Chemical Reactivity and Molecular Geometry

I finished my comps and turned them in. Now it is up to the department to judge my worth as a philosopher and a historian of science. In the meantime, I thought you might want to judge as well. So here is a series of excerpts from the philosophy comp, in which I argue for a new theory of chemical classification based on chemical microstructures. If you want more, e-mail me!

Extended Abstract

The microstructural individuation of chemical kinds was taken as the received view in the literature on chemical reference in the decades following Putnam’s and Kripke’s proposals that gold is the substance with the atomic number 79 and that water is the substance made up of H2O. Recently, this view has come under attack. This essay defends the microstructuralist account of chemical kind individuation, arguing that microstructure individuates chemical terms according to their ability to enter into chemical reactions and does so in accordance with chemical practice.
While many philosophers in the reference literature and philosophy of chemistry have discussed how to individuate chemical kinds, few have offered comprehensive analyses of why and how kind individuation happens in chemistry. My aim is to answer these two questions. I first address why individuation happens, arguing that chemical kinds are individuated by their ability to enter into similar or different chemical reactions. I then discuss how individuation happens, demonstrating that microstructure, once properly understood, determines reactivity and so provides the basis for individuation. This saves the microstructural account of chemical kind individuation while improving its motivation and refining the definition of microstructure it uses. Refining microstructure also neutralizes the criticisms of it from the philosophy of chemistry literature.

Reactivity Determines Kind Membership

I take as a premise that the question of how to individuate chemical kinds is really a question about what things are important to chemists doing chemistry: what things need names is a matter of whether or not the things will be used. This is a common view of the nature and purpose of scientific kinds, famously argued by Ian Hacking.[1] His insight that kinds are categories of importance to homo faber, man the maker, informs the motivation to individuate chemical kinds by considering what is important to practitioners of chemistry.

So what do chemists do? Chemistry is about reactions, and chemical practice is best described as the investigation of the behavior of chemical reactions. Chemistry is sometimes referred to as the “science of substances,”[2] but substances are not practices, and the practice of chemistry is to engage particular substances in particular reactions. It follows then that chemical practice is the practice of engaging substances in reactions. Taking Hacking’s cue to define kinds relative to practice, chemical kinds should be individuated by reference to their differential or similar participation in chemical reactions.

Spelling this out a bit more formally, the intuitive principle of individuation for fundamental chemical kinds aligns the same-kind relation with a test of sameness of function in chemical reactions. In other words, some sample K bears the same kind as relation to another sample L just in case K enters into all the same chemical reactions as L and enters into no others.

“All the same chemical reactions” (hereafter ASCR) is a purposely vague relation, and some elaboration will make it clearer what falls under its umbrella and what fails to. It includes not only the simple test of whether or not every substance that can be combined with K can be combined with L, and the further test of whether or not the products of such combinations are the same in the two cases, but also the test of whether or not the rates of reaction of the two sample cases are the same. Of course, the tests here are assumed to take place under identical background conditions.

This principle of individuation is both intuitive and discipline specific, ensuring that the identities and differences it produces are chemical identities and differences, rather than e.g., physical or biological identities or spurious differences.

Refining Chemical Microstructure

It has been pointed out before[1] that there is no one standard definition of “chemical microstructural property,” although microstructural properties are frequently characterized by contrast with observable properties. When more detail than this contrast is given, CMPs are generally spelled out by way of examples. Two examples have become particularly prominent in the philosophical literature, and each illustrates one CMP type. I use the lessons of these examples as a foundation for a definition of chemical microstructure. I review them briefly before adding the notion of molecular geometry.

Two types of CMPs

Defining “gold” as “the thing with the atomic number 79” illustrates the first type (Type I) of CMP. These CMPs deal with the internal structure of individual atoms. While atomic number, or the number of protons in an atomic nucleus, is the most frequently discussed of Type I CMPs, other properties internal to individual atoms also make a difference to chemical microstructure. The number of neutrons in an atomic nucleus determines which isotope of an element is in a sample, and differences in isotope affect chemical reactivity. This point can be illustrated by the example of uranium, whose two isotopes, 235U and 238U, differ in reactivity such that the former can sustain a fission chain and the latter cannot.

Another aspect of chemical reactivity that is determined by Type I CMPs is the number of electrons in an atom. If an atom has an unequal number of electrons as compared with protons, it is an ion and as such is more likely to enter into a bond with another atom—it is more reactive than its neutral counterpart, so should be considered a distinct chemical kind.

The second kind of CMP already in the literature, call it Type II, is exemplified by the case of water being defined as the thing with the compositional formula H2O. This type of CMP deals with relations between atoms. CMPs of this type consider ratios of species of atoms in a compound, such as 2 hydrogen:1 oxygen. Type II CMPs have come under attack for their insufficiency to describe chemical kinds. Paul Needham,[1] for instance, points out that while compositional ratios are necessary for the individuation of chemical kinds, they cannot be sufficient. In the next subsection, I argue that expanding Type II CMPs to include a class of properties that describes the internal geometry of a molecule remedies the insufficiency. Before doing so, though, it is important to make the problem explicit.

An example will illustrate why compositional ratios are insufficient to individuate fundamental chemical kinds. The drug thalidomide was prescribed as a sedative until it was found responsible for a number of radical birth defects.[2] It was later discovered that thalidomide, C13H10N2O4, has two stereoisomers—that is, two different geometric arrangements that are not superimposable. The difference between the two isomers is not one that can be accounted for by counting the components of the molecules nor the components of any part of the molecule; it arises simply by a twisting of one ring of carbon molecules around a pivot point called a chiral center. But that difference makes a difference: one isomer of thalidomide was shown to be responsible for the birth defects, and the other for the sedative effect the drug was intended to produce.[3]

While the effects are more pronounced at the biological level than the chemical level, it is clear that the two molecules engaged in different reactions to produce such divergent effects. Thus they are distinct chemical kinds, but because they have identical chemical composition they meet the criteria for the same chemical kind as given by this first-pass formulation of Type II CMPs. Their distinctness can be recovered, however, by expanding the formulation of what it means to be a Type II CMP to include molecular-geometric properties. Doing so also aligns the resulting definition of CMPs more closely with chemical practice. This is the expansion of chemical microstructure that is needed to individuate chemical kinds such that each fundamental kind meets the ASCR principle.

Molecular-Geometric Properties

Molecular-geometric properties are properties that express particular kinds of spatial relations between atoms in a molecule.  These properties are attributable to the bonding behaviors of molecules, which produce regular and repeatable three-dimensional arrangements. For example, it is well known that methane (CH4) takes a tetrahedral shape: hydrogen atoms surround a central carbon, orienting themselves at the four corners of a tetrahedron, each about 109º apart.

Properties like methane’s tetrahedral shape, as well as the distance between the central carbon and each of the hydrogen atoms, are molecular-geometric properties. They express spatial relations between atoms in a molecule, treating molecules as more complex than mere clumps of atoms. This kind of description is available to any molecule: as soon as one atom bonds with another, it is possible to describe the bond as more than just the juxtaposition of two atoms. One does so by describing features such as bond energy, bond length, bond angle, and associated geometric features such as tendency to form a tetrahedron.

These properties are microstructural, as the arrangements of atoms in a bond is not something observable to the naked eye. They are similar to the Type II CMP used by Putnam to individuate water, insofar as they deal with relations between atoms. But whereas describing water as H2O gives nothing more than a compositional formula—that is, a simple ratio of clumps of atoms, with no comment on the spatial arrangement of those atoms—adding molecular-geometric properties to Type II CMPs permits further elaboration on the structure of a chemical substance.

Moreover, this further elaboration is necessary for the individuation of chemical substances by the ASCR principle. Without the addition of molecular-geometric properties to the class of things that count as chemical microstructure, substances with radically different reactive behavior could not be distinguished from one another. As an example, consider the element phosphorus. Phosphorus has a number of allotropes, which are different arrangements of bond lengths and bond angles that are correlated with different physical and chemical observable properties. Two allotropes of solid phosphorus include white phosphorus and violet phosphorus. White phosphorus is composed of tetrahedral arrangements of four atoms, and among its interesting chemical properties is its ability to spontaneously combust in air during warm weather, beginning at temperatures of about 30º C. It also dissolves in some common solvents, such as benzene and sulfur monochloride. Violet phosphorus is crystalline. It does not combust at temperatures below 500º C and it is not soluble in any common solvent.

The differences in solubility and combustibility of these two substances make them distinct chemical kinds by the ASCR criterion. But the individual atoms of each kind of phosphorus can have[4] all the same Type I CMPs. The substances can be composed of clumps of atoms of the same size, so CMPs of the initial Type II, which merely expressed ratios of atoms with no consideration for internal molecular geometry, would classify the two substances as identical.

But with the additional characterization provided by molecular-geometric properties, the difference is easy to see. I described white phosphorus as tetrahedral, which means molecules of white phosphorus are composed of groups of four atoms that are distributed spatially as if at the four corners of a trigonal pyramid. Violet phosphorus, on the other hand, is crystalline, meaning it takes on a geometry in which all atoms of a crystal are bonded into one macroscopic molecule. The geometry of violet phosphorus’ crystals is such that atoms are located at the corners of rectangular prisms. The molecular-geometric properties of white phosphorus and violet phosphorus differ from one substance to the next, permitting individuation. No other microstructural properties need differ, so without molecular-geometric properties, the substances could not be individuated microstructurally.

Not only is it possible to individuate molecular species in these terms, it is what chemists in fact do on a regular basis. Tables of internuclear distances and descriptions of common molecular geometries are present in any basic chemistry textbook.  Experiments to determine bond angles and distinguish molecules of identical composition based on their internal geometries take place regularly. Adding molecular-geometric properties to the class of Type II CMPs both reflects chemical practice and permits further individuation of chemical kinds into partitions that conform to the ASCR principle, whereas leaving molecular geometry out of the picture does not. Only by including molecular-geometric properties as a part of chemical microstructure can a microstructural individuation of chemical kinds correlate with the ASCR principle.

So far, I have been primarily concerned with individuating fundamental chemical kinds by the ASCR principle using this new notion of chemical microstructure. While this will remain the focus of the project, it should be mentioned that individuation by reactivity, done in microstructural terms, can and does occur at higher levels in the chemical taxonomy. One need look no further than the periodic table of the elements to see such individuation.

Reactivity Determines Microstructure

Consider what happens in a chemical reaction: chemical bonds break, form, or both. The breaking and formation of chemical bonds is a microstructural process, and often it affects both Type I and Type II microstructural properties of the substances involved in the reaction. While chemical reactions often display observable changes between the initial and final states of the system of substances involved in the reaction, these changes are always attributable to changes in the system’s microstructure.

To elaborate: Chemical reactions can be classified a number of different ways, but each classification scheme relies on reference to the behavior of chemical bonds over the course of the reaction. For instance, one classification scheme divides chemical reactions as endothermic or exothermic. The former requires the input of energy to occur and the latter outputs energy during its occurrence. Energy is a necessary component of the formation or dissolution of chemical bonds. In endothermic reactions, input energy raises energetic states of certain electrons involved in a bond, which increases the likelihood of the bond breaking and different bond with a different atom forming. In exothermic reactions, energy is output as a result of atoms seeking lower-energy bonds than the ones in which they were originally participating.

The bond structure of the system, which is a CMP by the definition we are using, changes during a chemical reaction. For example, when copper sulfate and sodium hydroxide are mixed, they react to form copper hydroxide and sodium sulfate. The four substances have distinct compositional formulas; thus they are distinct CMPs by the Type II criterion. In order, the substances are CuSO4, NaOH, Cu(OH)2, and Na2SO4. The reaction can be described in terms of observable changes—white flakes drop into blue liquid, and as the flakes dissolve a blue gelatinous solid forms—but these observable changes are precisely correlated with measurable changes in the microstructure of the system. Without changes in microstructure, there would be no occurrence of a reaction whatsoever.

Application: Against LaPorte’s Diagnosis of Topaz and Ruby

LaPorte[1] uses the examples of topaz and ruby to argue for two claims: first, that the extensions of chemical kind terms are chosen, rather than discovered, and second, that extensions of chemical kind terms do not always map onto differences in microstructure. While I do not contest LaPorte’s first claim, a closer look at this pair of examples shows that the second is unfounded, because microstructure plays a key role in differentiating the chemical kinds in question. LaPorte argues that the extension of the term “topaz” includes all and only examples of a particular mineral kind, whereas the extension of the term “ruby” includes some but not all examples of a different mineral kind. I demonstrate that both terms refer to particular chemical microstructures, but whereas “topaz” refers to all minerals of a particular compositional formula, “ruby” refers to just one subclass of minerals of a particular compositional formula. The subclass can be characterized in terms of CMPs.

The term “topaz” was coined before the advent of modern crystallography and was used to signify a brilliantly yellow-orange gemstone. After von Laue and Ewald developed x-ray crystallography in 1912, Leonhardt published the first Laue photographs of topaz in 1924, determining its basic chemical composition, Al2SiO4(F,OH)2. Around the same time, it was recognized that crystals with the same basic chemical composition and the same orthorhombic crystal structure were found in colors besides yellow-orange—as early as 1901 reports from Brazil came back describing rose and blue ‘topaz.’[2] Differences in the colors of the minerals were due to minor aberrations in the crystal structure due to increased levels of F, OH or chromium deposits. Scientists and other speakers determined the crystals of other colors were part of the extension of the term “topaz.”

The term “ruby” was also coined before the advent of crystallography and was used to signify a brilliant red gemstone. When its chemical composition was investigated, it was found that ruby’s basic chemical composition is Al2O3. Around the same time, it was recognized that crystals with the same basic chemical composition and the same hexagonal crystal structure were found in colors besides red, including blue, yellow, and pink. Differences in the colors of the minerals were due to the presence of chromium, titanium, iron, or some combination thereof. Scientists and other speakers determined crystals of other colors were not part of the extension of the term “ruby.”

LaPorte reports the different determinations of extension as an exemplary case of choice among alternative possible extensions and against microstructuralism, for, as he explains, the microessentialist should be committed to saying that all colors of Al2O3 are ruby in the same way that all colors of Al2SiO4(F,OH)2 are topaz—and history did not say that, although it could have. He writes,

Did we discover that, while ruby must be red, topaz need not be yellow? It seems not. It seems we could as well have concluded otherwise. Before the microstructure of topaz was explored, people knew that they used ‘topaz’ to refer to minerals of the same kind as the yellow ones they had picked out. But whether yellowness was a defining criterion of “topaz” was, I think, not worked out. … That ‘topaz’ refers to all of one chemical compound and ‘ruby’ to only the red of another seems to represent decision, not discovery.[3]

One interesting consequence of LaPorte’s view is that while he has no problem deeming topaz a natural kind, he is initially ambivalent about the status of ruby[4] and eventually decides it is not a natural kind.[5] This differential treatment of the two terms, and the classes of objects they pick out, represents the fundamental difference between my own view and LaPorte’s: I view both ruby and topaz as equally legitimate chemical kinds, different only in the scope of substance they designate.

LaPorte’s diagnosis of the present situation, namely that “topaz” refers to all colors of a crystal where “ruby” refers only to red variants of Al2O3, is correct. But the buck simply doesn’t stop there, because color variation in these and all crystals is not a matter of unprincipled chance. Rather, color variation is the result of the presence or absence of a few nuclei of additional elements, or of aberrations in internuclear distances in the crystal structure.

For instance, the brilliant red of rubies is due to the presence of chromium instead of aluminum in a few of the aluminum bond sites, and the more chromium, the redder the ruby. The general class of Al2O3 crystals, with chromium aberrations or without, is known as “corundum.” The general class might have all been called “ruby,” but it wasn’t. Rather, the presence and quantity of chromium nuclei replacing aluminum nuclei determines the redness of a piece of corundum, and when chromium is present, the corundum is part of the extension of “ruby.” This variation has different reactive properties than non-chromiated samples of corundum, because if the aluminum and oxygen in the sample were dissolved, chromium would precipitate out from the samples of ruby and not from the other samples.

Systematic explanations for the existence and intensity of different color variations in topaz can also be given in terms of CMPs. Blue topaz, for instance, obtains its color from slight aberrations in the internuclear distance between some of the aluminum and silicon bond sites. This measure of internuclear distance is no more or less than a molecular-geometric property of the sample.

The further division of the classes of topaz and corundum into color-dependent subclasses thus turns out to be microstructural, and as such it is indicative of differences in reactivity, as I discussed above. The color range of topaz, as well as that of corundum, is a result of differences in molecular geometry from one sample to the next, whereas the difference between topaz and corundum is a difference in compositional formula. But both kinds of variation are due to Type II CMPs.

So ruby, as the chromiated subclass of corundum, is an individuable chemical kind, as is topaz. The terms apply to two different levels of their respective taxonomies, with “topaz” occupying a place more similar to “alkali metal” and “ruby” one more similar to “sodium.” Regardless of whether one believes that the extensions of these and other chemical kind terms are chosen or discovered, this example demonstrates that the extensions do map onto differences in chemical microstructure.


[1] Laporte 1996, 122-124; 2004, 100-102.

[2] Derby 1901, 25

[3] LaPorte 1996, 122-123

[4] Ibid, 123

[5] Ibid 2004, 102.


[1] Needham 2000, 14

[2] Adams-Spink 2002

[3] Eccles and Ratcliff 2002, 170

[4] They need not have all the same Type I CMPs, though, as there are multiple isotopes of phosphorus.


[1] e.g. Needham 2000, 13


[1] c.f. Hacking 1991 and 1993

[2] e.g. Pauling 1970, 1

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About burstenj

Assistant Professor of Philosophy
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4 Responses to Chemical Reactivity and Molecular Geometry

  1. Philip says:

    Interesting read. As a chemist I found this post very engaging. I am also very interested in philosophy. Your blog seems right up my alley 🙂 Thanks for sharing!
    Although I am not sure what exactly you are proposing. A new nomenclature? I was tracking along with you for the most part but failed to see the approach you take to overcome the supposed difficulties. Classifying chemicals (or properties) into different categories based on “microstructure” seems very arbitrary. What is to be gained? How would that system play out in the big picture?

    • burstenj says:

      Thanks for the comment, Philip! Apologies for the delay in my response…I blame grad school. I am not proposing a new nomenclature in the microstructure account, at least not for chemists. Rather, I am trying to get philosophers to align themselves with chemical practice when looking at the reference of their terms. By way of analogy, if I want to know what makes a duck a duck, I go ask someone who knows about ducks. If I want to know what makes oxygen oxygen, I go ask someone who knows about oxygen–i.e., a chemist.

  2. Pingback: Blogrolling: Reaction Crate. | Adventures in Ethics and Science

  3. Osikoya Samuelel says:

    I love the explanation

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