Science & Education 10: 243–266, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands.

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How Important are the Laws of Definite and Multiple Proportions in Chemistry and Teaching Chemistry? – A History and Philosophy of Science Perspective MANSOOR NIAZ Chemistry Department, Universidad de Oriente, Apartado Postal 90, Cumaná, Estado Sucre, Venezuela; E-mail: [email protected]

Abstract. The main objectives of this study are: (1) to elaborate a framework based on a rational reconstruction of developments that led to the formulation of the laws of definite and multiple proportions; (2) to ascertain students’ views of the two laws; (3) to formulate criteria based on the framework for evaluating chemistry textbooks’ treatment of the two laws; and (4) to provide a rationale for chemistry teachers to respond to the question: Can we teach chemistry without the laws of definite and multiple proportions? Results obtained show that most of the textbooks present the laws of definite and multiple proportions within an inductivist perspective, characterized by the following sequence: experimental findings showed that chemical elements combined in fixed/multiple proportions, followed by the formulation of the laws of definite and multiple proportions, and finally Dalton’s atomic theory was postulated to explain the laws. Students were found to be reluctant to question the laws that they learnt as the building blocks of chemistry. It is concluded that by emphasizing the laws of definite and multiple proportions, textbooks inevitably endorse the dichotomy between theories and laws, which is questioned by philosophers of science (Lakatos 1970; Giere 1995a, b). An alternative approach is presented which shows that we can teach chemistry without the laws of definite and multiple proportions.

1. Introduction The French chemist Joseph Louis Proust (1754–1826) was the first to express and provide experimental verification of the law of definite proportions in 1799. The law is generally enunciated in textbooks in the following form: “Different samples of a substance contain its elementary constituents (elements) in the same proportions” (Pauling 1964, p. 25). For example, it was found by analysis that the two elements hydrogen and oxygen are present in any sample of water in the proportion by mass of 1 : 8. Another French chemist Claude Berthollet (1749–1822) was quick to oppose the law by arguing that there was no essential difference between chemical compounds and solutions, which showed variable composition. There ensued an eight year controversy between Proust and Berthollet, which ended with the law of definite proportions being firmly upheld (cf. Fujii 1986; Ihde 1964).

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The law of multiple proportions is generally attributed to the English chemist John Dalton (1766–1844), who first discovered it in August 1803, according to textbook accounts while working on the composition of the hydrocarbons methane and ethene. Most textbooks enunciate the law in the following terms: ’When an element combines with another to form more than one compound the masses of the second element combining with a fixed mass of the first element bear a simple ratio to one another’ (Taylor 1942, p. 2). For example, the series of oxides formed by nitrogen and oxygen (N2 O, NO and NO2 ) is considered to be a good illustration of the law. According to Christie (1999), this is the 20th century form of the law, which differs considerably from the original meaning and intent of the law in the 19th century. Some scholars (Thomson 1825) in the early 19th century popularized the positivist version that Dalton was led to his atomic theory by the discovery of the law of multiple proportions while working on the two hydrocarbons (methane and ethene). According to Rocke (1984): “This inductivist version was quite concordant with the then prevalent Victorian model of heroic science” (p. 27). Linus Pauling (1964) clarifies the issue by stating categorically: ’The discovery of the law of simple multiple proportions was the first great success of Dalton’s atomic theory. This law was not induced from experimental results, but was derived from the theory, and then tested by experiments’ (p. 26). Most chemistry textbooks present the laws of definite and multiple proportions in a simple and uncontroversial manner. In spite of such presentations, a critical appraisal of the history and philosophy of science literature shows that the development of the two laws is closely related to the controversial origin of Dalton’s atomic theory, starting from the early 19th century (cf. Christie 1994; Frické 1976; Fujii 1986; Ihde 1964; Moore and Hall 1939; Nash 1956; Rocke 1978, 1984; Russell 1988). This study attempts to develop a framework in order to understand the relationship between empirical findings, laws and theories. It is also important to note that philosophers of science differ considerably on such issues. For example, the laws of definite and multiple proportions were interpreted by some scientists as a manifestation of Gay-Lussac’s law of combining volumes. On the other hand, an alternative interpretation considered the laws to be a manifestation of the atomic nature of matter. These opposing interpretations continued almost to the first decade of the 20th century (cf. Pauling 1952, pp. 135–136). At this stage it is important to note that the framework developed in this study is based primarily on the interpretations of historians and philosophers of science (Cartwright 1983; Christie 1994; Frické 1976; Lakatos 1970; Rocke 1978, 1984), and Pauling’s (1952, 1964) coincidence with them is indeed helpful and reassuring for science educators. Interestingly, although Pauling was neither a historian nor a philosopher of science, he found it appropriate to include such issues in general chemistry textbooks. The main objectives of this study are:

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(1) To elaborate a framework based on a rational reconstruction of developments that led to the formulation of the laws of definite and multiple proportions. (2) To ascertain students’ views of the laws of definite and multiple proportions. (3) To formulate criteria based on the framework that could be useful in evaluating chemistry textbooks’ treatment of the two laws. This would help in ascertaining textbooks’ views of the two laws. (4) To provide a rationale for chemistry teachers to respond to the question: Can we teach chemistry without the laws of definite and multiple proportions? 2. History and Philosophy of Science Framework Research in science education has recognized not only the importance of history and philosophy of science but also its implications for textbooks (Brackenridge 1989; Burbules and Linn 1991; Duschl 1994; Hodson 1988; Kauffman 1989; Kovac 1991; Mahaffy 1992; Matthews 1994c, 1998; McComas, Almazroa and Clough 1998; Niaz 1998, 2000; Siegel 1978; Solomon 1991; Stinner 1992). Among philosophers of science, Kuhn (1970) has recognized the ahistoric nature of science textbooks: “Textbooks thus begin by truncating the scientist’s sense of his discipline’s history and then proceed to supply a substitute for what they have eliminated. Characteristically, textbooks of science contain just a bit of history, either in an introductory chapter or, more often, in scattered references to the great heroes of an earlier age” (pp. 137–138). 2.1.

LAKATOS ’ METHODOLOGY

Lakatos’ methodology of competing research programs provides a useful framework for the reconstruction of students’ and teachers’ understanding of science content, and this methodology has been applied previously to interpret research in science education (cf. Blanco and Niaz 1997, 1998; Chinn and Brewer 1993; Gilbert and Swift 1985; Kelly 1997; Linn and Songer 1991; Niaz 1993a, b, 1994a, b, 1995). Lakatos’ methodology has been the subject of criticism in the philosophy of science literature. Nevertheless, a recent critical evaluation concluded: “We have shown that the rational reconstruction of Lakatos, though not incorrect in its main line of argument, can be refined in many points . . . . There is no doubt, however, that the method of rational reconstruction has had a positive influence on the philosophy of science” (Hettema 1995, p. 323). Lakatos’ research programs are characterized by a “negative heuristic/hard core” which consists of methodological principles (theoretical assertions), stipulating that the components in the hard core are not to be abandoned in the face of anomalies. For example, in the case of Bohr’s research program, Lakatos (1970, p. 141) considers the five postulates of Bohr’s theory (found in most textbooks) as constituting the “hard core”. Guidance on what is to be done in the face of anomalies is provided by the “positive heuristic” of the program, which “. . . consists

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of a partially articulated set of suggestions or hints on how to change, develop the ‘refutable variants’ of the research programme, how to modify, sophisticate, the ‘refutable’ protective belt” (Lakatos 1970, p. 135). The positive heuristic enables the scientist to build models by ignoring ‘. . . the actual counterexamples, the available data’ (Lakatos 1970, p. 135, original italics). A research program is progressing if it frequently succeeds in converting anomalies into successes, that is, explainable by the theory, referred to as “progressive problemshifts”. 2.2.

DALTON ’ S ATOMIC RESEARCH PROGRAM

The origin of Dalton’s atomic research program can be traced to 1801 when he formulated his first theory of mixed gases. According to Dalton (1810): . . . the atoms of one kind [of gas] did not repel the atoms of another kind, but only those of their own kind. (p. 213) This theory was formulated to explain the constitution of the atmosphere and subsequently Dalton’s law of partial pressures of gases (cf. Frické 1976; Rocke 1978). The argument went as follows: If atoms repel only similar atoms and have no effect whatever on the atoms of another gas then, with a mixture of gases, each individual gas will distribute itself more or less uniformly throughout the available space in the atmosphere and a homogeneous mixture will be formed. Resolution of the atmosphere problem led Dalton to articulate his atomic research program. Frické (1976) considers the hard core (Lakatos 1970) of Dalton’s atomic research program to be based on the following assumptions: . . . that each chemical element consists of its own characteristic type of indivisible, indestructible atom, that the property which characterizes these atoms is their weight, that compounds are definite combinations of these different atoms, and that, during chemical reactions between compounds, atoms are neither created nor destroyed but only rearranged to form new compounds. (p. 283) Dalton’s atomic research program provided a rationale for Proust’s law of constant composition, explained Richter’s law of equivalents and predicted the law of multiple proportions by weight (cf. Frické 1976, p. 283; Pauling 1964, p. 26). Interestingly, just as Dalton was working out the details of his atomic theory, Gay-Lussac (1808) presented his law of combining volumes, which stated: ’The volumes of gases which react with one another or are produced in a chemical reaction are in the ratios of small integers’ (Pauling 1952, p. 161). Dalton rejected Gay-Lussac’s law on the grounds that it seemed to contradict his atomic research program. For Dalton to have accepted Gay-Lussac’s law would have amounted to the recognition of the experimental finding that gases combine in simple ratios with respect to their volumes, and thus ignore the explanation based on atomic theory. Gay-Lussac’s own reaction was somewhat ambivalent, as his work was supported by, “. . . his antiatomist mentor, patron, and friend Berthollet” (Rocke

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1984, p. 41). According to Frické (1976): “Gay-Lussac was not alone in rejecting atomism. There was a widespread tendency to replace the theoretical concept of ‘atom’ by the measurable notions of ‘volume’, ‘equivalent’, or ‘measure’. Dalton’s empirical laws, such as the law of multiple proportions, were considered to be of great scientific value, but his theories were discarded as speculations” (p. 285, emphasis added). It appears that Gay-Lussac’s work was conducted very much in the positivist tradition of the early 19th century, which emphasized the visible and measurable (volumes of gases) aspects of chemistry at the detriment of the invisible/hypothetical (atoms/molecules) entities. This background explains Dalton’s strong reaction against Gay-Lussac’s law of combining volumes. At this stage it is important to appreciate that the atomic theory faced opposition from the very beginning. For example, Thomas Thomson (1830) refers to the opponents of the atomic theory in the early 19th century in the following terms: “The only alteration he [Davy] made was to substitute proportion for Dalton’s word, atom. Dr. Wollaston substituted for it the term equivalent. The object of these substitutions was to avoid all theoretical annunciations. But, in fact, these terms proportion, equivalent, are neither of them so convenient as the term atom; and unless we adopt the hypothesis with which Dalton set out, namely, that the ultimate particles of bodies are atoms incapable of further division, and that chemical combination consists in the union of these atoms with each other, we lose all the new light which the atomic theory throws upon chemistry, and bring our notions back to the obscurity of the days of Bergman and of Berthollet” (reproduced in Dickerson et al. 1984, p. 124). This testimony from an exceptional witness, like Thomas Thomson, is indeed revealing. It shows clearly how science does not necessarily progress from experimental observations to laws and then theories. Furthermore, it shows how scientists with a positivist framework did not foresee the transition from experimental observations (proportions, equivalents) to hypothetical entities(atoms). The opposition to hypothetical entities became even more fierce in the late 19th century: “An important group of scientists led by Wilhelm Ostwald and Georg Helm developed in the 1870s and 1880s a metatheory of science, which later turned into an almost religious cult with the following hard-core metaphysics: all hypotheses should be banned from science and all observable phenomena should be reduced to one fundamental [observable] principle, namely the principle of energy” (Elkana 1974, p. 265). These philosophical debates had their influence on chemistry textbooks and teachers. An exceptional witness reported in the early 20th century to the National Academy of Sciences (Washington, DC) in the following terms: “. . . it is of interest to recall that less than 20 years ago there was a revolt by a limited number of scientific men against the domination of the atomic theory in chemistry. The followers of this school considered that the atomic theory should be regarded as a mere hypothesis, which was of necessity unverifiable by direct experiment, and should, therefore, not be employed as a basis of explanation of chemistry. . .. This tendency advanced so far that textbooks of chemistry were

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written in which the word atom or molecule was taboo, and chemistry was based instead on the law of combination in multiple proportion” (Rutherford 1915, p. 176, emphasis added). This statement from Ernest Rutherford, an experimentalist par excellence, is indeed thought provoking. Dalton’s atomic research program (hard core, see above) in order to be operationalized required the following items as part of the Lakatosian positive heuristic (cf. Frické 1976, p. 285): (1) Chemical formulas to represent the number and type of atoms in a compound. (2) Atomic weights (masses) to measure the relative mass of an atom. (3) Composition by weight of the compound, viz., gravimetric combining proportions. Early in Dalton’s career only the third item was known and hence the positivist approach precisely concluded: “. . . the superfluous atomic weights and formulas should be replaced by combining ‘equivalents’, ‘measures’, or whatever” (Frické 1976, p. 285). It is plausible to suggest that the law of definite proportions is basically an elaboration of the third item of Dalton’s positive heuristic. Furthermore, Gay-Lussac’s law of combining volumes provided the antiatomists a rationale for accepting the laws of definite and multiple proportions, without the “superfluous” atomic theory of Dalton. At this stage it is interesting to note that textbooks generally ignore the fact that, when the laws of definite and multiple proportions were formulated, chemists did not know how to calculate chemical formulas and atomic masses of the elements (first two items of the positive heuristic of Dalton’s research program). This suggests that our present-day general chemistry textbooks besides using the laws of definite and multiple proportions, could also explore alternative approaches to teaching chemical combination. 2.3.

SCIENTIFIC LAWS AS IDEALIZATIONS

In order to understand the nature of scientific laws let us consider Newton’s law of gravitation. According to Lakatos (1970), it is one of the, “. . . best-corroborated scientific theory of all times . . .” (p. 92). Note that Lakatos refers to it as a theory. Feynman (1967) endorses the view that it is, “. . . the greatest generalization achieved by the human mind” (p. 14). In spite of such impressive credentials, Cartwright (1983) asks: “Does this law (gravitation) truly describe how bodies behave? ” (p.57) and responds laconically: “Assuredly not” (p. 57). She explains further: “For bodies which are both massive and charged, the law of universal gravitation and Coulomb’s law (the law that gives the force between two charges) interact to determine the final force. But neither law by itself truly describes how the bodies behave. No charged objects will behave just as the law of universal gravitation says; and any massive objects will constitute a counterexample to Coulomb’s law. These two laws are not true: worse they are not even approximately true” (p. 57, emphasis added). Interestingly, in a recent study (Blanco and Niaz

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1998) many freshman students gave Newton’s law as an example of a scientific law that is universal and has not been modified over the years. At this stage it is important to pause and reflect, as a skeptical science educator may ask: Did Newton ever say that gravity is the only force between bodies? Interestingly, Giere (1995b) has responded to this question in the following terms: “Thus most of the laws of mechanics as understood by Newton would have to be understood as containing the proviso that none of the bodies in question is carrying a net charge while moving in a magnetic field. That is not a proviso that Newton himself could possibly have formulated, but it would have to be understood as being regularly invoked by physicists working a century or more later” (p. 129). The crux of the issue is that following Galileo’s method of idealization (considered to be at the heart of all modern physics, by Cartwright 1989, p. 188), scientific laws, being epistemological constructions, do not describe the behavior of actual bodies. Newton’s laws, gas laws, Piaget’s epistemic subject – they all describe the behavior of ideal bodies that are abstractions from the evidence of experience and the laws are true only when a considerable number of disturbing factors, itemized in the ceteris paribus clauses, are eliminated (cf. Ellis 1991; Kitchener 1993; Matthews 1987; McMullin 1985; Niaz 1991). At this stage, it is important to point out that Cartwright’s (1983) thesis about the nature of physical laws has not gone unchallenged and is the subject of considerable debate in the philosophy of science literature (cf. Cartwright 1989, 1991; Christie 1994; Franklin 1988; Needham 1991; Nugayev 1991; Papineau 1991). Chemistry students and teachers generally tend to understand the difference between scientific theories and laws in the following terms: A scientific theory has not been proved in its totality, whereas a scientific law has not only been proved but is also universal (Blanco and Niaz 1997, 1998). Ryan and Aikenhead (1992) reported that most students expressed a simplistic hierarchical relationship in which hypotheses become theories and theories become laws, depending on the amount of “proof behind the idea”. With respect to teachers, Smith and Scharmann (1999) reported: “Research over the past 45 years, however, has consistently shown that many American science teachers have a grossly inadequate understanding of the nature of science . . .” (p. 506). A recent review has corroborated these findings (McComas et al. 1998). In contrast to these findings, Lakatos (1970) for instance, conceptualizes progress in science within a pluralistic model, in which, “. . . the clash is not ‘between theories and facts’ but between two high-level theories: between an interpretative theory to provide the facts and an explanatory theory to explain them; and the interpretative theory may be on quite as high a level as the explanatory theory” (p. 129, original italics). This suggests that progress in science need not be characterized as a dichotomy between theories and laws, but rather as a “progressive problemshift” (Lakatos 1970), from one tentative theory to another. At this stage it is instructive to consider Lakatos’ (1970) interpretation of the Bohr model of the atom. Bohr’s main objective was to explain the paradoxical stability of the Rutherford atom, and still most textbooks consider Bohr’s major

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contribution to be the explanation of the Balmer and Paschen series of the hydrogen line spectrum (cf. Blanco and Niaz 1998). Lakatos (1970) goes on to show the importance of this event in the history of science: “Since the Balmer and the Paschen series were known before 1913 [year of Bohr’s first publication], some historians present the story as an example of a Baconian ‘inductive ascent’: (1) the chaos of spectrum lines, (2) an ‘empirical law’ (Balmer), (3) the theoretical explanation (Bohr)” (p. 147). Lakatos is referring to the positivist interpretation, according to which experimental findings are followed by a law, which in turn is followed by a theory. Given this widely held positivist perspective on the history of science, it is no wonder that most textbooks consider scientific theories to lag behind experimental findings and the scientific laws. Interestingly, in the case of Bohr, he had not even heard of the Balmer and Paschen formulae before he wrote the first version of his paper (cf. Heilbron and Kuhn 1969, p. 255). The framework presented in this section is helpful in understanding the laws of definite and multiple proportions within a history and philosophy of science perspective. Christie (1994) has traced the historical origin of the laws of definite and multiple proportions and presented an interpretation based on a philosophy of science perspective. Various developments in chemistry have presented considerable problems for the law of definite proportions. In the case of the non-stoichiometric compounds (e.g., aluminum oxide), known as the “network solids”, atoms are not bonded in discrete clusters as molecules, but each to several neighbors in the form of a network. Similarly, synthetic polymers like nylon and polystyrene consist of large numbers of repetitions of a basic structural unit. According to Christie (1994), given these difficulties the law of definite proportions, although is still mentioned in the textbooks, it is not used in an explicit sense in modern chemistry (p. 616). In the case of the law of multiple proportions, the problem lies with the word “simple” or “small”, which appears in its statement (Christie 1994). Although most of the time the ratios are small, there are thousands of different compounds containing just carbon and hydrogen, where the law is not instanced. It appears that, “The law of definite proportions can be seen . . . as an exact rule with exceptions [and] the law of multiple proportions is not even a precise proposition” (Christie 1994, p. 619). In conclusion, Christie’s (1994) work shows how even one of the most cherished laws of most chemistry textbooks, viz., the law of multiple proportions is not even a precise proposition and concludes: “. . . on a more revolutionary note, . . .. many quite respectable laws of science are non-universal, and even that there are a few that cannot be formulated as precise propositions” (p. 613). In this context it is important to note that Giere (1995a, b) has presented an alternative account which provides a way of understanding the practice of science without the laws of nature in the following terms: But one need not appeal to history to deconstruct the concept of a law of nature. The concept is theoretically suspect as well. For example, any law of nature refers to only a few physical quantities. Yet nature contains many quantities which often interact one with another, and there are few if any truly

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isolated systems. So there cannot be many systems in the real world that exactly satisfy any purported law of nature. Consequently, understood as general claims about the world, most purported laws of nature are in fact false. So we need a portrait of science that captures our everyday understanding of success without invoking laws of nature understood as true, universal generalizations. (Giere 1995a, p. 10) It is interesting to observe that there are many common elements in the treatments of Cartwright (1983), Christie (1994), Giere (1995a, b) and Lakatos (1970) with respect to their understanding of laws and theories. All of them would subscribe to the thesis that as scientific knowledge is tentative, it is advisable not to establish a dichotomous/hierarchical relationship between laws and theories. In other words our knowledge progresses from one idea/hypothesis/theory to another. With this background, it is essential that science teachers reconsider the dichotomous presentation found in most textbooks of scientific progress in terms of theories and laws, and that many of our well known laws are in a sense “irrelevant” (cf. Blanco and Niaz 1997 1998). 3. Students’ Views of the Laws of Definite and Multiple Proportions This section is based on students’ views of the laws of definite and multiple proportions, after having taken a course entitled: “Epistemology of science teaching”. The course is based on readings from cognitive science, history and philosophy of science (HPS). The unit on HPS included the following readings: Acevedo Díaz (1989), López Rupérez (1990), Matthews (1994a, b), Mellado and Carracedo (1993), Niaz (1994a) and Pessoa de Carvalho and Castro (1992). Results reported here are based on 7 chemistry students who were about to finish their “Licenciatura” (five year course with dissertation) degree in chemistry. As part of their final exam students were asked (among others) the following question: According to Feynman (Nobel prize in physics), Newton’s law of gravitation can be summarized in the following terms: . . . two bodies exert a force between each other which varies inversely as the square of the distance between them, and varies directly as the product of their masses. (Feynman 1967, p. 14) [Lines 29–41, from page 6 were reproduced, with small changes]. In chemistry, according to the law of multiple proportions: If two elements form more than one compound, then the different masses of one which combine with the same mass of the other are in the ratio of small whole numbers. For example, copper forms two oxides. 100 g of copper combine with 12.598 g of oxygen to produce Cu2 O or with 25.196 g of oxygen to produce CuO. The amount of oxygen that combined in CuO is double that of Cu2 O. In other words,

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in the relation 12.598 : 25.196 or simply 1 : 2. This shows that the law of multiple proportions is instanced in this case. Let us now consider the following compounds of C and H: (a) Ethyne (C2 H2 ) and ethylene (C2 H4 ). (b) Butane (C4 H10 ) and heptane (C7 H16 ). (c) Ethyne (C2 H2 ) and pentane (C5 H12 ). Do you think that the three cases mentioned above are instances of the law of multiple proportions? Explain your answer. The example of the oxides of copper and the three cases of hydrocarbons used in this question were adapted from Christie (1994). Students’ responses can be classified into the following categories: (1) Two of the students did all the pertinent calculations, with no comments. (2) Two of the students did all the pertinent calculations and concluded that the law is instanced in case (a) and not instanced in cases (b) and (c). No further comments were made. (3) One of the students did all the pertinent calculations and concluded that the law is instanced in case (a) and not instanced in cases (b) and (c). After this the following comment was made: “Although the law is not instanced in some cases, it has something in its favor, as it tells us that two elements can form more than one compound”. (4) One of the students pointed out that the law is instanced in unsaturated hydrocarbons but is not instanced in saturated hydrocarbons. After this the following comment was made: “However, the novelty is not affirming that the law is not instanced in 2 of the 3 cases, but to go beyond and reflect: Do they comply with the law of definite proportions? This reflection shows that the hydrocarbons provide evidence to the effect that the law of definite proportions is not instanced as well”. (5) One of the students did all the pertinent calculations and pointed out that the relation between the different hydrocarbons is not of small integers. This was followed by the following comment: “This shows that the law is a limited one and does not explain many cases. We can conclude that such laws are not absolute, but rather explain a phenomenon only under certain conditions”. It can be argued that the exam question gave the students a fair amount of information and feedback in order to reach the conclusion that the law of multiple proportions is not instanced in many cases and hence is not of much use in chemistry. However, results obtained show that at least 5 of the 7 students (categories 1, 2 and 3) were reluctant to question the utility of the law in chemistry. Only two students (categories 4 and 5) responded in a manner that can be considered as a willingness to question the validity of one of the cherished laws of their academic and intellectual framework. This also shows how students like scientists resist changes on issues that are considered to be fundamental and form part of the

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“hard-core” of their epistemological beliefs (cf. Chinn and Brewer 1993; Lakatos 1970). At this stage it is important to point out that students’ responses could have been different if, for example, Feynman’s authority had not been invoked. This is an empirical point and shows the need for further studies. Furthermore, neither the teacher nor the textbook discuss Cartwright/Giere/Lakatos, to show that there are alternative interpretations of these laws. In this context Christie (1999, personal communication) has raised a pertinent issue and recognized the importance of history and philosophy of science for science education: “. . . student responses [presented above] illustrate to me a problem that I continually find with science students – an unfamiliarity with thinking critically; an expectation that any question has a ‘right’ answer, and a mechanical/algorithmic route to finding that answer. In my view, one of the most important contributions that a history and philosophy of science module can and should make to a science student’s education is a challenge to break that mould . . .” (p. 3).

4. Textbooks’ Views of the Laws of definite and Multiple Proportion This section reports the views of freshman/college chemistry textbooks on the laws of definite and multiple proportions.

4.1.

CRITERIA FOR EVALUATING TEXTBOOKS ’ VIEWS

Based on the previous sections of this article, the following criteria were elaborated in order to evaluate the textbooks: (1) The objective of this criterion is to evaluate if textbooks follow one of the following interpretations with respect to the law of multiple proportions: (a) Inductivist (I): Dalton was led to his atomic theory by the discovery of the law of multiple proportions. According to Lakatos (1971) for an inductivist, “. . . only those propositions can be accepted into the body of science which either describe hard facts or are infallible inductive generalizations from them” (p. 92). In the present case the “gravimetric combining proportions” would constitute the hard facts. (b) Lakatosian (L): This law was not induced from experimental results, but was derived from Dalton’s atomic theory and then tested by experiments. (c) No mention (N): Textbook makes no mention explicitly to any of the two interpretations, mentioned above. (2) The objective of this criterion is to evaluate whether textbooks follow one of the following interpretations with respect to the laws of definite and multiple proportions:

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(a) Inductivist (I): Gay-Lussac’s law of combining volumes provided a rationale for accepting the laws of definite and multiple proportions, without the “superfluous” atomic theory of Dalton. (b) Lakatosian (L): Dalton’s atomic theory predicted and explained Gay Lussac’s law of combining volumes. (c) No mention (N): Textbook makes no mention explicitly of either of the two interpretations, mentioned above. Notes: (1) In contrast to Criterion 1 (which evaluates the relationship between Dalton’s atomic theory and only the law of multiple proportions), this criterion evaluates the relationship between Gay-Lussac’s law of combining volumes and the laws of definite and multiple proportions; and (2) In criteria 1 and 2, the Lakatosian interpretation could have been named after Cartwright (1983, 1989), Frické (1976), Rocke (1978, 1984) or Giere (1995a, b). (3) The objective of this criterion is to evaluate if textbooks in order to explain that chemical elements combine to form compounds, explicitly enunciate the law of definite proportions. Textbooks were evaluated on the following bases: (a) Mention (M): Textbook explicitly enunciates the law. (b) No mention (N): Textbook explains the combination of chemical elements, but makes no-mention of the law. (4) The objective of this criterion is to evaluate if textbooks in order to explain that the same two elements can combine to form more than one compound, explicitly enunciate the law of multiple proportions. Textbooks were evaluated on the following bases: (a) Mention (M): Textbook explicitly enunciates the law. (b) No mention (N): Textbook explains the combination of chemical elements to form more than one compound, but makes no mention of the law. (5) The objective of this criterion is to evaluate if textbooks after explaining that chemical elements combine to form compounds, point out the existence of non-stoichiometric compounds. Textbooks were evaluated on the following bases: (a) Mention (M): Textbook briefly describes the existence of non-stoichiometric compounds. (b) No mention (N): Textbook makes no mention of the non-stoichiometric compounds. To implement the criteria, a university chemistry professor with a Ph.D and 25 years of teaching experience at both the freshman and higher levels, and the author, applied the criteria separately to evaluate three textbooks (selected randomly). It was found that both evaluators coincided on the evaluation of all five criteria on two of the textbooks and on four criteria on the third textbook. Each evaluator explained the points of disagreement and after some discussion consensus was achieved. With this experience, the rest of the textbooks were then evaluated by the author.

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It is important to note that although the interpretations of some textbooks were classified as Lakatosian, it does not follow that these authors held explicitly or implicitly, this philosophical position. 5. Evaluation of Textbooks: Results and Discussion Criterion 1 Table 1 shows that four textbooks presented the law of multiple proportions in a manner that supported the inductivist (I) interpretation, viz., Dalton was led to his atomic theory by the discovery of the law of multiple proportions. The following examples illustrate such inductivist interpretations: In 1803, after analyzing compounds of carbon and hydrogen such as methane . . . and ethylene . . . and compounds of nitrogen and oxygen, Dalton first clearly enunciated the law of multiple proportions. (Joesten 1991, p. 58) But chemists are never satisfied with simply observing general laws such as the Law of Constant Composition and the Law of Multiple Proportions. Instead, they set about searching for some explanation of why matter “obeys” these laws of combination. In the early nineteenth century, John Dalton offered as an explanation of these laws of composition a scientific adaptation of the atomic theory . . . . (Quagliano et al. 1969, p. 18) The second example clearly establishes a dichotomy between scientific laws and theories, that provide the explanation, referred to as a Baconian “inductive ascent” by Lakatos (1970, p. 147). Table 1 shows that seven textbooks interpreted the law of multiple proportions and its relationship to Dalton’s theory within a Lakatosian framework. The following examples represent the Lakatosian interpretations: Like most new ideas, Dalton’s model was not accepted immediately. However, Dalton was convinced he was right and used his model to predict how a given pair of elements might combine to form more than one compound. For example, nitrogen and oxygen might form . . . NO, NO2 , and N2 O. When the existence of these substances was verified, it was a triumph for Dalton’s model. The fact that Dalton was able to predict correctly the formation of multiple compounds between two elements led to the widespread acceptance of his atomic theory. (Zumdahl 1990, p. 95, original italics) If a scientific theory is any good, it should lead to predictions about behavior of nature that have not yet been recognized. Reasoning from his theory, Dalton was able to predict a regularity in the weight relations for the case of the same two elements forming two different compounds. . . This relationship was borne out by repeated experiments and has come to be called the law of multiple proportions. (Sienko and Plane 1971, p. 12, original italics)

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Table I. Evaluation of chemistry textbooks based on a history and philosophy of science framework Criteria No.

Textbook

1

2

3

4

5

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

Ander and Sonnessa 1981 Anderson et al. 1973 Bodner and Pardue 1989 Brady and Humiston 1996 Brown et al. 1998 Burns 1996 Chang 1999 Daub and Seese 1996 Dickerson et al. 1984 Ebbing 1997 Hein and Arena 1997 Holtzclaw et al. 1988 Joesten et al. 1991 Keenan et al. 1976 Mahan and Myers 1990 Masterton et al. 1985 Mortimer 1983 Newell 1977 Oxtoby et al. 1990 Quagliano et al. 1969 Segal 1989 Sienko and Plane 1971 Sisler et al. 1980 Stoker 1990 Whitten et al. 1998 Wolfe 1988 Zumdahl 1990

N N N L L N I N N L N N I I N L L N N I N L N N N N L

I N N N N N N N N N N N N N I N N N N N N N N N N N N

M M M M M M M M N M M M M M M M M N M M N M M M M M M

M M N M M M M N N M M N M M M M M N M M N M M N M N N

N N N M N N M N N M N M N M M M M N M N M M M N N N N

I = inductivist; L = Lakatosian; M = mention; N = no mention.

Note: This presentation deals with an important aspect, viz., the role of prediction and accommodation, which has been recognized in the history of science (cf. Brush 1996, p. 612). The inductivist and the Lakatosian interpretations contrast sharply and show their particular approaches to understanding the difference between laws, theories and experimental evidence. Table 1 also shows that although 16 textbooks did not mention (N) the issues involved in an explicitly inductivist/Lakatosian perspect-

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ive, they nevertheless followed the approach that scientific theories are preceded by scientific laws, which are in turn preceded by experimental observations. The following examples illustrate such an approach: A theory is a model that explains observations and data congruently. (Burns 1996, p. 99, original emphasis) Dalton’s ideas have been so extensively tested that we now refer to the atomic theory. (Holtzclaw et al. 1988, p. 11) . . . a common pattern of scientific progress: experimental observation of parallel behavior leads to the establishment of a law, or principle. Further, more accurate, studies may then reveal exceptions to the general principle, the explanation of which leads to deeper understanding [theory]. (Oxtoby et al. 1990, p. 10) Criterion 2 Table 1 shows that two textbooks followed the inductivist interpretation, viz., Gay Lussac’s law of combining volumes provided the rationale for the acceptance of the law of definite and multiple proportions and hence the atomic theory. Such presentations emphasized that although Dalton had studied the mass relationships in many reactions, he could find no explanation for the volume relationships of reactions of gases, that is, Gay-Lussac’s law of combining volumes. None of the textbooks presented the issues involved from a Lakatosian perspective. On the other hand, 25 textbooks made no mention (N) of the issues involved, in an explicitly inductivist/Lakatosian perspective. Nevertheless, it is important to note that most of the textbooks which were classified as (N) confused the issues by pointing out that Dalton had not understood Gay-Lussac’s and Avogadro’s laws as he did not accept the existence of diatomic molecules. The following is an example of such a treatment found in many textbooks: [Gay-Lussac’s] law of combining volumes [can be illustrated by the following example]: 2 vol. hydrogen + 1 vol. of oxygen –> 2 vol. of water vapor. Gay-Lussac did not theorize on his experimental findings, but shortly after their publication, an Italian chemist, Amedeo Avogadro, used them to formulate an important hypothesis in 1811 . . . known as Avogadro’s hypothesis: Equal volumes of different gases (at the same temperature and pressure) contain equal numbers of particles. The obvious question immediately arose: are “particles” of the elements the same as Dalton’s atoms? Avogadro took the point of view that they were not, but rather that elements could exist as diatomic molecules. With his hypothesis, Avogadro could explain Gay-Lussac’s law of combining volumes. . . . One might think that Dalton and others would have welcomed Avogadro’s brilliant hypothesis, but he did not. Dalton and others remained

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firm in their conviction that elements could not exist as diatomic molecules. (Oxtoby et al. 1990, pp. 15–16) This version of the events is not supported by historical evidence. Besides the fact that Gay-Lussac did not share Dalton’s research program (mentioned earlier in this article) there was another major problem with Avogadro’s explanation of Gay-Lussac’s law of combining volumes. According to Frické (1976): “It is often said that Avogadro was responsible for the great theoretical advance of considering the elementary gases as being diatomic. This is not true, for the molecules of gases were permitted to have any degree of submolecularity, provided that there was either one atom or an even number of atoms in a molecule” (p. 290). Indeed, according to Avogadro (1811) himself, the actual number of atoms in a molecule was, “. . . exactly what is necessary to satisfy the volume of the resulting gas” (reproduced in Frické 1976, p. 290). For example, if six volumes of steam had been produced, Avogadro would have described the reaction as: 2H6 + O6 –> 6H2 O. Criterion 3 Table 1 shows that 24 textbooks explicitly mentioned (M) and enunciated the law of definite proportions and used it for presenting stoichiometry and other related concepts. Interestingly, three textbooks (Dickerson et al. 1984; Newell 1977; Segal 1989) made no mention (N) of the law. In other words, these 3 textbooks explained chemical combination, stoichiometry and other related concepts without enunciating or referring to the law. This finding was somewhat unexpected, as according to the philosophy of science literature (cf. Christie 1994), general chemistry teachers and programs consider the law to be important. Later in this article, an adaptation of the approach used by Segal (1989) will be presented as an alternative for teaching chemical combination and stoichiometry, without referring to the law of definite proportions. Criterion 4 Table 1 shows that 18 textbooks explicitly enunciated (M) the law of multiple proportions and 9 made no mention (N). It is interesting to observe that the number of textbooks which did not mention the law of multiple proportions increased to nine, in comparison to the three which did not mention the law of definite proportions. Furthermore, textbooks seem to be consistent, as all three textbooks that did not mention the law of definite proportions (Criterion 3) also did not mention the law of multiple proportions. Apparently, textbooks consider the law of definite proportions as perhaps more indispensable than the law of multiple proportions. Criterion 5 The objective of this criterion was to see if textbooks go beyond the stoichiometric compounds as illustrations of the law of definite proportions, by mentioning the nonstoichiometric compounds. Table 1 shows that 15 textbooks made no mention (N) of the nonstoichiometric compounds and 12 textbooks did mention (M) them.

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Of the three textbooks that made no mention (N) to the law of definite proportions (Criterion 3), one (Segal 1989), mentioned (M) the nonstoichiometric compounds, in the following terms: The majority of compounds are stoichiometric, that is, they have a fixed and definite atomic composition, and the molar ratios of the different atoms that make up the compound are ratios of small whole numbers (simple integral ratios). Stoichiometric compounds are also called daltonides, in honor of John Dalton, the English chemist and physicist whose pioneering work led to the acceptance of the atomic theory of matter. There are, however, compounds that are nonstoichiometric, whose composition may vary within a certain range. Such compounds are also called berthollides, after the French chemist Claude Louis Berthollet, who proposed that the composition of a compound depends on the manner of its preparation (Segal 1989, p. 83, original italics). Mahan and Myers (1990) after mentioning (M) the nonstoichiometric compounds, concluded that although the law of definite proportions had played an important role in the development of the atomic theory, at present it was considered as merely an approximation. This suggests that textbooks can recognize the importance of these laws and yet suggest alternative approaches. 6. Can We Teach Chemistry Without the Laws of Definite and multiple Proportions? Based on the previous sections of this article, the objective of this section is to show that we can consider teaching chemistry without referring to the laws of definite and multiple proportions. Without any attempt at being exhaustive or definitive, it is suggested that such an approach is plausible by implementing the following sequence of steps: (1) Examples to suggest that atoms are the building blocks of all matter. A brief mention of the Greek philosophers can be helpful. (2) Postulates of Dalton’s atomic theory. Consideration of the hard core and the positive heuristic of Dalton’s research program can be helpful. Dalton’s theory provides an example for the students, as to how a theory can be postulated without having all the experimental details worked out. (3) Modern atomic theory: electrons, protons, neutrons and atomic masses. (4) Avogadro’s number and the mole. (5) Molar formulae. For example, Segal (1989) at this stage instead of enunciating the law of definite proportions, presents the following: “The great majority of compounds have a fixed and definite atomic composition; we call such compounds stoichiometric. All gaseous compounds are stoichiometric and are composed of discrete (individual) molecules or atoms. The formula of a substance specifies its atomic composition” (p. 30, original italics). For example,

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carbon dioxide has the formula CO2 . This means that one molecule of carbon dioxide contains 1 atom of carbon and 2 atoms of oxygen. (6) Dalton’s atomic theory was the first to provide an explanation of the formation of stoichiometric compounds. (7) Describe how nitrogen and oxygen form various compounds with different molar formulae, for example: N2 O, NO, and NO2 . Once again, at this stage, Segal (1989) in contrast to most textbooks does not enunciate the law of multiple proportions, but provides the following description: “Note that nitrogen and oxygen combine in several different ratios, that each is ratio of small integers, and that each combination results in a different substance with different physical and chemical properties” (p. 31). (8) Based on his atomic theory Dalton predicted and then explained the formation of more than one compound by the same two chemical elements. These experimental findings provided strong support for Dalton’s atomic theory. This provides an opportunity to familiarize students with the complex relationship between theory and experiment, that goes beyond the positivist presentations found in most textbooks. (9) Emphasize molar ratios rather than weight (mass) relationships between different elements, which combine to form compounds. For example, Segal (1989) provides the following example: “The commonly used pain reliever, aspirin has the molecular [molar] formula C9 H8 O4 . If a sample of aspirin contains 0.968 g of carbon, what is the mass of hydrogen in the sample?” (p. 33). In order to solve this problem students are obliged to conceptualize the molar ratio of carbon to hydrogen of 9 : 8. At this stage it is interesting to observe that the enunciation of the law of definite proportions leads to an emphasis on the macro aspects (percentage composition of the elements in a compound) and sort of ignores the micro aspects (particulate nature of matter). Most textbooks emphasize the macro, observable aspects and the following is an example: “A direct result of the law of constant composition is that each element in a compound can be expressed as a mass percent. . . . The percent composition of water is 11% H and 89% O, and the percent composition of table sugar (sucrose) is 42.1% C, 6.4% H, and 51.5% O” (Wolfe 1988, p. 169, emphasis added). (10) Balanced chemical equations. After explaining the difference between empirical and molar formulae, Segal (1989) goes on to describe the concept of a balanced chemical equation in the following terms: “When we speak of a balanced chemical equation, we mean an equation that describes a physical or chemical change, and is consistent with the requirement that in any process both mass and charge are conserved, that is, they remain the same before and after the change has taken place” (p. 39, original italics). It is interesting to note that Segal (1989) does not enunciate the law of conservation of mass here or any place else in her textbook.

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7. Conclusion and Educational Implication Based on the results obtained in this study the following suggestions can be helpful for chemistry teachers: (1) Most of the textbooks do not present the laws of definite and multiple proportions within a history and philosophy of science perspective, viz., by ignoring the historical and controversial origin of these laws. These textbooks, nevertheless do have a philosophical (inductivist) stance, viz., scientific progress was characterized by the sequence: (a) experimental findings that showed that elements combined in fixed/multiple proportions; (b) followed by the Laws of definite and multiple proportions; and (c) Dalton’s atomic theory was formulated to explain the laws. A few textbooks do interpret the laws explicitly within an inductivist/Lakatosian perspective, which clearly shows how the two perspectives are different. All the textbooks used in this study were published in the US. It would be interesting to analyze textbooks published in other parts of the world. Similarly, it is possible that the courses do not mention the laws but the textbooks do. (2) Most of the textbooks enunciate the laws of definite and multiple proportions and draw quite heavily on them to explain chemical combination and stoichiometry. Some of the textbooks complement the laws by including a brief description of the nonstoichiometric compounds. Similarly, students are somewhat reluctant to question the laws that they learnt as the essential building blocks of chemistry. (3) The use of combining weights of different elements to demonstrate the laws of definite and multiple proportions in a sense complies with the positivist requirement of measurable/visible quantities and the avoidance of entities like atoms and molecules. If you emphasize the weights of the elements, you fail to appreciate the atoms that underlie all chemical changes. (4) It is argued that by emphasizing the laws of definite and multiple proportions, textbooks inevitably endorse the dichotomy between scientific theories and laws. Given the perspective that the conflict/competition is not between theories and laws, but rather between different types of theories (explanatory or interpretative, cf. Lakatos 1970, p. 129), suggests that alternative approaches be explored. (5) An alternative tentative approach, more in tune with history and philosophy of science, is presented which shows that we can teach chemistry without the laws of definite and multiple proportions. An additional advantage of such an approach is that it emphasizes molar ratios of chemical elements that combine to form compounds, which facilitates the understanding of the particulate nature of matter. Christie (1999, personal communication) has provided support for this approach in the following terms: “I myself would also advocate omission of these laws from a chemistry syllabus . . . Definite proportions is merely a convenient excuse for concentrating elementary chemistry on daltonides . . . .

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Multiple proportions as normally presented is a corrupt and impoverished form of the original law, with few instances, and no conceivable purpose other than a simplistic re-inforcement of the principles of atomic theory” (pp. 3–4). It is precisely the “simplistic re-inforcement” that leads students to memorize the laws and use them as algorithms. This study does not suggest we should “expunge” these laws (or for that matter other laws) from the textbooks. On the contrary, discussion of the laws (along the lines suggested here) could provide students and teachers alternative approaches that can facilitate a deeper understanding of the subject. Finally, it is important to mention that it is not the objective of this study to down play empirical findings, but rather establish a framework in order to understand the relationship between empirical findings, laws and theories. According to Lakatos (1970): “Even then experience still remains, in an important sense, the ‘impartial arbiter’ of scientific controversy. We cannot get rid of the problem of the ‘empirical basis’ if we want to learn from experience . . .” (p. 131). In other words, what we need is not a simple description of the experimental findings, but rather an epistemology of science (Matthews 1994c, p. 118). Acknowledgements Thanks are due to Maureen Christie (Department of History & Philosophy of Science, University of Melbourne, Australia) and María Asunción Rodríguez de Aguirrezabala (Dept. of Chemistry, Universidad de Oriente, Venezuela) for making valuable suggestions towards the improvement of the manuscript. Research reported here was supported by a grant from the Consejo de Investigación, Universidad de Oriente (Project No. CI-5-1004-0849/99). References Acevedo Díaz, J. A.: 1989, ‘Comprensión Newtoniana de la Caída de Cuerpos. Un Estudio de su Evolución en el Bachillerato’, Enseñanza de las Ciencias 7, 241–246. Ander, P. & Sonnessa, A. J.: 1981, Principles of Chemistry (Spanish edition), Macmillan, New York. Anderson, C. B., Ford, P. C. & Kennedy, J. H.: 1973, Chemistry: Principles and Applications, Heath, Lexington, MA. Avogadro, A.: 1811, ‘Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies, and the Proportions in which they enter into these Compounds’, Alembic Club Reprints 4, 28–51 (Edinburgh 1923). Blanco, R. & Niaz, M.: 1997, ‘Epistemological Beliefs of Students and Teachers about the Nature of Science: From “Baconian Inductive Ascent” to the “Irrelevance” of Scientific Laws’, Instructional Science 25, 203–231. Blanco, R. & Niaz, M.: 1998, ‘Baroque Tower on a Gothic Base: A Lakatosian Reconstruction of Students’ and Teachers’ Understanding of Structure of the Atom’, Science & Education 7, 327– 360. Bodner, G. M. & Pardue, H. L.: 1989, Chemistry: An Experimental Science, Wiley, New York. Brackenridge, J. B.: 1989, ‘Education in Science, History of Science, and the Textbook – Necessary vs. Sufficient Conditions’, Interchange 20, 71–80.

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