William Goodwin Department of Philosophy




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William Goodwin

Department of Philosophy

Swarthmore College

How do Structural Formulas Embody the Theory of Organic Chemistry?



Organic chemistry provides fertile ground for scholars interested in understanding the role of non-linguistic representations in scientific thinking. In this discipline, it is plausible to think of textual representation as supplementing theories whose principle expression is diagrammatic. Among the many sorts of diagrams employed by organic chemists, structural formulas are the most important. Structural formulas are the products of an evolving norm governed practice and they play several important roles in the thinking of organic chemists. For one, structural formulas are used to unambiguously denote chemical kinds. The norms governing the appropriate generation of structural formulas have evolved in response to chemists’ developing awareness of the individuating properties of chemical compounds. In some sense, then, the range of allowable structural formulas reflects or encodes chemists’ understanding of the domain of their investigations. Additionally, structural formulas are used as models in chemists’ attempts to explain the chemical or physical properties of compounds in terms of their structural characteristics. As theories of chemical bonding have changed and organic chemists have appealed to new structural features in their explanations of chemical behavior, the rules for producing and interpreting structural formulas have evolved as well. Thus, the appropriate ways of appealing to structural formulas in explanations also reflects chemists’ understanding of why compounds have the chemical and physical properties that they do. In this paper, by examining two important episodes in the development of structural formulas -- Kekulé’s proposal of a structure for benzene and Ingold’s explanation of dipole moments in terms of ‘mesomerism’ – I investigate how the norms for the production and interpretation of structural formulas evolve in response to experimental results. I conclude that one principle way in which structural formulas embody the theory of organic chemistry is through these norms. The evolving norm governed practice of producing and employing structural formulas ‘stores the wisdom’ of organic chemists because these norms have been continuously refined in response to experimental (and theoretical) results. By developing a rich appreciation for how structural formulas and the norms constraining their use embody the theory of organic chemistry, I hope to have shed some light on how diagrammatic or pictorial representations may support the cognitive enterprise of science more generally.
The use of structural formulas to represent the constitution and arrangement of atoms in organic compounds, sometimes called Structural Theory, was the product of the convergence of several important ideas that were developed in the 1850’s and 1860’s. Central among these ideas were the tetravalency and chain forming capacity of carbon (Benfey, 1964, Ch. 8 & 9). By putting these ideas together with experimentally determined empirical formulas, it became possible to speculate about the arrangements of atoms that give rise to the empirical formulas. Aleksandr Butlerov was one of the early advocates for Structural Theory, and in 1861 he clearly expressed the ambitions of this new approach to organic chemistry. He asserted:
Only one rational formula is possible for each compound, and when the general laws governing the dependence of chemical properties on chemical structure have been determined, this formula will express all of those properties.

(Brock 2000, p. 256)


This quote brings out two principles that have been a part of, and evolved with, organic chemistry ever since. First is the idea that there is a correspondence between the range of allowable structural formulas and the domain of potential organic compounds. Not only does this facilitate the use of structural formulas as denoting expressions, but also many of the early experimental successes of the Structural Theory were consequences of this principle because they depended upon predicting or explaining the number of compounds that would be found to have a particular empirical formula. Second is the ambition to explain the chemical properties of compounds in terms of features recognizable in their structural formulas. By establishing connections between features of the structural formulas and empirically accessible characteristics of the compounds they denote, chemists have been able to explain an increasing range of chemical phenomena in term of structural features. Much of the success of modern organic chemistry can thought of as a realization of this ambition to understand reactivity in terms of structure. In the two examples to follow, I will show both how these principles guided the use of structural formulas in the explanation and prediction of experimental results and, reciprocally, how the norms for the production and interpretation of structural formulas were adapted, in the face of experimental results, in order to support the continued applicability of these principles.
Example 1: Kekulé’s Structure for Benzene
In addition to playing a central role in the establishment of both the tetravalency and chain forming capacity of carbon, Friedrich August Kekulé was also responsible for the crowing achievement of early Structural Theory – the cyclohexatriene formula for benzene. Kekulé proposed that aromatic compounds, which were a class of unusually stable organic compounds that had high ratios of carbon to hydrogen, were all built upon a nucleus of six carbon atoms arranged in a hexagon with alternating single and double bonds. The six remaining valencies of this aromatic nucleus could be occupied by hydrogen, thereby resulting in benzene, or in other chemical groups, resulting in the large class of aromatic compounds. Though his original depictions of the structure of benzene made use of his “sausage-shaped graphic formulae”, by 1866 Kekulé had settled on the hexagonal representation familiar to contemporary chemists (Rocke, 1985).
The principle empirical support for Kekulé’s structure for benzene came from isomer counting tests. The basic idea of such a test is to determine, assuming the validity of Kekulé’s structure, how many related chemical compounds of a certain type are possible. This prediction can then be compared with the number of compounds of that type that have actually been distinguished by their chemical or physical properties. For example, Kekulé’s structure for benzene predicts that there should be only one distinct compound that results from the chlorination of benzene (substituting chlorine for one of the hydrogens in benzene, resulting in a compound with empirical formula C6H5Cl). Indeed, chemists had found – in many cases before Kekulé’s proposed structure – that for any particular substituent there was only one monosubstituted form of the corresponding benzene derivative. This sort of test depends on the principle that the number of distinct allowable structural formulas of a certain type (e.g. those which can be produced by replacing a hydrogen in benzene by a chlorine) will reflect the number of distinct (or at least distinguishable) chemical compounds with the appropriate empirical formula. If either more than one compound corresponds to a structural formula or there might be multiple structural formulas that depict the same compound, then such a test would not be useful.
In spite of the fact that Kekulé’s structure for benzene was regarded, in some circles, as the “most brilliant piece of scientific production to be found in the whole of organic chemistry” (Brock, 2000, p. 269) it was not without its problems. There were two primary shortcomings of the cyclohexatriene structure (Russell, 1971, Ch. XII). Each of these shortcomings tended to undermine one of the principles of the Structure Theory. The first shortcoming was that by representing benzene as containing three double bonds, Kekulé’s structure suggested that benzene should undergo reactions similar to those of other carbon compounds containing double bonds (alkenes). In fact, benzene, and aromatics generally, did not display the propensity for addition reactions that was characteristic of alkenes; instead, they tend to undergo substitution reactions. This fact undermined, or at the very least complicated, Butlerov’s aspiration to understand chemical reactivity in terms of structural characteristics represented in the formulas. Kekulé could provide no reason why the double bonds in his formula should behave so differently from double bonds in other chemical contexts. In response to this difficulty, several investigators tried to modify how structural formulas represented double bonds (or benzene rings) in such a way that they could provide a non-ad hoc structural explanation for the stability of aromatics that was reflected in the corresponding formulas1. It was only in the 1920’s and 1930’s, after the development of the electronic theory of valence and the applications of quantum mechanics to chemical bonding, that a satisfactory explanation of the stability of the benzene ring was available and reflected in the structural formulas by introducing what are now called ‘resonance structures’.
The second difficulty facing Kekulé’s structure was more pressing because it threatened to undermine the correspondence between structural formulas and organic compounds upon which the empirical support for Kekulé’s structure rested. The cyclohexatriene structure differentiates between the two carbon-carbon bonds emanating from each vertex: one is a double bond and one is a single bond. As a consequence, there are actually two distinct ortho (with adjacent substituents) structural formulas possible for a disubstituted benzene, one with a double bond between the substituted carbons and one with a single bond between the substituted carbons (see Figure 1). Chemists were not able to distinguish compounds corresponding to these structures. This amounted to a negative result in an isomer counting test. Kekulé’s structure predicts two isomers in such cases, but only one isomer was ever found. To abandon the principle that the allowable number of structural formulas should reflect the number of distinct chemical compounds would be to give up on the Structural Theory and to undermine all of its empirical triumphs. Rather than such drastic measures, most chemists attempted to accommodate this negative result in such a way that the basic principle of structure theory was preserved. Some proposed alternative structures for benzene, some explained why the predicted distinct compounds shouldn’t be expected to be empirically distinguishable, and others – like Kekulé himself – suggested that the rules for what counts as a distinct structural formula should themselves be modified (Russell, 1971, Ch. XII).
The basic idea of Kekulé’s response was to provide a principled reason to suppose that the each of the possible structures for an ortho disubstituted cyclohexatriene was a partial and somewhat misleading representation of the actual structure of the compound. Each of these structures was understood to provide a ‘snapshot’ of what is actually a dynamic equilibrium. He claimed:
Each carbon atom collides with both the others with which it is joined together equally often, and therefore stands in exactly the same relation to its two neighbors. The usual benzene formula naturally expresses … the one phase, and thus one has been misled by the view that [the two distinct ortho] biderivatives must necessarily be different. (Russell, 1971, p. 255)
The two distinct diagrams, which had led to the mistaken prediction of two distinct ortho biderivatives of benzene, are no longer to be regarded as distinct structural formulas. Instead they are now to be regarded as parts of one and the same formula, which is less misleadingly presented as a sort of oscillation between the two original diagrams. Though Kekulé’s oscillation hypothesis did not prove very popular at the time, eventually something very much like it – resonance theory-- was adopted. Interestingly, however, resonance theory was not adopted primarily to accommodate the correspondence principle associated with Structural Theory, but instead to accommodate the aspiration to explain the physical and chemical characteristics of molecules in terms of their structure.
Example 2: Ingold and the Theory of Mesomerism or Resonance
The idea that the elements each had their own distinctive valence (or valences), which had played an essential role in the development of Structural Theory, underwent significant development at the beginning of the 20th century. The principle lasting innovations were an account of valency in terms of the electronic structure of the elements and an interpretation of covalent chemical bonds in terms of the sharing of electrons between atoms. Christopher Ingold played a central role in successfully and comprehensively exploiting the new theories of the electronic structure of chemical bonds in order to explain the chemical and physical properties of organic systems. By considering the electronic structures of organic molecules and the way those structures evolved during organic transformations (the study of mechanisms), Ingold was able to realize –to a limited extent – Butlerov’s aspiration of accounting for the properties of chemical systems in terms of their corresponding structural formulas2. I will consider one example of the sort of explanation that Ingold was able to provide in order to show how this explanation depends on updating Kekulé’s idea of understanding some individual structural formulas as somewhat misleading partial representations of the actual structure of organic molecules. In contrast with Kekulé, Ingold does not reject the legitimacy of particular structural formulas because he is concerned to maintain the principle that every legitimate formula corresponds to a distinct chemical compound, rather he rejects particular structural formulas because they do not represent the electronic structure of the molecule that they purport to denote in a way that allows for an explanation of their chemical or physical properties.
One of the properties of organic molecules that became experimentally accessible in the first part of the twentieth century was the dipole moment. Dipole moments are important to organic chemists because they reflect the overall distribution of electrons in molecules. Molecules with large dipole moments have significant charge separation (or uneven distribution of valence electrons relative to atomic nuclei), while those with small dipole moments either have little charge separation or are symmetrical. Given the new found importance of the electronic distribution for understanding both chemical bonding and chemical change, the general information provided by dipole moment measurements provided a useful experimental constraint on early speculations about the electronic structure of molecules (Ingold, 1953, pp. 94-108). In accordance with the general structural approach to understanding the properties of organic compounds, early investigators began trying to understand the experimental dipole moment results by analyzing “molecular dipole moments … into characteristic contributions attributable to atoms and atomic groups” (Ingold 1953, pp. 38). More specifically, the basic approach was to understand the overall molecular dipole as the vector sum of dipoles that were the result of the unequal sharing of electrons in individual chemical bonds (the extent of which could be inferred on the basis of the atoms or groups involved in the bond). By adding up the characteristic dipoles due to the various types of bonds in a molecule, it was then possible to make predictions of the resultant molecular dipole. While this additive strategy was somewhat successful, “it became increasingly clear that the deviations from additivity were very general and much too large to be neglected” (Ingold, 1953, pg. 39). These deviations from additivity are the anticipated result of intramolecular electronic interactions, and thus the next step in understanding the dipole moments of organic molecules was “the correlation of the deviations [from additivity] with structure, and with other phenomena dependent on internal interactions” (Ingold, 1953, pg. 39).
Ingold’s innovations in thinking about and representing molecular electronic structure allowed him to both anticipate and explain some surprising deviations from the additive molecular dipole predictions. According to Lewis’ electronic theory of valence, each atom strives to have a complete octet (or duet) of valence electrons around it. These privileged electronic configurations are attained in organic molecules by either the sharing or transfer of the valence electrons of the constituent atoms. At the heart of Ingold’s approach to molecular electronic structure was the recognition that there are often multiple possible ways of distributing valence electrons around the nuclei in a molecule that are consistent with Lewis’ understanding of the electronic nature of chemical bonding. Each of the distinct possibilities for distributing valence electrons among the atoms of a molecule can be represented by its own Lewis dot structure (which is just a modified structural formula with dots added to indicate the distribution of valence electrons). In many cases where the chemical properties of a molecule could not be explained by considering the structure of its most natural Lewis dot structure, Ingold found that by regarding the actual structure of the molecule as a superposition of its possible Lewis dot structures, he could account for the recalcitrant chemical properties. In the particular case of molecular dipole moments, there are several significant classes of organic compounds that evidence dramatic deviations from the dipoles predicted according to the additive strategy. Ingold’ appeal to superpositions of possible Lewis dot structures allowed for a systematic, qualitative explanation of these deviations from additivity.
In order to understand how Ingold’s explanations worked, it will be useful to sketch how one arrives at an additive prediction of expected molecular dipole for a particular organic molecule. By measuring the dipole moments associated with paradigmatic molecules that have a particular type of polar covalent bond, it is possible to estimate the (vector) contribution of recurring types of polar covalent bond to the molecular dipoles of compounds in which they occur. For instance, because nitrogen is significantly more electronegative than carbon, bonds between carbon and nitrogen will be polar covalent with an accumulation of electrons around the nitrogen and a dearth of electrons around the carbon. As a result, molecules like methyl amine, CH3 –NH2, will have a dipole moment that indicates a relative lack of electrons at the carbon and excess of electrons on the nitrogen. According to the additive strategy, the overall molecular dipole of other compounds containing this sort of carbon/nitrogen bond will include the contribution of a dipole resulting from the carbon/nitrogen bond(s) they contain. For molecules that do not contain any other significant polar covalent bonds, one would expect the molecular dipole moment to be principally determined by the contribution from the carbon/nitrogen polar covalent bond. So, while the numerical value of the dipole moment will vary somewhat as more complicated hydrocarbons are substituted for the hydrogens in methyl amine, the direction of the dipole and its ballpark magnitude would be expected to stay the same so long as no more electronegative atoms (resulting in polar covalent bonds) are substituted into the methyl amine structure.
One analog of methyl amine whose dipole moment does not confirm the additive prediction is aniline, C6H5-NH2, which is obtained by substituting a benzene ring for the methyl (-CH3) group in methyl amine. Since a benzene ring contains only carbon and hydrogen, substitution of such a ring for a methyl would not introduce any new, significant polar covalent bonds into the methyl amine framework. As a consequence, according to the additive strategy, one would expect the dipole in aniline to indicate the same sort of uneven distribution of electrons as in methyl amine. However, the experimental dipole moment of aniline indicates that there is an excess of electrons on the carbon side of the molecule and a lack of electrons on the nitrogen side (Ingold, 1953, pp. 102-3). This is a qualitative reversal of what is to be expected on the basis of the analogy with methyl amine and the additive strategy. In order for Ingold to account for this deviant dipole moment he must explain why the overall electronic distribution in aniline is substantially different than the distribution suggested by considering only the arrangement of polar covalent bonds in the molecule. To do this, Ingold appeals to the fact that there are three possible Lewis structures for aniline over and above its most common structure3. All four of these distinct Lewis structures correspond to distributions of electrons around the nuclear skeleton of the molecule that are consistent with Lewis’ electronic theory of valence. In each of the three additional structures, there is an excess of electron density on the carbon side of the molecule. Ingold’s proposal is that all these allowable Lewis structures are partial characterizations of the electronic structure of aniline (see Figure 2), whose actual electronic distribution is a superposition of these partial characterizations called the mesomeric state (nowadays it would be called the resonance structure). He is careful to point out that, “the unperturbed structures [in this case the four original Lewis structures] … are only of the nature of intellectual scaffolding, and that the actual state is the mesomeric state” (Ingold, 1934, pp. 251-2). In the mesomeric state, the valence electrons are distributed around the nuclei in a way that reflects (in varying proportion) the distribution indicated in each allowable Lewis dot structures.
In the case of aniline, the standard Lewis dot structural formula provides an insufficient representation of the electron distribution in the molecule. To explain the dipole moment of aniline on the basis of its structure, a more nuanced depiction of its electronic distribution is required. Ingold supplied this more nuanced depiction by substituting a more complex structural formula for the inadequate Lewis dot formula. This more complex structural formula is meant to reflect the insights of the theory of mesomerism, according to which the actual mesomeric state is intermediate between the allowable idealized states describable with standard Lewis dot formulas. Though Ingold actually suggested several different ways of writing these more complex structural formulas (Ingold, 1934, pp. 249-53), it is now standard to write them as the bracketed sequence of all the significant Lewis dot structures that contribute to the mesomeric state. When this new, more complex structural formula is used to represent aniline, it again becomes possible to understand its dipole moment as issuing from its structure, as depicted in its new, more complex structural formula.
Ingold’s applications of the theory of mesomerism were not limited to accounting for dipole moments. Instead, he systematically demonstrated, in his research and in his textbooks, the usefulness of the theory in explaining the characteristics of molecules of most interest to organic chemists. Because of the widespread usefulness of the theory, the symbolic devices and policies for representing mesomeric states were rapidly integrated into the representational repertoire of organic chemists. Employing this enhanced repertoire, theoretical organic chemistry rapidly expanded its capacity to provide structurally grounded explanations of the properties of organic compounds, thereby fulfilling much of the promise that Butlerov had envisioned for the Structural Theory (though, of course, as organic chemistry developed it moved beyond the resources originally employed by Ingold). Additionally, one of the things that the theory of mesomerism allowed Ingold to explain was Kekulé’s failed isomer counting test. Recall that the two different structural formulas possible for an ortho disubstituted benzene derivative had not been found to correspond to distinct compounds, thus threatening the aspiration to have a unique structural formula for each chemical compound. According to Ingold’s theory, both of these structural formulas are properly regarded as idealized partial descriptions of the mesomeric state of a single molecule. The more accurate structural formula for such a benzene derivative required by the theory of mesomerism does not distinguish two different possible compounds, and so it restores the correspondence between formulas and compounds essential to the first of Butlerov’s principles for the Structural Theory. Thus, by introducing his theory of mesomerism and the innovations in representation that reflect it, Ingold allowed the Structure theory to advance in accord with both of Butlerov’s principles.
Philosophical Implications of these Examples
Structural Theory can be understood as a methodological strategy for predicting and explaining the properties of organic compounds and their transformations. However, it is not a theory in the traditional philosophical sense – it does not consist of a fixed set of claims about what the world is like. Instead, it includes two principles, or policies, that guide the development of the representational repertoire of organic chemists. At the heart of this representational repertoire is the structural formula, which is the principle device employed by Structural Theory in confronting the phenomena of organic chemistry. What counts as a structural formula and the norms for employing and interpreting those formulas have evolved as new empirical evidence, such as dipole moment measurements, and new theoretical developments, such as the electronic theory of valence, have been incorporated into organic chemistry. However, the overall strategies of employing symbolic descriptive names for organic compounds and then explaining the chemical and physical properties of these compounds on the basis of recognizable features of these symbols has endured across many developments, both empirical and theoretical. Organic chemists did not abandon structural theory when they were unable to isolate two distinct compounds corresponding to the two possible structures of ortho disubstituted benzene derivatives. Rather, chemists ended up amending what counts as a structural formula, initially by way of Kekulé’s oscillation hypothesis, and finally by way of the concept of mesomeric, or resonance, structures. Similarly, in the face of their failure to account for newly available dipole moment measurements, organic chemists did not give up on the strategy of trying to explain the physical properties of organic molecules (such as dipole moment) on the basis of the structure of the molecules. Instead, they modified structural formulas in such a way that it became possible to rationalize the newly available empirical results. So while the formulas themselves change, organic chemists’ commitment to employing these formulas as both descriptive names and explanatory tools does not.
Organic chemists’ commitment to structural formulas, and to their continued development according to the principles of Structural Theory, ultimately stems from the usefulness of formulas developed in this way. It is possible to understand structural formulas developed under the guidance of these principles as playing many of the same roles played by scientific theories as they are more traditionally conceived. By revising structural formulas in order to preserve a one-to-one correspondence between them and distinguishable organic compounds (this is the first principle of Structural Theory), organic chemists ensure that the space of possible structural formulas maps onto the space of possible organic compounds as they understand it at a given time. Understanding structural formulas to support such a mapping requires taking a stand on what features of structural formulas make a difference to (or reflect) the chemical and physical properties of the compounds to which they correspond. It is these features of the structural formulas that are used to individuate them. As a result, by continually tuning their conception of a structural formula, organic chemists are in effect refining their conceptions of the sorts of things and properties that are the subject of their discipline. In more traditional philosophical conceptions of science, the domain and important properties of a discipline might be specified by listing a set of axioms true of all elements of the domain, or by characterizing the state space to which any model of the theory must conform. In organic chemistry, as I have characterized it, the domain is instead reflected in a set of norms for generating and interpreting a particular sort of diagram, namely the structural formula.
The refinement of structural formulas to facilitate the explanations of organic chemistry reveals another sense in which these formulas embody the theory of the discipline. Structural formulas, along with the rules for interpreting and manipulating them, play their role in explanation by acting as models of the compounds they denote. When a structural formula is used as a model, some characteristics of that formula as an object are invoked in order to support a claim about the compound that the formula names. Both the actual object types used as structural formulas, and the characteristics of those objects that are taken to be significant have co-evolved with the theory and experimental results of organic chemistry to allow explanations of this sort. In some cases, such as Lewis dot structures, additional symbolic devices (dots) were introduced to reflect the newly recognized importance of electronic structure for chemical bonding. In other cases, such as Ingold’s theory of mesomerism, the original Lewis-dot structures were re-interpreted as partial representations of a compound more accurately modeled as a superposition of these partial representations. After this reinterpretation, it was possible to invoke features of the refined model --the range of allowable Lewis dot structures for a given compound and the distribution of ‘valence electrons’, or dots, within those structures -- to explain the dipole moments of many compounds. As a result of these sorts of innovations in the production and interpretation of structural formulas, the models that organic chemists use in their explanations have been repeatedly refined. By mastering the production and interpretation of structural formulas -- knowing what counts as a model of an individual chemical compound and what features of that model are important to understanding the behavior of the compound – an organic chemist is equipped to supply and appreciate many of the explanations and/or predictions characteristic of his discipline. The structural formulas of organic chemistry embody the theory of this discipline because they are both descriptive names and models, the production and interpretation of which has been continuously refined to accommodate the theoretical innovations and experimental results in the discipline.
Bibliography
Benfey, O. T. (1964), From Vital Force to Structural Formulas. Boston: Houghton Mifflin Company.
Brock, William H. (2000), The Chemical Tree: A History of Chemistry. New York: W. W, Norton and Co.
Ingold, C. K. (1953), Structure and Mechanism in Organic Chemistry. Ithaca: Cornell University Press.
Ingold, C. K. (1934), “Principles of an Electronic Theory of Organic Reactions” Chemical Reviews 15: 225-74.
Leicester, Henry M. and Klickstein, Herbert S. (1963), A Source Book in Chemistry 1400 - 1900. Cambridge: Harvard University Press.
Rocke, A. J. (1985), “Hypothesis and Experiment in the Early Development of Kekulé’s Benzene Theory” Annals of Science, 42 (1985), 355-81.
Russell, C. A. (1971), The History of Valency. New York: Humanities Press.



1 The most famous attempt was by Friedrich Thiele. Excerpts from his work are reprinted in (Leicester, H. and Klickstein H., 1963, pp. 510-11)

2 A summary of Ingold’s contribution and surrounding developments can be found in (Brock, 2000, Ch. 14). Ingold’s program was laid out in his landmark paper, (Ingold, 1934), and subsequent textbook, (Ingold, 1953).


3 See (Vollhardt and Schore, 1994, pp.14-19) for a modern description of Lewis-dot structures and their contributions to resonance. Ingold appeals to Pauling’s work in quantum mechanics in order to ground the significance of these alternative structures see (Ingold, 1956, pp. 82-8).





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