The Development of Dalton's Atomic Theory As a Case Study in The

Sci & Educ (2010) 19:75–90 DOI 10.1007/s11191-008-9182-2

The Development of Dalton’s Atomic Theory as a Case Study in the History of Science: Reﬂections for Educators in Chemistry

He´lio Elael Bonini Viana Æ Paulo Alves Porto

Published online: 4 February 2009 Springer Science+Business Media B.V. 2009

Abstract The inclusion of the history of science in science curricula—and specially, in the curricula of science teachers—is a trend that has been followed in several countries. The reasons advanced for the study of the history of science are manifold. This paper presents a case study in the history of chemistry, on the early developments of John Dalton’s atomic theory. Based on the case study, several questions that are worth discussing in educational contexts are pointed out. It is argued that the kind of history of science that was made in the ﬁrst decades of the twentieth century (encyclopaedic, continuist, essentially anachronistic) is not appropriate for the development of the competences that are expected from the students of sciences in the present. Science teaching for current days will beneﬁt from the approach that may be termed the ‘‘new historiography of science’’.

1 Introduction

The inclusion of the history of science in science curricula is a trend that has been followed in several countries. In some countries, it has been recommended for decades; in other countries, the discussion is more recent. Without intending to give a complete review of such proposals, we would like to illustrate this point with three examples. In the United Kingdom, one can ﬁnd an early exhortation in favour of the historical approach to science teaching, made by the Duke of Argyll before the members of the British Association for the Advancement of Science. In his 1855 presidential address, he stated: ‘‘what we want in the teaching of the young, is, not so much mere results, as the methods and above all, the history of science’’ (Jenkins 1990, p. 274). According to

H. E. B. Viana Á P. A. Porto (&) Instituto de Quı´mica, Universidade de Sa˜o Paulo, Av. Prof. Lineu Prestes, 748 B 7 Sup, Sa˜o Paulo, SP 05508-900, Brazil e-mail: [email protected] H. E. B. Viana e-mail: [email protected] 123 76 H. E. B. Viana, P. A. Porto

Matthews, this claim has been scarcely followed—although there is a minority tradition of including the history of science in science education in the United Kingdom (Matthews 1994, p. 49). More recently (1988), the National Curriculum Council (NCC) recommended that part of the school science curriculum should be dedicated to the history and philosophy of science (NCC 1988). In the United States, the history of science has been included in science education projects for a long time. Maybe one of the most well-known of such materials is the series entitled, Harvard Case Histories in Experimental Science, edited by J. B. Conant (1957). However, the ‘‘post-Sputnik’’ science teaching projects of the 1960s—designed to help students grasp the theoretical basis of the natural sciences—hardly included historical aspects. In more recent years, documents such as the American Chemical Society guidelines for undergraduate education in chemistry recommended the historical approach—but, again according to Matthews, the guidelines are ‘‘more often ignored than followed’’ (Matthews 1994, p. 57). As a last example, let us consider the case of Denmark. Following a national educational reform in the late 1980s, a new physics curriculum was proposed. Its goal was to present physics as a human activity, instead of focusing on the contents of physics. To accomplish that, the history and philosophy of science approach was suggested (Nielsen and Thomsen 1990). The reasons advanced for the inclusion of the history of science in science education are manifold, as suggested by authors such as Matthews (1994) and Cachapuz et al. (2005), among others. In summary, these reasons include: (a) a historical approach can present science as a human enterprise, relating it to ethical, political and social aspects; (b) history of science can contribute to meaningful learning, by relating scientific concepts to other aspects of students’ knowledge; (c) it can make lessons more interesting and reflective, by stimulating critical thought; (d) it can improve teacher education, by enriching their epistemological views; (e) it can help teachers to understand the learning difficulties of the students; (f) it can help teachers to reflect over educational matters, by means of a more complex epistemological approach. It is the purpose of this paper to present a case study in the history of chemistry designed to be used in the context of chemistry teaching. The case study is presented here to show some points that should be discussed in the initial or in-service education of chemistry teachers. We argue that the kind of history of science that was available in the first decades of the twentieth century is not appropriate for the development of the competencies that are expected from science students in the present, and science teachers need to be aware of that. Science teaching will benefit from the approach that may be termed, the new historiography of science, in order to meet the challenges posed by current educational guidelines.

2 The New Historiography of Science

Until recently, the main approach to the history of science was based upon an encyclopaedic, continuist and cumulative model. It was an essentially anachronistic model, for it looked to the past with the eyes of the present: historians searched for ‘‘red lines’’ that led from past concepts to present-day concepts, and for the ‘‘precursors’’ of the ideas established in current science. Moreover, much of the history of science was written under an internalist perspective. This historiographical approach might have been appropriate for a more ‘‘dogmatic’’ science teaching approach, concerned only with the transmission of content; or in science teaching projects designed to emulate the so-called idealized 123 The Development of Dalton’s Atomic Theory 77

‘‘scientific method’’ that did not reflect what really happens in research laboratories. However, this kind of historiography does not fulfil the requirements of present science teaching demands. If our goal is to develop in our students the ability to approach scientific knowledge in a critical way, and to understand the complexity of the process of making science, then the new historiography of science may have much to offer. The contemporary approach of historians of science is marked by the well-delimited and profound analysis of case studies, aimed at the characterization of specific episodes and documents. Another aim is to contextualize the ideas of the past, in search of their meaning within the peculiar scientific thinking of the period under analysis. By doing so, it is possible to identify different, superimposed levels of continuities and ruptures with former ideas, as well as the peculiarities of the interpretations of the same sources that contributed to the development of a certain scientific work. Moreover, it is necessary to consider the influences that do not belong to the strict domain of science, such as psychological and social influences. By following such an approach, the relationship between the case studies and the broader context of the history of science acquires new meanings, which help to make a more detailed picture of the complexity of the scientific enterprise over time (Alfonso-Goldfarb and Beltran 2004; Debus 1984). This new historiography of science has also been influenced by developments in philosophy of science itself, after the works of Popper, Hanson, Polanyi, Kuhn, Feyerabend, Lakatos, Laudan and others. Considering this, we believe that the use of case histories—developed according to the new historiography of science—should be part of the training of science teachers. This would enable them to critically assess didactic materials related to the history of science, and use them to develop the desired abilities among their students. When one considers a case study, one can find several points that may be discussed with pre-service teachers, or with students, that can be helpful for two main purposes: the construction of a complex view of the scientific activity; and the construction of scientific concepts. In this paper, we take the development of Dalton’s atomic theory as an example. Atomic theory is an important part of chemistry education, and as such it has been an object of concern for chemistry educators. Niaz (2001), for example, presented some questions that were the subject of debate in the early years of Dalton’s atomic theory. Starting from historical and epistemological questions, Niaz went on to discuss if the teaching of the laws of definite and multiple proportions is really necessary in present curricula. In another paper, Rodrı´guez and Niaz (2002) detail the lack of an historical approach to the development of atomic theories in chemistry textbooks. We agree with Niaz and Rodrı´guez that aspects of the history of science should be presented to students— not to ‘‘indoctrinate’’ them in a naive version of inductivism, but rather to challenge such a view. We also agree with Brush (1978), when he argued that: Chemical education should be revised to take account of the improved conception of the nature of chemistry that emerges from a study of its history. If we really believe that Lavoisier and Dalton were great chemists, we should be able to live with a more accurate account of how they made their discoveries… (Brush 1978, p. 290). In the present paper, we follow Brush’s suggestion of taking the work of Dalton as an example of the complexity of the process of developing scientific knowledge that may be discussed in science education. Or, as Chalmers put it, ‘‘exploring this piece of the history of science [i.e., the history of atomism] is an especially instructive one if the aim is to capture distinctive features of science, and its distinction from, for example, philosophy’’ (Chalmers 1998, p. 82).

123 78 H. E. B. Viana, P. A. Porto

In this paper, we will briefly present some aspects of the process that led Dalton to the formulation of his atomic theory. It was a long process, and it would not be possible to deal with all the details and controversies in one paper. Thus, we will focus on Dalton early theories and the emergence of the concept of atomic weight and its determination, up to the publication of the first part of his book, A New System of Chemical Philosophy (1808; reprint, 1964). The choice of such an approach may be justified given that the atomic weights were Dalton’s most original contribution to modern chemistry. In the sequel to the case study, we will call attention to some points that are worth discussing in didactic contexts.

3 The Case Study—the Development of Dalton’s Atomic Theory

John Dalton1 (1766–1844) was born in Eaglesville, and was educated as a member of the Society of Friends (protestant sect founded in the middle of the seventeenth century, whose adepts became known as Quakers). At the early age of twelve, Dalton started to teach mathematics, under the influence of his teacher Elihu Robinson—a Quaker interested in natural philosophy and meteorology. Dalton never had a formal education in chemistry, but it was probably at this point that he had his first contact with popular books on Newton- ianism from which he began to build his scientific ideas. In 1780, Dalton moved to Kendal, where he became a teacher in a Quaker school and delivered lectures on science for the general public. In Kendal he acquired the habit of keeping records of meteorological phenomena—a habit that he would keep for his entire life. Dalton settled in Manchester in 1793, to teach mathematics and natural philosophy. In the same year he published his first book, Meteorological Observations and Essays, about his researches on the atmosphere. Dalton’s interest in meteorology eventually led him to a series of related questions. At the end of the eighteenth century, the composition of the atmosphere (mainly, nitrogen, oxygen, carbon dioxide and water vapour—to use current nomenclature) had been already determined. However, there was a debate among natural philosophers as to whether the gases in the atmosphere were chemically combined, or only mechanically mixed. Moreover, if one assumed that the atmosphere was a mixture and not a compound, it was not clear to the researchers of that time why the gases did not separate in layers according to their densities. Dalton was interested in this question, and performed experiments to investigate it. From these early studies on the composition of the atmosphere, Dalton started to develop his atomic theory. Dalton approached the problem using corpuscular ideas derived from his Newtonian background. According to Isaac Newton (1642–1727), matter was constituted of several types of particles hierarchically organized. The smaller ones were called ultimate particles; the juxtaposition of these gave origin to the first composition particles, which were responsible for the macroscopic properties of bodies. This conception was influenced by the works of Robert Boyle (1626–1691), in which are combined aspects of ancient atomism (the idea that matter is made of indivisible particles, the atoms), as well as the Aristotelian theory about minima naturalia (small parts of matter that keep the properties of the bulk). The result was a corpuscular theory with peculiar characteristics. Based on Boyle’s ideas, Newton tried to use his own ‘‘universal laws’’ for the movement and interactions among particles to explain phenomena such as the behaviour of gases. For example, in Proposition 23, Section V, Book II of Principia, Newton suggested an

1 Data on the biography and work of Dalton may be found in: Thackray (1972), Partington (1962), Lappert and Murrell (2003). 123 The Development of Dalton’s Atomic Theory 79 explanation for ‘‘Boyle’s Law’’ based on the repulsion of particles, according to a force that would decrease with the square of the distance between them: [P]articles flying each other, with forces that are reciprocally proportional to the distances of their centres, [will] compose an elastic fluid, whose density is as the compression [i.e., the fluid will obey Boyle’s Law] (Newton 1848, p. 301). For Newton, however, these ideas were a preliminary hypothesis, and philosophers of Nature would still have to prove if this hypothesis was true or false. Immersed in this English tradition of corpuscular theories, Dalton was bound to relate them to the new ideas developed by chemists in the last decades of the eighteenth century.

4 The First Theory of Mixed Gases and the Law of Partial Pressures

In Newton’s time, it was supposed, by the majority of natural philosophers, that there was only one gaseous fluid, common air, taken as an element due to its homogeneity. This view changed during the eighteenth century with a series of studies done by the ‘‘pneumatic chemists’’ who suggested that the atmosphere was formed of several kinds of ‘‘airs’’. As a consequence, new models to explain such diversity became necessary (Thackray 1970). As mentioned above, at the end of the eighteenth century, Dalton was investigating the composition of the atmosphere. His results, together with data from other researchers, suggested that atmospheric gases were mixed, and not chemically combined. He then developed an explanation for the fact that the atmosphere is homogeneous, with no sep- aration in layers of different gases. It was ‘‘an elegant variation on the Newtonian model’’ (Fleming 1974, p. 563), derived from a free interpretation of Question 31 of Opticks2 and the abovementioned Proposition 23 of Principia: in a mixture, each gas behaved as a Newtonian elastic fluid, acting as if the other gases were not present in the container. In Dalton’s words: When two elastic fluids, denoted by A and B, are mixed together, there is no mutual repulsion amongst their particles; that is, the particles of A do not repel those of B, as they do one another (Dalton 1802, p. 540). In short, this is the core of what may be termed Dalton’s ‘‘first theory of mixed gases’’. Dalton observed that, when different gases were mixed in a closed vessel, the total pressure was equal to the sum of the pressures of the different gases taken individually. This fact is now known as ‘‘Dalton’s law of partial pressures’’. With the model expressed by his ‘‘first theory of mixed gases’’, one could explain such behaviour. If one admits that the particles of a pure gas repel each other, they will distribute homogeneously in a given vessel; if another gas is then mixed with the former, and no interaction occurs between particles of different gases, this second gas will also become homogeneously distributed—and the total pressure will be as described by ‘‘Dalton’s law’’. The theory, however, was not free from criticism: even John Gough, former teacher of Dalton in Kendal, criticized its principles as being aleatory. On the other hand, William Henry (1774–1836) found Dalton’s theory very enlightening.

2 ‘‘[I]t seems probable to me that God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles, of such sizes and ﬁgures, and with such other properties… even so very hard, as never to wear or break in pieces… [C]hanges of corporeal things are to be placed only in the various separations and new associations and motions of these permanent particles…’’ (Newton 1730, pp. 375–376). 123 80 H. E. B. Viana, P. A. Porto

5 Dalton, Henry, and the Solubility of Gases in Water

In Dalton’s first theory, equal atoms—that is, atoms of the same substance—repelled each other; but there were no interaction between atoms of different substances. When Dalton published his theory, Henry was dealing with a series of experiments on the solubility of carbonic gas in water. Henry was acquainted with many studies on gases, and he had a special reason for that: his family owned a factory that produced, among other things, magnesia alba3 and Pyrmont’s artificial water.4 Henry also taught the ‘‘new chemistry’’, using Lavoisier’s Elements of Chemistry as the textbook. Around 1802/1803, both Henry and Dalton were studying the solubility of gases in water. By measuring the solubility of carbonic gas in water, Henry observed a great variation in the amounts of that gas that were absorbed by water, under conditions in which pressure and temperature were kept the same. Henry did not find the cause of such behaviour, but Dalton found what the problem was: Of the cause of these variations I was not aware, till my friend Mr. Dalton suggested, that they probably depended on the variable amount of the residues of undissolved gas; and on repeating the experiments, with different proportions between the gas and the water, this suggestion was fully confirmed (Henry 1803). If the gas used by Henry was pure enough, the variations would not be observed. However, due to the techniques available, all samples contained residues of air. Thus, the solubility of carbonic gas could be determined only after the analysis of the mixed gases and the use of Dalton’s law of partial pressures. Henry, who at first did not accept Dalton’s first theory of mixed gases, then recognized that it was a good explanation for his observations. On this matter, Dalton wrote: … Dr. Henry became convinced, that there was no system of elastic fluids which gave so simple, easy and intelligible a solution of them, as the one I adopt, namely, that each gas in any mixture exercises a distinct pressure, which continues the same if the other gases are withdrawn (Dalton 1964, p. 141). Henry’s researches included around 50 different gases, and led him to the conclusion that, at a given temperature, the mass of the gas that is absorbed by water is directly proportional to its partial pressure—which is now known as ‘‘Henry’s Law’’.

6 The Solubility of Gases and the First Table of Atomic Weights

The successful explanation of Henry’s results encouraged Dalton to continue his studies of the solubility of gases in water, and to elaborate further his atomic model. After observing that different gases had different solubilities in water, Dalton speculated as to whether the differences were related to the weights of the atoms that constituted the gases. In a paper read before the Manchester Literary and Philosophical Society in October 1803 but printed only in 1805, under the title ‘‘On the absorption of gases by water and other liquids’’, Dalton presented his ideas on the solubility of gases. Here, he tried to classify different gases according to their solubility fractions, following an ingenious mathematical relation:

3 Magnesia alba was the name given to a substance then used as an antacid medicine, and it corresponds to what is called magnesium carbonate today. 4 An artiﬁcially carbonated mineral water. 123 The Development of Dalton’s Atomic Theory 81

If a quantity of water thus freed from air be agitated in any kind of gas, not chemically uniting with water, it will absorb its bulk of the gas, or otherwise a part of it equal to some one of the following fractions, namely, 1/8, 1/27, 1/64, 1/125, &c. these being the cubes of the reciprocals of the natural numbers 1, 2, 3, &c. or 1/1, 1/ 23, 1/33, 1/43, &c. the same gas always being absorbed in the same proportion, as exhibited in the following table:

Bulk absorbed, the bulk of water being unity

1/13 = 1 Carbonic acid gas, sulphuretted hydrogen, nitrous oxide 1/23 = 1/8 Oleﬁant gas, of the Dutch chemists 1/33 = 1/27 Oxygenous gas, nitrous gas, carburetted hydrogen gas, from stagnant water 1/43 = 1/64 Azotic gas, hydrogenous gas, carbonic oxide 1/53 = 1/125 None discovered (Dalton 1805)5

In order to explain the different solubility values, Dalton speculated as to whether the different masses of the atoms were the cause of these variations: The greatest difficulty attending the mechanical hypothesis, arises from the different gases observing different laws. Why does water not admit its bulk of every kind of gas alike? This question I have duly considered, and though I am not able yet to satisfy myself completely, I am nearly persuaded that the circumstance depends upon the weight and number of the ultimate particles of the several gases: those whose particles are lightest and single being least absorbable, and the others more according as they increase in weight and complexity [Footnote: Subsequent experience renders this conjecture less probable]. An enquiry into the relative weights of the ultimate particles of bodies is a subject, as far as I know, entirely new: I have lately been prosecuting this enquiry with remarkable success. The principle cannot be entered upon in this paper; but I shall just subjoin the results, as far as they appear to be ascertained by my experiments (Dalton 1805). In the sequel of this quotation, the paper presented, for the first time in printed form,6 a table of relative atomic weights. The method used to obtain the figures was not explained in the paper, but it was based on data about the elementary composition of substances (as will be presented further in this paper). Several data were available in the literature, such as the weights of the elements involved in the composition of water, ammonia, carbonic gas, etc. (Nash 1956, pp. 111–112). It is curious to note that, in the text, Dalton speculated on the relative atomic weights as the cause of the different solubilities; but, in the footnote, he changed his mind due to experimental results obtained after the original text was written.

5 As the modern reader may have observed, the numerical relations proposed by Dalton here have no meaning in the rationale of current chemistry. One can relate the names of the gases mentioned by Dalton with current names as follows: carbonic acid gas = carbon dioxide; sulphuretted hydrogen = hydrogen sulphide; nitrous oxide = dinitrogen monoxide; olefiant gas = ethene; oxygenous gas = oxygen; nitrous gas = mononitrogen monoxide; carburetted hydrogen gas = methane; azotic gas = nitrogen; hydrogenous gas = hydrogen; carbonic oxide = carbon monoxide 6 One can find the figures of the first relative atomic weights calculated by Dalton in his extant notebook dated 1803. 123 82 H. E. B. Viana, P. A. Porto

To understand this, one must remember that the paper was presented in 1803, but published in the Memoirs of the Literary and Philosophical Society of Manchester in 1805. Dalton had no problem in changing the text in the meantime, since he was the editor of the Memoirs—and thus he could choose which articles would be published, and when they would be published. According to Leonard Nash (1956), Dalton’s development of a quantitative atomic theory was directly linked to the problem of the solubility of gases. However, as Theron Cole Jr. (1978) pointed out, the extant evidences are not decisive about this point. Cole Jr. suggests, in turn, that the solubility problem was one of the ﬁrst applications that Dalton found for his concept of relative atomic weights, which was developed at the same time but not as a consequence of the solubility problem.

7 The Rule of Greatest Simplicity

To calculate the relative atomic weights, Dalton had to develop a model capable of explaining chemical combinations, and which also allowed the determination of formulas for the compounds. Considering his first theory of mixed gases, Dalton proposed an explanation for chemical combinations that may be exemplified by the case of an oxygen–hydrogen mixture. There was repulsion among oxygen atoms, as well as among hydrogen atoms— which resulted in an equilibrium situation for this gaseous mixture. In this situation, although there was an affinity between oxygen and hydrogen atoms, they could not combine with each other, and the system stayed as a mechanical mixture of the two gases. However, if some- thing broke such an equilibrium, a transformation could take place, as the ‘‘powerof affinity’’ would lead one atom of oxygen to unite with one atom of hydrogen. In Dalton’s words: Heat, or some other power prevents the union of the two elements, till by an electric spark, or some other stimulus, the equilibrium is disturbed, when the power of affinity is enabled to overcome the obstacles to its efficiency, and a chemical union of the elementary particles of hidrogen and oxigen ensues (Dalton 1811, p. 145). Dalton did not give many details about this ‘‘power of affinity’’, that would be the key to understanding the cause of chemical combinations. Dalton tried to explain how atoms combined with each other, even if the cause remained obscure. In the example just mentioned, consider that, before the combination, there were more atoms of oxygen than of hydrogen. It follows that, after the combination between oxygen and hydrogen, there were a mixture of water vapour and oxygen. If a further combination were possible, the ‘‘atoms of water’’7 and the atoms of oxygen would then group in pairs. In Dalton’s model, combinations took place in 1:1 sequence—according to the so-called ‘‘rule of greatest simplicity’’. Thus, several combinations were possible, which would follow what Dalton named the law of multiple proportions:

1 atom of A ? 1 atom of B = 1 atom of C, binary. 1 atom of A ? 2 atoms of B = 1 atom of D, ternary. 2 atoms of A ? 1 atom of B = 1 atom of E, ternary. 1 atom of A ? 3 atoms of B = 1 atom of F, quaternary. 3 atoms of A ? 1 atom of B = 1 atom of G, quaternary.

7 For Dalton, particles made of more than one atom were called ‘‘compound atoms’’—as was the case for water. 123 The Development of Dalton’s Atomic Theory 83

&c. &c. (…) 1st. When only one combination of two bodies can be obtained, it must be presumed to be a binary one, unless some cause appear to the contrary. 2nd. When two combinations are observed, they must be presumed to be a binary and a ternary. 3rd. When three combinations are obtained, we may expect one to be a binary, and the other two ternary. 4th. When four combinations are observed, we should expect one binary, two ternary, and one quaternary, etc. (…) 7th. The above rules and observations equally apply, when two bodies, such as C and D, D and E, etc., are combined (Dalton 1964, pp. 163, 167).

The number of atoms combined in the compound particles resulted in several kinds of geometrical disposition, which the atoms would assume to minimize the repulsive forces among equal ones: When an element A has an affinity for another B, I see no mechanical reason why it should not take as many atoms of B as are presented to it, and can possibly come in contact with it… except so far as the repulsion of B among themselves are more than a match for the attraction of an atom of A (Dalton 1811, p. 147). Thus, one ‘‘compound atom’’, made of four atoms, would present a trigonal structure, with three atoms disposed at angles of 120 around a central atom. If the ‘‘compound atom’’ had five atoms, then the structure would be of a square, with four atoms disposed at angles of 90 around a central atom. Here, Dalton offered a theoretical justification for the rule of greatest simplicity.

8 The Determination of Relative Atomic Weights

Besides the mechanism for the proposition of formulas for the ‘‘compound atoms’’ that resulted from chemical transformations, the determination of relative atomic weights required also the use of the weights of the substances involved in the combination. Some of the values used by Dalton were already known: he took them from papers published by other authors. It is important to note that Dalton’s work was possible within an environ- ment in which chemistry started to become a quantitative science, beginning with Lavoisier’s emphasis on conservation of mass as a fundamental principle, followed by the stoichiometric program developed from the end of the eighteenth century. With the values of weights involved in chemical combinations, and taking into account the rule of greatest simplicity as a guide for the proposition of formulas, Dalton established a bridge between the macroscopic and the microscopic worlds, in the form of relative atomic weights. By analyzing, for instance, the proportions by weight found by Lavoisier for water, one could see that in water there was 15 g of hydrogen for 85 g of oxygen, that is, 1 g of hydrogen for 5.66 g of oxygen.8 According to the rule of greatest simplicity, one atom of oxygen would unite with one atom of hydrogen to produce one ‘‘compound atom’’ of water. Since hydrogen was always the element that took part in the reactions with the smaller proportion in weight among all, Dalton considered that it should be the standard to which the other atoms should be compared, and attributed the value one to the relative

8 These were the first values used by Dalton; later more accurate determinations resulted in different figures. 123 84 H. E. B. Viana, P. A. Porto atomic weight of hydrogen. Thus, one atom of oxygen should have a relative atomic weight equal to 5.66 (meaning that one atom of oxygen is 5.66 heavier than one atom of hydrogen). By following the same rationale, and taking the composition of ammonia determined by Austin (20% of hydrogen and 80% of nitrogen by weight, that is, 1 g of hydrogen for 4 g of nitrogen), Dalton arrived at a relative atomic weight of four for nitrogen. These examples may suffice to show how the relative atomic weights of other elements and compounds were determined. From the relative atomic weights of nitrogen and oxygen, Dalton explained the proportions by weight involved in the synthesis of the several nitrogen oxides, using the rationale of the law of multiple proportions (Dalton 1810). Table 1 shows the elementary percentage, by weight, for different oxides of nitrogen. Considering the figures in the table, one can see that, according to Dalton, nitrous gas resulted from the combination of 42.1 g of nitrogen and 57.9 g of oxygen. As mentioned above, the relative atomic weights of nitrogen and oxygen were, respectively, 4 and 5.66. Thus, the proportion of atoms involved in the synthesis of nitrous gas was (42.1/4) of nitrogen to (57.9/5.66) of oxygen—that is, approximately 1:1 (the figures are not exact due to experimental error in the determination of weights). In other words, this compound was formed when one atom of nitrogen combined with one atom of oxygen—following the rule of greatest simplicity. Using the same approach for the other two compounds in Table 1, one may conclude that nitrous oxide was formed by two atoms of nitrogen and one atom of oxygen, and that nitric acid gas resulted from the combination of one atom of nitrogen with two atoms of oxygen. One can clearly see a practical application of the law of multiple proportions. In 1804, Dalton reported that two hydrocarbons also obeyed the law of multiple proportions: carburetted hydrogen gas—nowadays called ‘‘methane’’—was formed by one atom of carbon and two of hydrogen; and olefiant gas—currently called ‘‘ethene’’—was formed by one atom of carbon and one atom of hydrogen. In 1808, William Hyde Wollaston (1766–1828) also reported that many of his results—about analyses of the salts obtained in neutralization reactions—could be explained by using the law proposed by Dalton.

9 Further Developments of Dalton’s Theory

Dalton was interested in the parts of his theory that were being subjected to criticism. In his ﬁrst theory of mixed gases, he stated that equal atoms repelled each other, but he was not sure about which were the forces involved in such repulsion. In the limit, one would have to assume that there were as many repulsive forces as were different kinds of atoms—an obvious weakness of the theory. Moreover, Dalton had problems in explaining how atoms

Table 1 Dalton’s ﬁgures for the composition of three different oxides of nitrogen Nitrogen Oxygen (%, by weight) (%, by weight)

Nitrous gas 42.1 57.9 Nitrous oxide 62 38 Nitric acid gas 26.7 73.3

As the discussion in the text shows, the compounds, in modern notation, are NO (nitrogen monoxide), N2O (dinitrogen monoxide) and NO2 (nitrogen dioxide), respectively, (Viana 2007, p. 51) 123 The Development of Dalton’s Atomic Theory 85 interact in chemical changes. The main problem, in fact, was related to the concepts of mixture and combination, that was the subject of a contemporary debate between Claude L. Berthollet (1748–1822) and Joseph L. Proust (1754–1826)—in which Dalton took the side of Proust, since the idea of definite composition agreed with Dalton’s view of a definite number of atoms involved in the constitution of a compound. Around 1804/1805, Dalton developed his second theory of mixed gases, identifying heat as the universal force of repulsion between atoms. He created a model in which each atom was surrounded by an ‘‘atmosphere’’ of heat (identified with caloric), whose size was characteristic of the atom. It meant that the bigger the specific heat of the substance, the bigger its atoms. The difference in the sizes of the ‘‘atmospheres’’ of caloric was, according to Dalton, the cause of the repulsion between equal atoms and of the lack of interaction between different atoms. ‘‘Atmospheres’’ of equal atoms fit exactly, keeping them apart. On the other hand, if the ‘‘atmospheres’’ of caloric had different sizes, they would not fit, and could permeate each other—resulting in the mixture of the two different gases. In a chemical combination, some kind of ‘‘power’’ had to interfere with the established balance, allowing the chemical affinity to prevail thus giving rise to a new ‘‘compound atom’’. This was formed by the union of two (or more) of the former atoms (of different kinds), that after the combination would became surrounded by a new ‘‘atmosphere’’ of caloric, whose size would not be the sum of the two previous ones, but would be of a different size, characteristic of the formed substance. As the modern reader may have already noticed, Dalton’s speculations on the size of the atoms did not play a significant role in the eventual development of chemistry. The first published account of Dalton’s atomic theory, showing how to determine the relative atomic weights, was in a book by Thomas Thomson, dated 1807. Dalton’s own book, A New System of Chemical Philosophy, appeared in the following year. The theory was subjected to criticism, but also received support from Thomson, Wollaston, and others. In addition Dalton rejected J. L. Gay-Lussac’s (1778–1850) observations on the combining volumes of gases. Gay-Lussac showed, in 1809, that the volumes of gases involved in chemical reactions (if measured under the same conditions of pressure and temperature) obeyed simple, integer-number relations (e.g., 1 volume of nitrogen reacts completely with 1 volume of oxygen to yield 2 volumes of nitrous gas). Such results would seem favourable to Dalton’s atomic theory at first sight, if one admitted that equal volumes of different gases contained equal numbers of atoms. Dalton, however, could not admit such a hypothesis, for it was not compatible with some aspects of his theory (in the abovementioned example, it would not be possible to explain why the proportion was 1 nitrogen:1 oxygen:2 nitrous gas, if one admitted, with Dalton, that the particles were, respectively, . There were other problems, related to the size of the atoms of different elements, which will not be discussed here. See Conant 1957, vol. 1, pp. 250–275). Many chemists, throughout the whole nineteenth century, preferred to work with measurable quantities of ‘‘equivalent weights’’ or ‘‘volumes’’—without using the theoretical concept of the atom (Rocke 1984; Niaz 2001, pp. 246–247). The atomic theory was bound to remain an object of debate for decades after Dalton.

10 Reﬂections on the Case Study

The case study presented above reveals that the construction of Dalton’s atomic theory was a complex process, and it is a good example of how scientific knowledge has been 123 86 H. E. B. Viana, P. A. Porto constructed in the past. This case study presents, besides the interest in the history of science itself, the opportunity for chemistry educators to consider some important points. Science teachers must be aware of the richness of the possibilities for discussion that a case study offers. So, science teachers have to be presented with case studies and have to be prepared to discuss them with the students. In this section, we suggest some points that may be important for the teacher to consider when preparing historically-based classes that are appropriate for his/her specific situation. The case study reveals different aspects and dimensions of the scientific endeavour: the intellectual process of constructing scientific concepts, the nature of scientific knowledge, and even sociological aspects of science. To understand why and how Dalton proposed his atomic theory, one has to consider the context of his work. Dalton was strongly influenced by eighteenth century Newtonianism, and he dealt with the scientific questions of his time, such as the composition of the atmosphere and the difference between chemical combination and ‘‘mechanical’’ mixture in terms of Newtonianism. Dalton’s first theory of mixed gases was an ingenious elaboration of Newtonian corpuscularism—a paradigm in which Dalton had been working for years. This first theory was based on his peculiar if not incorrect interpretation of two points of Newton’s works (Rocke 2005).9 Dalton started with meteorological concerns, proposed a model for the behaviour of gases, and this research line finally led him to the quantification of the atoms. If one follows the case study, one can see that Dalton’s works make a coherent whole. Two parts of Dalton’s work are usually studied quite independently in science courses: the law of partial pressures and the atomic theory. In general, chemistry textbooks present the law of partial pressures in a chapter on gases, and the atomic theory in a chapter on the development of ideas on the structure of matter. However, there was a strong connection linking these ideas. Dalton arrived at his law of partial pressures while he was studying the composition of the atmosphere, and determining why different gases mix completely and do not separate in layers. He observed that water vapour could be mixed in any proportion with air, arrived at the law of partial pressures, and realized that a mechanical model from a Newtonian inspiration could explain that. Such a model was not free from the criticism of his contemporaries, and Dalton knew that it was not complete. He continued to explore the model, investigating further consequences and how well it could explain other observations. Dalton considered that if the mechanical model, expressed in his first theory of mixed gases, could explain the mixture of water vapour with air, it might also explain the mixture of different gases in water—conceived as the ‘‘reverse’’ situation. However, he observed that one cannot always dissolve the same quantity of different gases in a given amount of water: each gas has its own solubility. Based only on the repulsion of equal atoms, Dalton was not able to explain that. At this point, he conjectured using what was probably the first application of his quantitative atomic theory: maybe the different solubilities were due to different atomic weights. Dalton soon realized that this hypothesis was wrong, but he also realized that the determination of atomic weights had important consequences, and continued to work upon them.

9 According to Rocke (2005), Dalton considered that Newton ‘‘had demonstrated clearly’’ that ‘‘an elastic ﬂuid is constituted of small particles of atoms of matter, which repel each other’’—when Newton, in fact, just considered this as a hypothesis that could explain Boyle’s law. Moreover, Dalton considered that in his 31st ‘‘Query’’ of his Opticks, Newton admitted the existence of a considerable number of elementary principles—which Dalton associated with Lavoisier’s notion of elements. 123 The Development of Dalton’s Atomic Theory 87

Thus, by approaching the development of Dalton’s ideas by means of a case study, one can see that two aspects that are usually studied separately—the law of partial pressures and the quantitative atomic theory—were in fact parts of a coherent set of ideas. Each one of these subjects may be further explained by the teacher, depending on the teacher’s educational goals. In any case, by making explicit the connections between them in a historical approach, the teacher may help students develop an idea about the internal consistency of science, and even establish significant connections between concepts. The case study may also help to introduce other aspects of the nature of science. Dalton initially was dealing with meteorological matters and, in particular, he was trying to solve a problem, related to the composition of the atmosphere. Usually, scientific knowledge is not created as an end in itself, as many students think, but emerges from the search for the solution of a problem. In this case, the original subject—meteorology—may appear very distant conceptually from atomic weights for current students, showing that the development of scientific ideas is not a linear process, but sometimes leads to unexpected outcomes. As mentioned above, Dalton published his relative atomic weights for the first time in a paper on the solubility of gases in water, trying to explain the differences in the solubilities of different gases. However, this hypothesis was soon abandoned. One can see that a concept that fails to explain a specific phenomenon may be eventually elaborated, and applied in very different, and initially unexpected, contexts. Another evidence of the dynamic and complex character of science is that the ‘‘rule of greatest simplicity’’, which was essential for the early development of Dalton’s theory, was eventually abandoned. Nevertheless, the theory continued to be elaborated, based upon different concepts that were subsequently developed. Moreover, Dalton’s atomic theory was not universally accepted at once. If students are presented with the criticisms that a given scientific theory was subjected to at the time of its origin, they will be more likely to develop the idea that scientific theories are not capable of solving every related problem at once, but are subjected to elaboration throughout time. Students may also benefit from gaining some insight into sociological aspects of science. The idea that scientific knowledge is built within a given social context, and is strongly influenced by the interaction of people, may be discussed from this case study. One can see that the conversations between Dalton, Henry, and Thomson allowed them to exchange ideas, and mutually influenced their works. Also, in the determination of relative atomic weights, Dalton used not only his own results, but a great deal of data available in the scientific literature, published by other researchers. Such examples may help to present science as a collective enterprise: scientists interact via publications, and seek for vali- dation of their work by submitting their results to their peers’ scrutiny. Moreover, personal communications between scientists are very common features in the making of science. A curious aspect of this case is that Dalton did not have a formal training in chemistry, and so he was not influenced by ideas that were common among contemporary chemists. Rocke (2005, p. 130) suggested that this alternative perspective was very important for the proposition of the concept of relative atomic weights. One may take this as another instance in which the social interactions—or, better, the lack of interactions with a specific community of scientists—influenced the making of science. In this section, a few themes that emerged from the case study were suggested for reflection. How teachers will present and discuss them with students will depend on their educational goals and the peculiarities of each group of students.10 Based on the case

10 Very good examples of different strategies used in different educational levels are presented by Stinner et al. 2003. 123 88 H. E. B. Viana, P. A. Porto study, teachers may prepare didactic materials, select the better strategy to work with them (group discussions, written essays, concept maps, etc.), focusing on the aspects that they consider most relevant for their group of students.

11 Final Remarks

As part of another research project, a survey was conducted among chemistry undergraduate students, enrolled at the University of Saõ Paulo (Saõ Paulo, Brasil). A sample of 28 chemistry students answered, among others, the following question: ‘‘In your opinion, why was Dalton important in the history of chemistry?’’ In their answers, it was possible to identify a total of 30 statements in response to the question. Mention of an atomic model, or an atomic theory, was found in 43% of the answers, and another 13% of the statements were also considered adequate (e.g., Dalton proposed a law on the behaviour of gases). However, in 27% of the answers, students regarded Dalton as the ‘‘inventor of the atoms’’, or as the person who revived the idea of the atom, lost since the philosophers Democritus and Leucippus proposed it in Ancient Greece. Moreover, another 17% of the statements were vague or imprecise (e.g., Dalton proposed the ‘‘plum pudding’’ model for the atom; Dalton stated that molecules are made of atoms, etc). An important omission shall be noted: no students mentioned the creation of the concept of relative atomic weights (Cheloni et al. 2006). Although based on a small sample, we believe that this survey reveals an important point. In general, students have only a superficial contact with the history of science. In this case, they were acquainted with the name of Dalton, but have only a faint idea of what his work was about. The fact that Dalton’s quantitative atomic theory played a very important role in the development of chemistry in the nineteenth century seems to be easily accepted by chemical educators. However, given the superficiality of the approach to this subject in didactic contexts, students usually do not realize that the essential aspect, the core of Dalton’s atomic theory, is the development of the concept of relative atomic weights. It was an innovative concept, which established a dialogue between the macroscopic and the microscopic levels of matter—and was bound to influence the development of chemistry later in the nineteenth century. A more detailed approach—in the form of a case study— could generate new perspectives for chemical education (Viana 2007). The case study can give rise to discussions on the interrelation that was established between concepts in order to build a coherent structure, and on how scientific concepts are built. Concepts that students consider obscure (like relative atomic weights, the law of multiple proportions, Dalton’s law of partial pressures, Dalton’s atomic model) can be presented in context, by means of the case study, leading to the creation of meaningful relations between them in the students’ cognitive structures. Inappropriate ideas, such as the view of Dalton as the ‘‘creator of the concept of atom’’, or that he took the idea of ‘‘atom’’ directly from the works of Leucippus and Democritus in Ancient Greece, should be banished from chemical education. If students were familiar with the idea that corpuscular theories spread throughout Europe from the seventeenth century, they would be able to develop better conceptions about how scientific knowledge was elaborated, for in this case Dalton had a well-established background of corpuscular ideas. The case study can also show that Dalton’s theory was not a consequence of the ‘‘discovery’’ of the laws of chemical combination. This myth can be seen in high-school textbooks, and is an expression of an empiricist/inductivist conception of science, which also helps to perpetuate the idea that there is a one and only ‘‘scientific method’’. Current 123 The Development of Dalton’s Atomic Theory 89 trends in history and philosophy of science show that science is a complex activity: if we want students to understand that, this case study can serve as an example of such complexity. The use of historical case studies in science education is not novel: James B. Conant’s Harvard Case Histories in Experimental Science, for example, dates from the 1950s. One of the case histories, edited by Leonard Nash, is exactly about ‘‘The Atomic-Molecular Theory’’ (Conant 1957, vol. 1, Case 4), and is still a useful reference. However, from Conant’s time to the present day, the historiography of science experienced important changes, and so did science education. If we want to meet the goals of science education for the twentyfirst century, we have to establish a dialogue between historians of science and science educators. By means of such a dialogue, it will be possible to learn from the history of science the lessons that will help teachers and students to have a better understanding of the many (and complex) ways science is constructed over time.

Acknowledgments The authors thank the editor and three anonymous reviewers for their valuable sug- gestions, and Dr. Kevin de Berg for the copyediting. This research was supported by FAPESP (2007/02542- 4) and CNPq.

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Author Biographies

He´lio Elael Bonini Viana is a chemistry teacher at secondary schools and a Ph.D. student. He received his B.Sc. in Chemistry from the University of Sa˜o Paulo (USP), Brasil, and his M.A. in Science Education from the same university. His research interests include nineteenth-century chemistry, specially the early debates on Dalton’s atomic theory.

Paulo Alves Porto is currently a professor at the Institute of Chemistry of the University of Saõ Paulo (USP), Brasil. He received his B.Sc. in Chemistry from USP, his M.A. and Ph.D. in History of Science from the Pontifical Catholic University of Saõ Paulo (PUC-SP), Brasil. Among his publications are: ‘‘Summus atque felicissimus salium: the medical relevance of the liquor alkahest’’, Bulletin of the History of Medicine, 76 (2002), 1–29, (winner of the 2004 J. Worth Estes Award, from the American Association for the History of Medicine); and ‘‘Primo Levi and The Periodic Table: teaching chemistry using a literary text’’, Journal of Chemical Education, 84 (2007), 775–778. His research interests include history of chemistry, teachers ideas about the history of science, and the content of history of science in science textbooks.

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