow rates convinced Nernst and Jost that they had measured the true equilibrium position.

Although Nernst’s publication was meant as an overview for the conference, the presentation of his results is notable. In reporting on the observed values of the partial pressures of ammonia obtained at different temperatures, the usually precise researcher gave only the averages from many experiments. He did not elaborate on the composition of the precursor gas mixture or exact experimental pressures. A “precisely calibrated manometer”²⁶ was used to measure the pressure, which was between 50 and 70 atmospheres, and Nernst had to calculate the equilibrium constant for 1 atm. These were Nernst’s first experimental results (Table 11.4)—up until this point he had only published theoretical findings. However, the data and description were not specific enough to allow his experiments to be reproduced. Jost’s 1908 publication of the same study provided the details missing in Nernst’s report (Jost 1908a).²⁷ The expansion of published information meant that Nernst’s overview played a similar role to Haber and van Oordt’s 1905 preliminary letter, namely, establishing a presence in the field of ammonia synthesis from the elements.

Table 11.4 Values for ammonia equilibrium given by Walther Nernst in 1907 (Nernst 1907). t is the temperature in^∘C, T in K, $\sqrt {K}$ the square root of the equilibrium constant, and 100 ⋅ x obs. and 100 ⋅ x cal., 100 times the observed and calculated values for $x=p_{NH_3}$ (100⋅ x =  Vol.-%). The calculations are based on Eq. 11.8. For further details see Jost (1908a) in Sect. 11.1.5

Fitting the data points to thermodynamic theory, Nernst made use of Eq. A.27, which contained the simplified expression for the heat of formation of ammonia from Eq. A.25. He obtained:

$$\displaystyle \begin{aligned} logK=-\frac{Q}{4.571\ T}+B=-\frac{6130}{T}+12.86 {} \end{aligned} $$

(11.7)

or

$$\displaystyle \begin{aligned} log\,x=+\frac{3065}{T}-6.918 {} \end{aligned} $$

(11.8)

From this equation, he determined the heat of reaction for two moles of NH₃ to be 28,020 cal at room temperature. His results contradicted Thomsen and Berthelot’s determination of 24,000 cal, which had been used by Haber in 1905 and 1907, and by Nernst himself in 1906. With this new value, combined with Haber and van Oordt’s 1905 partial pressure of ammonia, x = 0.12 ⋅ 10⁻³ atm (0.012 Vol.-%), Eq. 11.8 indicated a temperature of 1023 K. According to Nernst, the result was “in far better agreement”²⁸ with his theoretical value of 893 K than Haber’s original value of 1293 K (Nernst 1906).²⁹ Referring to his heat theorem, if he had chosen a value higher than 24,000 cal in his 1906 calculations, the temperature resulting from Eq. 11.4 would have been “practically in full agreement” with 1023 K.³⁰ However, the controversy on the equilibrium of ammonia was not yet settled.

The final two pages of Nernst’s 1907 publication consist of an excerpt from the discussion following the presentation of his results at the Bunsen Society meeting. The exchange has taken on a central role in the history of ammonia synthesis to illustrate the dynamic between Walther Nernst and Fritz Haber. As indicated in Part I, there is more behind the circumstances of their interaction than only the vitriol and even subjugation suggested in an array of historical and popular literature. While the discussion was pointed and both men were defensive, it also facilitated the combination of different fields of knowledge: Haber, the application-oriented experimentalist, and Nernst, the fundamental truth-oriented theorist, engaged in an exchange of ideas. However, even this description oversimplifies the two men’s expertise and intentions.

1.4 14th Meeting of the Bunsen Society, Hamburg, 1907

The discussion between Fritz Haber and Walther Nernst in Hamburg, published as the final two pages in Nernst’s 1907 paper (Nernst 1907), has been cast as a dramatic showdown between the famous Prof. Nernst of Berlin and the little-known Prof. Haber of Karlsruhe (Coates 1937, p. 1652), (Goran 1967, pp. 46–50), (Suhling 1993), (Stoltzenberg 1994, pp. 154–156), (Szöllösi-Janze 1998b, pp. 167–169), (Charles 2005, pp. 87–91), (Bartel and Huebner 2007, p. 167), (Erisman et al. 2008; Hager 2008), (Sheppard 2020, chapter 5).³¹ Nernst’s direct criticisms and Haber’s anxious persona are used to illustrate a situation in which a senior researcher publicly humiliated his junior colleague and in doing so, provided him with the sharpened physical insight that sent him on his way to a scientific breakthrough.

I will present the discussion in Hamburg in a different light by detailing the motivation and state of knowledge of both scientists.

The interaction at the Bunsen Society meeting is justly described as a crucial moment in the history of ammonia synthesis. The exchange of insight, the dynamic between experiment and theory (as discussed in Part I, Chap. 6), and Nernst’s statements indeed provided the impetus for Haber to perform new measurements. However, Haber’s comments in Hamburg were also of great relevance. After the publication of his 1907 results, Haber was less influenced by Nernst’s comments than existing literature leads us to believe. As we have seen, Haber’s approach to ammonia synthesis had already undergone a transformation by this time, and he was now confident in his results. The discourse was rather an interaction between two men, both mature in their physicochemical understanding, who had grasped the profound meaning of the initial experimental and theoretical results on ammonia equilibrium.

This important aspect, absent from the literature, is integral in examining Haber and Nernst’s discussion. They were the only two scientists in that time who had a detailed understanding of how the equilibrium of ammonia with nitrogen and hydrogen had been (approximately) determined. They also both understood that a successful industrial application depended on the behavior of the system at lower temperatures and on the identification of a more effective catalyst. The outcome could not yet be conclusively assessed: the inaccuracies in the thermal measurements used to extrapolate the data allowed for either conclusion. The examinations of this topic in the historical literature make it appear as if Nernst meant to discredit Haber’s results because they were off by a factor of three or four. This deviation would have been significant if there had been an established expectation of what the equilibrium value should be. But there was not. The earlier numbers obtained by Ramsay and Young, Le Chatelier, Ostwald, and Perman were either inaccurate or widely fluctuating. Or Both. Furthermore, some of their results were not based on any actual ammonia production at all. It is clear from their discussions that none of these researchers expected the small amount of ammonia Haber measured. Nernst’s critical stance was rather due to his limited data (his calculations and initial measurements) and he still had reason to doubt the accuracy of his own reported results.

It must be emphasized again that Haber’s 1905 numbers established a reliable order of magnitude for what had previously been a completely unknown quantity. There was also still no experimental evidence that the ammonia system obeyed Le Chatelier’s principle (König 1954). Before Nernst’s calculations and Haber’s measurements, the equilibrium of ammonia could have been, according to the expectations at the time, orders of magnitude away from what Haber had found. When Nernst completed the calculations for ammonia with his heat theorem and saw the similarity to Haber’s results (even if off by a factor of three or four) he must have immediately understood what it meant. The results of their independent methods had suddenly converged with an accuracy that could not have been accidental. If Nernst had not been convinced, he would have had no reason to contact Haber. He would not have written a letter to the junior scientist if he thought Haber’s result was nothing but another in a long line of erroneous measurements on ammonia. That is, he did not engage Haber to teach him a lesson, but rather he knew Haber’s results were of meaningfully accuracy and perhaps just favorable enough for industrial application. Nernst wanted in on the action.

The published excerpt of the discussion begins with Haber covering his 1905 results with van Oordt in light of the presentation made by Nernst. His older study was “not carried out in order to determine the equilibrium of ammonia [but rather to determine industrial feasibility].” It was Nernst’s letter “and the verification of [Nernst’s] theory…that prompted [Haber]…to supplement the few, older measurements made with crude means with a large number of [new measurements] made with the utmost care…”³² Haber took the same approach as in his 1907 paper (Haber and Rossignol 1907e) by describing a range of values and noting the 1907 numbers were closer to those measured by Nernst and Jost. At 1000 ^∘C (1273 K) Haber reported the new value as 0.0048 Vol.-%, while Nernst measured 0.0031 Vol.-%. Haber also drew attention to the consequences of the uncertainty in the heat of formation of ammonia and its temperature dependence.

Nernst agreed that the outcomes of the new experiments were more acceptable but still cast doubt on the accuracy Haber was able to achieve with low yields at atmospheric pressure. “I would like to propose,” Nernst responded, “that Herr Prof. Haber now use, instead of his earlier method…a method [under pressure] that will surely result in truly accurate values due to the higher yields.”³³ This comment, that the use of pressure favored ammonia generation at equilibrium, is often cited as Nernst’s lesson, or “decisive advancement in insight” (Szöllösi-Janze 1998b, p. 167),³⁴ to Haber. However, it was nothing more than a suggestion: Haber, like Wilhelm Ostwald before him,³⁵ understood the effects of working at higher pressures and had made explicit reference to it in 1905 (Haber and van Oordt 1905b, p. 344). By 1907, Haber was an established physicochemist. The expressions in Appendix A, taken from his book Thermodynamik technischer Gasreaktionen (Haber 1905b), show his mathematical and theoretical proficiency, including when describing the effect of pressure. The book had been well received and his publications had reached an international audience–in some ways Haber was even more a modern theorist than Nernst. He was comfortable with the concept of entropy and often used it in publications and correspondence,³⁶ which helped break down chemists’ inhibitions toward its application (Coates 1937, p. 1650). Nernst, on the other hand, who decided not to use entropy to express his initial formulation of the third law, “thought the notion of entropy lacked concreteness and was inappropriate (Haberditzl 1960, p. 408), (Suhling 1972).”³⁷ In short, Haber’s derivations contained the same mathematical rigor as Nernst’s, and he was aware of the theoretical effect increased pressure would have on his ammonia experiments.³⁸

It is rather Haber’s reaction to Nernst’s suggestion that gives us insight into why there was a deviation between their respective numbers, that is, why Nernst’s measurements of ammonia equilibrium were lower than Haber’s. “With Herr Geheimrat Nernst’s apparatus,” Haber said, “equilibrium can only be reached from one side, while I can reach it simultaneously from both sides.”³⁹ Haber had mentioned this opinion in his 1907 publication and Nernst’s response now in Hamburg was that he could reach equilibrium from both sides in his pressure oven–but not that he had done so. Haber’s point was that during ammonia formation experiments from nitrogen and hydrogen, a sub-optimal catalyst (such as Nernst’s platinum compared to Haber’s iron) would not increase the reaction rates to those found in dissociation reactions because of a large energy barrier to formation. Nernst’s measured yields would then be smaller than the true equilibrium value. This point remained a target of Haber’s criticism and Nernst later changed his experimental approach.

At the end of the excerpt, Nernst reassessed the state of ammonia synthesis in reference to an industrial context in what has become a famous declaration. However, rather than only attacking Haber, he was also differentiating between Haber’s 1905 and improved 1907 results.

It is regrettable that the equilibrium of ammonia formation is shifted further toward the low end of the yield than one would have supposed from Haber’s highly inaccurate numbers. We could have then considered synthetically producing ammonia from hydrogen and nitrogen. But the situation is actually much less advantageous, the yields are roughly three times smaller than expected.⁴⁰

While Haber’s skepticism toward the industrial potential of direct ammonia synthesis from the elements remained (he still preferred the electric arc into 1908 and 1909 during his initial work with BASF), Nernst’s seemingly pessimistic attitude was not exactly as it seemed, for he was a business man. In 1897, while still in Göttingen, he had developed an incandescent lamp based on a mixture of zirconium and yttrium oxides that generated light more efficiently than the carbon filament lamp and did not require a vacuum. It became known as the Nernst-Lampe and the patent was sold to the AEG Aktiengesellschaft, providing Nernst with substantial financial gain. After a successful marketing campaign, it sold millions of units over a decade beginning in 1903 (Bartel 1989, pp. 45–49). Ammonia was simply another opportunity. In September of 1906, almost a full year before the meeting in Hamburg, Nernst had entered into a contractual agreement with the company Griesheim-Elektron to investigate the upscaling of ammonia synthesis from the elements (Farbwerke Hoechst 1966, pp. 19–24). Haber would not learn of this partnership until 1908 in Berlin, where Nernst himself informed Haber of his relationship with industry. Not surprisingly, this meeting led Haber to strengthen his own industrial pursuits. By that time, Nernst’s experiments were underway and seemed promising, however, any success they may have had was not formulated into a patent before BASF’s own patent application with Haber was submitted. In reaction, Nernst’s work became part of an ultimately unsuccessful nullification suit (Suhling 1993), (Stoltzenberg 1994, pp. 170–180), (Szöllösi-Janze 1998b, pp. 181–185).

Nernst looked not only to better his position where he could financially, but was also known to accept praise for scientific endeavors, even if his actual role was unclear. When Le Rossignol met Nernst years later, he acknowledged Nernst’s contribution to the work on ammonia synthesis: “Herr Geheimrat, it was also with your help,”⁴¹ the engineer remarked. Although Nernst had admitted by that time that he could not have performed the experiments any better himself, he took the compliment and “swallowed it like butter (Jaenicke 1959).”

The evidence that Nernst was more optimistic about industrial ammonia synthesis than he let on is not only provided by the possibilities inherent in Haber’s measurements. It is also found in Nernst’s theoretical results. The chemical constant for hydrogen that Nernst used in his theory (the number 2.2 that appears multiplied by a factor of 3 in Eq. 11.3) was determined by the thermal measurements available to him at the time. But in 1909, he revised the value to 1.6 (Nernst 1909). Later, Haber remarked on the influence of the different values (Haber 1924, p. 16, reference 5 (pp. 22–23)):

If one asks what the consequence would have been had [Nernst] at the time (1906–07) used the value of 1.6, which he later recognized to be true, in otherwise exactly the same conditions and methods of calculation, one can easily see he would have calculated an 8-fold increase in the ammonia yield. Thus, he would have come to the conclusion that my estimate was not to high, but rather too low [italics added] […] These circumstances become more acute through the fact that at the time of Nernst’s calculation neither the heat of formation of ammonia nor the specific heat were adequately known.⁴²

Thermal data was again at the root of discrepancies between experiment and theory. The issue was not only Nernst’s chemical constants used to calculate the integration constant, but also the heat of formation, Q. The value varied between 12,000 and 14,010 cal/mol,⁴³ and approximating its temperature dependence was a constant trade-off between manageability (complexity) and accuracy. The consequences for the value of Eqs. A.23 and A.27, for example, are noted in the next section. Remembering the attention to detail with which Nernst assessed his chemical constants in section two of his 1906 paper (Nernst 1906), it is difficult to accept that he did not consider the effect of deviations from the values he chose.⁴⁴ Nernst was aware of the uncertainty in thermal data that made a determination of the equilibrium yield at lower temperatures difficult. The equilibrium position and its temperature dependence, as it was speculated in 1907, did not exclude the possibility of industrial production—especially if one allowed for the error in thermal measurements. Nernst must have seen this in the numbers, otherwise he would not have approached Griesheim-Elektron.

Although Nernst’s assertions at the Bunsen Society meeting may be viewed as a deterrent to Haber or to others who had come to similar conclusions about industrialization (Szöllösi-Janze 1998b, p. 175), they should not be viewed as an unusually acrimonious attack. Nernst was not opposed to polemics at the highest level and was known to criticize friends and colleagues if he felt it necessary (Bartel 1989, p. 50), (Szöllösi-Janze 1998b, p. 220). Haber had also been involved in such disputes. The debate with Edgar Perman between 1905 and 1907 is one example and Haber frequently mentioned others in his correspondence along with his anxious reactions (Haber 1900a, 1901a,b,c, 1902a). “Apparently,” wrote Margit Szöllösi-Janze in another example (Szöllösi-Janze 1998b, p. 111),

Haber’s actions [at the 5th Annual Meeting of the German Electrochemical Society in Leipzig in 1898] had a provocative effect, at least on individual researchers…Years-old feuds were easing, the fallout of which had been publicized, and excessively occupied the temperamental, yet thin-skinned, and increasingly nervous Haber. He created scientific polemics [but was] held back and wisely advised by Richard Abegg who discretely moderated the attacks from his friend.⁴⁵

This comment is not meant to convey Haber’s actions and correspondence as mere gripes, attacks, and defensive posturing. As with his comparison of the state of physical chemistry in Germany and the United States in Chap. 10, Haber often gave meaningful commentary in his letters on the general state of science, documenting human interactions and the pursuit of publications. Some of the correspondences were quite gracious, even, for example, when it came to the rejection of one of his papers at the hands of Nernst in 1900. In that situation, Haber could only agree with Nernst’s reasoning (Haber 1900b).

Keeping with this balanced perspective, we find what has been portrayed in literature as Haber’s riled reaction to the encounter with Nernst to be not unusually adverse; when viewed in the wider context of Haber’s career it was part of a broad range of emotions. In fact, the junior scientist had the opportunity to change and approve the excerpt of the discussion in Hamburg that was printed in the Zeitschrift für Elektrochemie. “I hope to leave on Monday,” Haber wrote to Richard Abegg⁴⁶ in an undated letter before leaving for England to meet his friend at the Seventy-Seventh Meeting of the British Association for the Advancement of Science in Leicester, England between July 31 and August 7, 1907^{47 , 48} (Murray 1908, p. 480), (Zott 2002, p. 382, Letter 152: Abegg to Ostwald, March 29, 1907),

Let me know your exact itinerary, if possible in writing. I have written to [Heinrich] Danneel that in the revision of the discussion with Nernst I would like to have my best sentence stricken which begins “I consider it a significant result of Nernst’s theory but I must say that…”

In case you have the revision, please strike it.

The quarrel with Nernst has risen to a form that makes this necessary.⁴⁹

The public humiliation described in the literature to which Haber was subjected could have been countered by Haber himself, had he felt it necessary. This was neither the first nor last time that pointed language was used or that Haber was alerted to the content of a forthcoming publication on ammonia synthesis (results and commentary were often shared before printing) (Haber and Rossignol 1908g). Rather, his reaction was much the same as it had been to the other polemics he had had over his career: they caused him to vent in both public and private, and to redouble his efforts in the laboratory. The latter was not without reason. After the Bunsen Society meeting, there was no longer any doubt whether the equilibrium position of ammonia had been measured (or calculated)—only the accuracy of the measurements were still in question along with experimental details. And, of course, whether the process was suitable for industrial application. As for theory, Nernst had provided the missing concept that solved a central problem in chemical thermodynamics: the constant of integration in the formula for the free energies could now be calculated. But his results were only legitimate if backed by experiment, and the ammonia system had not conformed. After Hamburg, though, the deviations were no longer questioned on physical grounds; it was only the uncertainties in thermal data which posed a problem (Rossignol 1928).

Experimental work continued.

1.5 Über das Ammoniakgleichgewicht (On Ammonia Equilibrium) by Friedrich Jost, 1908

In March of 1908, Friedrich Jost published his detailed results underlying Nernst’s 1907 publication (Jost 1908a; Nernst 1907). As had been the case with Nernst in 1907, he began with a critique of Haber’s 1905 results. He argued that it was the small yields in Haber and van Oordt’s experiments that led to the fluctuating and inaccurate numbers. Jost sought to avoid this issue by using higher pressures in the pressure oven (the same as described by Nernst in 1907) and also corrected for oxygen in his precursor gases. Here Jost first explicitly stated he had determined the equilibrium from both sides–a shortcoming to which Haber had already thrice called attention.⁵⁰ It becomes clear here that the dissociation experiments were not included in those discussed by Nernst in Hamburg, but were added later. The dissociation experiments were fewer in number and, as is apparent from the summary of results, made under different experimental conditions than the generation experiments.⁵¹ The initial study, reported in 1907, was made only with a platinum catalyst and complementary experiments were later performed with iron and manganese. None of the dissociation experiments in the 1908 paper were performed with platinum. It is not clear when iron and manganese were first used, but it was likely after the meeting in Hamburg as a reaction to Haber and Le Rossignol’s criticism. Jost’s dissociation results do, however, support the trend seen in his generation experiments.

Jost summarized his large number of experiments made between 14.3 and 74.5 atm,⁵² 876 and 1040^∘C, and differing nitrogen-hydrogen mixtures into tabulated results, recalculated for 1 atm and a gas mixture of N₂:H₂ = 1:3. These are given in Table 11.5 and Fig. 11.10 as black squares. Jost fitted the same two-term equation as Nernst in 1907 (Eq. 11.8), which is shown in Fig. 11.10 as a solid line.

Table 11.5 Values for ammonia equilibrium given by Friedrich Jost in 1908 (Jost 1908a) (black squares in Fig. 11.10). t is the temperature in ^∘C, T in K, $\sqrt {K}$ the square root of the equilibrium constant, and 100 ⋅ x obs. and 100 ⋅ x cal., 100 times the observed and calculated values in Eq. 11.8 for $x=p_{NH_3}$ (100⋅ x =  Vol.-%), respectively

Jost also interpreted his results in terms of Nernst’s heat theorem. In 1906, Nernst did not yet have evidence the heat of formation, Q, of ammonia was higher than 12,000 cal/mol at room temperature, so he used exactly that value. However, Jost’s data was best fit with the assumption that Q was 14,000 cal/mol at working temperatures, which implied a somewhat higher value than 12000 cal/mol at room temperature. Jost also used the approximation for Q in Eq. A.22 while Nernst had used the simplified expression from Eq. A.25. Although Jost’s approximation for Q did not completely match experimental data—it was lower than the measured value at working temperatures (1150 K) but higher than the “classic” value of 12,000 cal/mol at room temperature—it had “adequate accuracy.”⁵³ The chemical constant for ammonia formation was now 6.62 instead of 6.6 in Eq. 11.3; the constant for hydrogen remained 2.2. Nernst’s 1906 equation for the equilibrium constant, Eq. 11.4, became:

$$\displaystyle \begin{aligned} \log\,K=log\,\frac{0.325}{x}=-\frac{2571}{T}+1.75\ log\,T-0.000385\,T+1.29 {} \end{aligned} $$

(11.9)

and is shown in Fig. 11.10 by the small-dashed line. Jost compared Eq. 11.9 with the experimental results in Table 11.5 and was satisfied with the agreement.⁵⁴ “The calculation,” he wrote with foresight,

is tentative until we have better knowledge of the specific heat of ammonia and of the “chemical constants” [in Eqs. 11.3 and 11.9] for nitrogen which are…the most uncertain for this gas⁵⁵

Jost’s expression for Q indicated a room temperature value of 12,753 cal/mol for the heat of formation of ammonia—higher than the value of 12,000 cal/mol accepted at the time. He also noted that if Q _o equaled 12,753 cal/mol in Eq. 11.4, then Nernst’s 1906 results would have been in better accordance with experiment (the dashed-dotted line in Fig. 11.10) because a higher value of Q _o led to a higher calculated ammonia yield. Comparing his results to Haber and Le Rossingol’s 1907 numbers, Jost still found inconsistencies. “I cannot,” he wrote, “give an exact single cause for the considerable deviation…however, I find no reason to view my results…as unreliable.”⁵⁶

There were conspicuous differences between this paper from 1908 and Nernst’s 1907 conference contribution. The changes went beyond the application of Nernst’s heat theorem; they were also experimental in nature. The importance of measuring the ammonia system “from both sides” and the use of different catalysts had become clear to Jost and Nernst after the Bunsen Society meeting (but Nernst never considered the catalyst to be as important to understanding ammonia synthesis as Haber did (Mittasch 1951, p. 69)). Nevertheless, through their interaction with Haber, Nernst and Jost learned more of the reality of meticulous experimental work.

This and later publications show that Haber was not the only one who had learned something in Hamburg.

1.6 Bestimmung des Ammoniakgleichgewichts unter Druck (Determination of Ammonia Equilibrium Under Pressure) by Fritz Haber and Robert Le Rossignol, 1908

During the second half of 1907, Haber and Le Rossignol had worked “feverishly” on the third round (second round with Le Rossignol) of experiments to assess the equilibrium position of ammonia, this time under pressure as Nernst had suggested (von Leitner 1993, p. 125). The new apparatus was different from Nernst’s and depended significantly on Le Rossignol’s engineering abilities. For example, he built the needle valves from scratch that were needed for the accurate dosing of gases (Krassa 1966; Travis 1993a). As Le Rossignol recollected years later, “Haber was not good as experimentalist [sic]…[he] did the theoretical side, and I did the engineering side (Jaenicke 1959).”

They were not working out of a need to appease Nernst. Haber was convinced his numbers were correct, and he knew why Nernst’s were not. They published in April of 1908 (Haber and Rossignol 1908f), beginning with a blunt assessment. “The question,” wrote Haber, “of the exact equilibrium position for the reaction $N_2 + 3\ H_2 \leftrightarrows 2\ NH_3$ is, between Herr Nernst and ourselves, controversial.”⁵⁷ He was also candid in regards to the quality of the measurements. “The result of these determinations,” Haber continued,

…shows that Nernst’s objection is not justified; the values determined [in our current study] under [30 atm] pressure completely confirm our earlier conclusions. The results of the experiments carried out and reported last year by Herr Nernst and his pupils [Jellinek and Jost] deviate from our findings to a degree that lies outside the margin of error. The values communicated by Herr Nernst have all been determined from the nitrogen-hydrogen side and lie below our values. We must conclude, therefore, that equilibrium was in no way reached during these experiments. The numbers communicated by Herr Nernst have a different trend than ours: they decrease faster with increasing temperature.⁵⁸

It was the same opinion Haber had expressed in Hamburg: Nernst had not properly determined the equilibrium position because he had only performed generation experiments (with a platinum catalyst). Furthermore, after having constructed their own pressure oven, Haber and Le Rossignol suspected Nernst’s apparatus had not given accurate temperature readings at the point of ammonia production. Not only were the equilibrium positions different, there was also a deviation in the overall dependence of equilibrium with temperature, meaning it was not simply a systematic error. As for the catalyst, Le Rossignol had repeated previous experiments with platinum instead of iron and found little catalytic effect, strengthening the argument that Nernst’s generation experiments did not reflect equilibrium conditions (Krassa 1966). “We found out,” said Le Rossignol later, “that Nernst’s equilibrium was very bad (Jaenicke 1959).” Even porcelain shards (probably containing small amounts of iron) had a better catalytic effect than platinum (Haber and Rossignol 1908g). In a detailed account of erroneous sources of ammonia production, Haber and Le Rossignol also concluded that the commercially available nitrogen-hydrogen mixture used by Nernst and Jost contained a small amount of oxygen which turned to water and absorbed some of the ammonia during the experiment, possibly reducing the yield. After drying this commercially available gas mixture, they obtained the same results as with their own nitrogen and hydrogen from pre-dissociated ammonia.

Haber and Le Rossignol’s new experiments were performed at different temperatures and pressures (22.35–30 atm) with iron and manganese catalysts, and an approximately 1:3 mixture of nitrogen-to-hydrogen. As in 1907, the increased reproducibility in comparison with the 1905 study is apparent. Average values for the experiments, as given in 1908, are collected in Table 11.6 and shown in Fig. 11.11.

Table 11.6 Average values for ammonia equilibrium given by Haber and Le Rossignol in 1908 with a 1:3 N₂:H₂ mixture and iron and manganese catalysts (Haber and Rossignol 1908f) (black squares in Fig. 11.11). At 974 ^∘C minimum values are given due to high gas fluxes; the numbers in parentheses denote the consideration of higher values found at lower fluxes

The results were used to determine the constant in Eq. A.27, which differed from 1907 (Eq. 11.5) in a notable way: the heat of formation was set at 12,800 cal/mol:

$$\displaystyle \begin{aligned} logK_p=\frac{12800}{4.571\ T}-6.06 {} \end{aligned} $$

(11.10)

However, because this expression did not adequately represent all of the data from the previous study in 1907, Haber also considered an equation with an expression for Q from his 1905 book (Haber 1905b, pp. 202–205):

$$\displaystyle \begin{aligned} logK_p=\frac{2215}{T}-3.626\ log\ T + 3.07\cdot 10^{-4}\ T + 2.9\cdot 10^{-7}\ T^2 + 4.82 {} \end{aligned} $$

(11.11)

where the heat of formation of ammonia at room temperature was again set at12,000 cal/mol. These expressions are found as the solid line (Eq. 11.10) and the dashed line (Eq. 11.11) in Fig. 11.11. “With this study,” wrote Haber, “we hope to a certain degree to have brought the task of determining the equilibrium of ammonia, begun four years ago by Haber and van Oordt, to a conclusion.”⁵⁹

However, he still felt the need to rationalize the misinterpretation of his 1905 data and the equilibrium value that had been too high. Haber had done the same at the Bunsen Society meeting where Nernst was set on considering both Haber’s 1905 and 1907 measurements instead of, as Haber would have preferred, only the 1907 results. It was part of Haber’s trend of defending himself against any attack, even after the third set of experiments at high pressures had confirmed his earlier results. He was still wary of Nernst. In December of 1907, he sent Richard Abegg a copy of the manuscript of the 1908 paper and wrote, after clarifying the results (Haber 1907b):

Nernst’s values are, therefore, shown to be incorrect. Because in this publication I have to counter Nernst, whose sensitivity is known, I ask you as an unbiased expert and friend to read the…manuscript and alert me to parts which seem in any way harsh so that I can change them.⁶⁰

This passage is at the end of the letter following scientific commentary on one of Haber’s favorite topics: dilute solutions. Haber did not go into scientific detail on the subject of ammonia and instead restricted his comments to the political developments with Nernst. At this point in his investigations, his interest in ammonia synthesis (if only with regards to industrialization) had grown since 1903, and the lack of correspondence on the subject may be due to the confidence in his 1907 and forthcoming 1908 results. A lengthy quote from the end of the 1908 paper illustrates this attitude and also summarizes the narrative up to this point. “With regards to the fact,” wrote Haber,

that [before the first measurements] there was absolutely no knowledge about the equilibrium position [of ammonia], one will recognize that the order of magnitude of the values [calculated with Eq. 11.2] is correct,⁶¹ and that the numbers were only used to justify two conclusions which are important and undisputedly correct. [These are] namely, “that from the beginning of red-heat onward no catalyst can produce more than traces of ammonia with the most favorable gas mixture if one works at normal pressure”, and “even with very high pressure the equilibrium position still remains unfavorable” […] The accuracy of the determinations of the position of equilibrium has gained a whole new importance through the theoretical developments of Herr Nernst. Uncertainties in the [initial] experiments…seem now to be unacceptable […] [We will] in no way deny that the remaining difference [between Haber’s measurements and Nernst’s heat theorem] can be reduced through new investigations of the heat data which may result in a change in the calculated values according to Nernst’s work. But we must absolutely counter the attempt to attribute the remaining difference to a deficiency in our experimental determinations as well as the underlying reason [which was] the experimentally oriented statement by Herr Nernst [to measure] the position of equilibrium [under pressure].⁶²

Nernst’s suggestion at the Bunsen Society meeting had not been necessary, though that only became clear after the fact. Fritz Haber’s commentary, on the other hand, proved pertinent. He identified the reason for Nernst’s lower experimental values—the measurements had only been made during ammonia production experiments—and offered a reason why Nernst’s calculations nevertheless supported those experiments. It was due to uncertainties in thermal data. While both men still agreed the equilibrium position of ammonia was unfavorable (even at high pressures), it was only in public. Nernst had long since begun his relationship with Griesheim-Elektron. According to Le Rossignol’s later account, it was the 1908 publication that prompted Haber and him to design an apparatus to continuously produce ammonia. The extrapolation of their data indicated an 8% ammonia yield at ∼600^∘ and, although it pushed technological limits, a pressure of ∼200 atm (Rossignol 1928), (Coates 1937, p. 1652).

In July, Jost published a letter responding to Haber and Le Rossignol’s experiments under pressure (Jost 1908b). There were points of methodological criticism, including the assertion that Haber and Le Rossignol’s assessment of the temperature was inaccurate. Mainly, though, it was a discussion of the discrepancies between their results, especially at higher temperatures. Jost did his best to draw them into agreement while noting, “there can be no discussion of a difference between Herr Haber and Herr Nernst, but rather only of such [a difference] between Herr Haber and me.”⁶³ Whether Jost was trying to protect Nernst from criticism or whether he wished to distinguish himself from the senior scientist is not clear, especially considering Nernst himself had not pulled back from the debate. Either way, Jost’s breadth of knowledge on the subject of ammonia synthesis is evident in his two publications from 1908 and shows that he was an independent researcher. At the end of the article, Jost suggested additional high temperature measurements as a solution to the remaining disagreement, but Haber and Le Rossignol already had something else in mind. An experimental and theoretical consensus was no longer the only objective.