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The Status of Equations Describing Reactions


Chemistry books and journal articles are replete with equations describing chemical reactions in the course of which a transformation of substances occurs. Taking equations as statements we never find them glossed as laws. Yet, as I hope to show, they are general in scope and meet at least a weak form of the requirements for the modal status of natural necessity.However, before this analysis can be developed we must show that chemical equations are not expressions of causal regularities. Why might we be tempted to suppose that chemical equations describe causal regularities? Like causal sequences production sequences follow a strict time line, or at least seem to do so. A certain collocation of substances is arranged and then, after a time, that region of space contains a collocation of different substances. As a matter of fact, the transformation of substances in production relations in chemistry is rarely, perhaps never complete.If chemical equations do turn out to be law-like on detailed analysis this is not a version of causality, at least not a version of causality as it has been commonly understood and analysed by philosophers, since Hume [1739-40]. Chemical equations do not describe sequences of like pairs of events. To see this, we can begin with an outline conceptual map of the Humean concept of causality.The ontology of Humean causality is rooted in events. Causality is a certain relation between events, as instances of types which satisfy the following requirements: a. Regular succession of pairs of similar eventsb. The members of each pair are contiguous in space and time.c. The succession of an effect event on the occurrence of a cause event, according to conditions a and b is necessary (in some non-logical sense)According to Hume, the necessity that is ascribed to a causal sequence derives from expectations induced in a person by the regularity with which pairs of contiguous events of certain types appear in succession. It is not a property of any pair of events that satisfy the causality requirements [Hume, 1739-40, Part 3, Section 2].Since chemical equations do not describe sequences of events, but successive stages of a process of production in which an initial cluster of substances is transformed into a cluster of products, the disparity between a substance ontology and an event ontology means that the Humean scheme cannot be used to analyse the production relations described in chemical equations. At best Hume's analysis could be defended as suggesting some criteria that should be met if a process evolving along a time line is to be construed as causal.A more promising candidate schema for a more widely applicable concept of causation has been proposed by John Mackie [1974]. His schema opens up the ontology of causation to include conditions rather than being exclusively focussed on events. According to Mackie, causes are among the conditions for an event of a certain type to occur. To pick out a cause one needs to have a rubric for identifying the conditions from which the cause can be abstracted. He suggested the acronym, INUS conditions, to summarise his schema. Some condition ‘X’ is ‘an insufficient but non-redundant part of an unnecessary but sufficient condition’. Many sets of conditions may be sufficient to produce an effect, so any which are not redundant are candidate causes. [Mackie, 1974]

To see how the Mackie conditions work let us take the example of the failed bombing of the London Underground. Suppose ‘PS’ means ‘Pressing the switch’. It is a candidate cause, but is insufficient by itself since in the case in point the explosive had degraded and did not detonate. It is not a necessary condition for the detonation of the charge, even if it had been in good condition, since before the new rules of engagement for armed police a shot from a security guard might have detonated the charge. PS is not redundant, since, had the bombers been successful, that is had the explosive not degraded, it would have been effective in causing the blast.A third approach to causation can be traced from the writings of Aristotle, through William Gilbert's researches into the laws of magnetism to the energetics of the present day. This is the idea of agent causation. When something occurs, be it an event or the transformation of substances or any regular time-line transformation of nature, we suppose that this is brought about by a material agent, a being with causal powers.The concept of a material agent with causal powers involves at least the following root ideas: a. Activity (exercise of a causal power brings about an effect, though not necessarily an event).b. Spontaneity (the causal power of the active agent is the source of the transformative activity).c. Persistence (the casual power of an agent can exist before, during and sometimes after it has been exercised).d. Conditionality (the exercise of a causal power occurs only in certain conditions).To give some body to these concepts, they can be identified in the way we understand what is meant by taking a magnet to be a causal agent.I propose to show that the concept of the causal agencies of various classes of powerful particulars plays an indispensable role in the examination of the idea that chemical equations might have the status of laws of chemistry.Since the main method of recording and representing chemical knowledge, that is knowledge of the transformation patterns of material substances, is the chemical equation, one might suppose that it would be the best candidate for the format of a law in chemistry. One way of testing this suggestion is to ask how far equations express causal relations. A test should include the main causal schemata, the Humean, the Mackiean and the Leibnizian, causes as regularities among concomitant events, causes as INUS conditions and causes as powerful particulars.


7. Which Concept of Causation is Exemplified in Chemical Discourse?


First of all let us test Mackie's INUS conditions in the context of a real chemical process, say one taken from among the myriad examples of redox reactions, in which oxidation and/or reduction occur. Since the beginning of the nineteenth century chemists have made use of Berzelius's proposal that chemical bonding is due to an electrostatic attraction between components of the interacting molecules. Humphrey Davy's spectacular experimental isolation of the alkali metals by the use of electric currents to disrupt electrostatic bonds and the rapid development of ionic chemistry settled the question of the nature of chemical bonds for most chemists.When pouring a dilute solution of HCl on to a strip of metallic magnesium in a test tube, a reaction occurs. Hydrogen is evolved as a gas, and magnesium chloride, MgCl2 is produced. In solution the ions are Mg+ and 2 × Cl-. Can this familiar story of a simple redox reaction be mapped on to Mackie's INUS conditions?Clearly not. That the ions Mg+and Cl- are co-present in a solution is a necessary condition for MgCl2 to be produced, tested by seeing whether that substance can be crystallised by evaporating the solution left after the hydrogen has evolved. The assembly of the necessary reactants is certainly non-redundant relative to the production of MgCl2 Nor is this assemblage of reactants part of an unnecessary but sufficient condition. There are other ways of making Magnesium Chloride, for example by passing chlorine gas through a solution of Magnesium Hydroxide, but the ionic constituents must be present. So the equation

is not a causal law à la Mackie.Our survey of the chemical literature showed that chemical equations describing chemical reactions in a rather loose way are not described as laws. What is their status?Granted that chemists do not refer to chemical equations as laws, still we can ask whether such equations are law-like. Take the case of a simple double replacement reaction. In symbols:

all in aqueous solution.The mechanism underlying this transformation of substances involves electron transfer among the ions so that a new pair of +/- charged entities comes into being, the electron configuration of each completed as a noble octet. The transfer of electrons also endows the molecular products with the Berzelian charge structure that accounts for their higher level stability. Electron transfer leads to new products either because one of them is insoluble and precipitates, or the new products are more stable than the reactants were.The complementary process of proton transfer, in which a hydrogen ion is transferred can also be an underlying mechanism of a chemical reaction . The reaction between ammonia and hydrochloric acid yielding ammonium chloride is explained this way. The ion equation is written as follows:

By deleting the Cl on either side of the equation we get a net ion reaction, which reflects the transfer of H+, a proton, from the complex water ion to the ammonium radical [Atkins and Beran, 1989].The underlying mechanism involving the transfer of electrons and protons endows the ions with the necessary electrostatic charges to sustain Berzelian bonding. Covalency is more complicated, but the principle of referring bonding ‘forces’ to elementary charges is made use of there too. I believe that this creates a fictional version of the reaction facilitating coherent writing of wave equations to represent the energy layout of the molecules involved. But pursuing that line is a matter for another occasion.The ionisation of compounds in aqueous solution raised a further question. Once the charged ions have separated why should they be stable? Albrecht Kessol (1853–1927) proposed that each ion emulates the electron configuration of a noble gas. Consider potassium bromide in aqueous solution. By losing one electron to the bromine atom ionised potassium acquires a net positive charge (a cation), and the outer shell of the remaining electrons is left as a noble octet. By acquiring an electron the bromine atom becomes a negatively charged anion, and the 7 electrons in the outer shell, by acquiring the electron from the potassium, means that the electronic structure of the ion also emulates the noble octet. Bettering Berzelius, this provides chemists with a unified account of the electrostatic intra-ionic forces and of the stability of ions.Surely these equations satisfy the requirements for the status of law-like propositions. They describe what happens in all like cases of double replacement reactions, that is they apply generally ceteris paribus, to instances or samples of these material stuffs. ‘Other things being equal’ clauses are more or less explicitly tacked on. For instance, in the later stages of the universe the Hubble expansion will open up such great distances between the surviving ions that no chemical reactions will occur. The ions will be there, but no products will come to be.Electron and proton transfer, the underlying processes of generalised oxidation and reduction, provide the mechanisms that support ascribing the relevant modal status, natural necessity, to such equations interpreted as propositions. This provides a heterogeneous extension of the homogeneous chemical regress.In short, the conditions for law-like-ness have been satisfied for two sample chemical equations. Moreover, the equations above, and any of the myriad others that constitute the body of chemical knowledge cannot be about the actual reactions taking place in nature, in the laboratory or in the plants of the chemical industry. Reactions are rarely complete, and all sorts of maverick ions are formed and resolve in the course of a real reaction. Chemical equations describe and at the same time prescribe a working model of the world, a natural descendant of Dalton's tidy clumps of spherical atoms. Nowadays the modelling is overt. A great deal of chemistry is done with the help of computational models, far from the laboratory bench.However, more must be said. The explanation schemata that back up the quasi-necessity and limited generality of chemical equations, so getting them on the lowest rung of the ladder of law-likeness, depend on a contestable model. The Berzelian style of mechanism makes use of a variety of particulate concepts. The charged ions that carry the Coulomb forces are treated as entities, while the very idea of electron exchange requires that we think of electrons in this story as moveable particles.The computation of the numerical value of attributes of the products of chemical productions requires the use of wave functions to describe the molecular set ups. But this introduces a quite different ontology, a metaphysics of fields, since this move enables the calculation of electron densities at different regions in the space occupied by the molecule. The question of whether the microstructure of molecules is to be taken ontologically as a representation of something real is very much a live issue, I believe. If molecules are bounded fields then the ‘structure’ maybe just a device for managing the wave functions. That again is matter for another occasion.


Date: 2015-01-12; view: 70

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