Structure Units: Aids in the Interpretation of Chemical
Those who study the learning process maintain that for a student to learn quickly and effectively, it is essential that he see a pattern or structure in the material that he studies.' Chemists make use of a variety of pat,tcrned relationships in their teaching and in their own development,. The best known example of these is probably the periodic table. I n trying to further improve instruction it will he helpful to find other patterns which knit together significant and otherwise diverse items. One possibility for improvement is inherent in the presentation of such concepts as atom, molecule, ion, unit cell, and polymer unit. This paper addresses itself to this problem by attempting to generalize the not,ion of a structure unit. Chemists find the idea that each element and compound can he represented by a structure one of the most helpful of the ideas currently in use for the interpretation of the behavior of chemicals. I t is an idea which is developed in several ways to serve somewhat diverse purposes. Thus, it is so far the only means that has proved a t all adapted to the task of interpreting the fact that chemical reactions occur so as to be described by integer numbers.2 Reagents can he imagined to represent one set of structures while the products of a reaction represent another set of structures. That chemicals behave like structures is supported by t,he observation that a crystalline substance forms in a fixed geometrical pattern. For certain materials two or more different crystalline forms are known. Yet as chemicals in a reaction, each of these forms produces exactly the same product. Thus it is found t,hat either diamond or graphite can contribute to the formation of carbon dioxide samples which are totally indistinguishable except for t,heir history. I n addition, t,he amounts of carbon dioxide produced are completely ident,ical whether one gram of diamond or one gram of graphite is used. I t seems quite impractical to account for the difference between graphite and diamond as other than some difference in arrangement, t,hat is to say, struc-
BnrrNm, J. S., "The Process of Education," Harvard University Press, Boston, 1961, p. 11. 2 P m ~ c a %I., , "Treat,ise on Thermodynsmics," Dover Pnblications, Inc., New York, 1926, p. 24. Planck suggests that physic? is largely concerned with continuously varying quantities, while chemistry is concerned more with discrete integers. For large ratios of sodium to chlorine and a t high temperatures t,he p m d i ~ l becomes , hlue rather than white and the ratio of sodium t,o chlorine forming the product increases. Some regard this hlue solid as a compound of variable composition but it is beLt,er regarded as a solulion farmed from sodinm chloride. Similar treatment earl be given for other so-called "rronst~oiehiometric wmpo~mds" that are described by a variable composition.
provocative t,ure--a difference that vanishes mhen carbon dioxide is formed. Probably the most important support for the idea that substances behave like structures is to be found in the feature uniquely characteristic of all chemical reactions. Among the interact,ions that are exhibited by the components of certain systems there is a set of interactions in which properties appear hut remain invariant. when the relative amounts of the initial components are varied over a considerable range. This invariant relationship is called the stoichiometric ratio. The striking fcature of the stoichiometric ratio is that the ratio of t,he amounts of the componends interacting remains fixed whether the ratio of the components initially mixed together is higher or lo\ver than the stoichiometric ratio. I t is this kind of invariant relationship among interacting components that characterizes chemical reactions. I t stands in cont,mst to the process of solution formation exemplified by mixing neon and helium gases or ethanol and water. So striking is the stoichiometric rat,io that it can be considered a central feature of n chemical system. It suggests that some entity appears in the system and that this entity has a set of properties that remains constant quite independent of the relative amounts of reagents used. I n many cases this entity can be isolated as a substance or a set of substances which comprises the reaction product. For example, mhen sodium metal and chlorine gas are brought together a white crystalline solid is produced. As the white solid appears in the system some of the sodium and chlorine disappear. The a m w n t of the white solid varies as the ratio of initial sodium and chlorine is varied but the properties of the white solid itself do not vary. Further, whatever the initial ratio of sodium and chlorine may be, the ratio of the amounts that disappear is always the same.a The chemist is inclined t o summarize all of this by saying that the white solid is composed of sodium and chlorine in a fixed ratio. Thus no matter what relative amounts of sodium and chlorine are put together in a system, the product, sodium chloride, is formed with a single unvarying ratio of the two reagents. Sodium chloride appears in the syst,em as if it is a material with an identity of its own-as if it is an entity. To propose that chemicals are like structures is one thing, but it seems to be quite another matter to choose the kind of structure best suited to interpreting the various phenomena observed. I n ordinary affairs we recognize at least three ways in which structures may be formed. There are structures exemplified by a brick wall in which many identical bricks are arranged in some desired form. There are structures like an autoVolume 45, Number
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mobile assembled from many different parts. There are structures similar to a bronze casting in which a single piece of material is given a particular exterior form while the material itself is continuous and plays relatively little role in determining exterior form. I n making a choice among possible ways of incorporating structure into our ideas about the nature of substances we can be guided by certain properties of chemicals. Indeed for the chemist the only purpose to be served by the structure idea is that of providing a means for interpreting observed properties. A sample of a chemical is observed to he homogeneous no matter how it may be cut up into small pieces. If it is to he thought of as a structure, then the details of the structures seem to be essentially independent ofhowsmallorlargeorwhat shape the sample may be. One fairly simple manner in which to think of a substance as a structure would be to assume it to be constructed of some small unit repeated over and over to generate the particular sample with the desired properties. Let us therefore imagine that the various properties of each chemical can be generated by the repetition of an appropriate small entity called a structure unit. This corresponds to the first of the three kinds of structures described in the previous paragraph. However, an interest in structure is more general than geometrical arrangements in three dimensions and includes such relations as those described by number and mass in addition to space filling ones.4 Elements react to form compounds and each reaction exhibits a stoichiometric ratio. Each element can he assigned a characteristic mass in a systematic way so that the stoichiometric ratios found in compound formation can all he represented as ratios of the characteristic masses. To account for the characteristic masses of the elements each element is assigned a structure unit called an atom with an appropriately chosen mass. The characteristic mass assigned to an element is called its atomic mass or its atomic weight. An atom is then to he regarded as the structure uuit with a mass which generates the element in terms of its characteristic mass as observed in reactions. Each compound can, in principle, be synthesized as the entire product of a set of elements. The stoichiometric ratio for the elementary synthesis reaction is customarily considered to be the composition of the compound. Therefore an appropriate set of atoms can he chosen to represent the composition of each compound both qualitatively and quantitatively. When the elements are represented by symbols and these symbols used to represent the set of atoms which account for the composition of a compound the set of symbols describe a structure unit which may he called a jon%ulaunit, hut is usually referred to simply as a formula. The set of atoms represented by the formula is thus a structure uuit which, when repeated, will generate a compound with the appropriate composition. It is in this sense that NaCl is the structure unit of sodium chloride or MgF2 the structure unit of magnesium fluoride. An atom as the structure unit for the mass of an element and a set of atoms as the structure unit for the composition of a compound are each units whose assignment is quite independent of whether particular substances are gas, liquid, or solid. Note that in this context a formula is a structure in the sense 'GORDON,C. K., Intemationd Science and Technology, May 1966, 61. A discussion of thc logic of generalized structures.
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of a numerical relationship rather than a three-dimensional relationship. Gases are characterized by a set of properties which are quite independent of the nature of the gas. Thus, a t constant temperature, the product of pressure and volume is invariant as the pressure is altered, at least for an ideal gas. At low pressure all gases shrink with decreasing temperature toward zero volume at a single chacteristic temperature. Gases that are involved in chemical reactions exhibit characteristic and invariant volume relations so that volume ratios of reacting gases are close to integer numbers that are usually small. To account for these and other invariant properties of gases a structure unit called the molecule has been invented. The molecule is assumed to be in motion and it is probably wise to think of the structure unit of a gas as a moving molecule. As a structure unit the moving molecule will generate the pressure-volume hehavior of a gas, its low temperature hehavior, and the volume relations among reacting gases. Some elements are gases at room temperature and any element can he a gas at sufficiently high temperature. Therefore an element must he representable not only by the atom as a structure unit but also by the molecule as a structure unit. I n some cases, for example helium or mercury vapor, both the atom and the molecule can be represented by the same structure unit. For other elements at moderate temperatures the molecule seems to be a set of atoms, as in oxygen represented by O2for the formula of the structure unit. Many solids develop characteristic outer forms and are referred to as crystals. Each crystal has a characteristic set of invariant properties, some are features described by the various symmetry relations of its outer form while others are revealed by the way the crystal interacts with radiation. Yet mere repetition of an atom, a molecule, or a formula unit will not necessarily generate a crystal. I n thinking about crystals the convenient structure unit is a unit cell. A unit cell is designed not only so it will generate the composition of a crystal, but also so that it will generate the appropriate geometric pattern in three dimensions. The unit cell is always chosen so that it represents one or more sets of formula units. Many liquids and solids have the ability to suppport a flow of electric charge even when the applied voltage approaches zero. I n some of these liquids and solids the flow of charge is accompanied by a flow of material. Invariant relations are observed for the direction in which material flows and in the ratio of material mass flow to charge flow. To deal with such phenomena the structure units are assumed to possess electrical charges and are called ions. Sodium chloride provides an example of how several diierent structure units may be used in dealimg with the various properties of a substance. The composition is accounted for by the assignment of the structure unit represented by the formula NaC1. The crystal form of solid sodium chloride is accounted for by a unit cell comprising four formula units. Molten sodium chloride in an electric field exhibits both charge flow and m* terial flow that is accounted for by the assignment of the ions, Na+ and C1- as structure units. Chemical reactions are a special case of the set of changes known as interactions. Atoms and molecules
have been introduced as structure units, but as described so far there is no basis for interpreting why the interactions are limited to the forms that are observed. Nor do the structure units provide for the energy effects observed for chemical reactions. However, electrical charges interact with one another and structure units based on charges provide a means of interpreting interactions. The structure unit which is competent to generate the interactions and energy changes characteristic of a chemical system is a set of negatively charged electrons and positively charged nuclei. Thus, each dierent element is assigned a nucleus with a characteristic positive charge and mass, while the electrons provide the space filling properties that lead to characteristic geometric features. Each of the other structure units used by the chemist-atoms, molecules, ions, unit cells, and many others-are considered to be assemblies of electrons and nuclei. Finally, for the chemist, each substance is differentiated from every other by a characteristic set of nuclei. The various structure units described here probably represent those most widely used. Other units are used for various problems and one might mention such items as structural formulas, atomic kernels, amino acid residues, polymer units, and activated complexes, to list only a few. It is found that the different structure units are interrelated and even some what overlapping. In the consideration of any particular chemical problem, it is necessary to decide which structure unit is the most effective aid to the consider* tion. For the chemist the most fundamental structure unit is presumably a set of electrons and nuclei, since it is believed that with an appropriate set of electrons and nuclei all the properties of any substance can be generated. The proposal to define structure units as generators of the various properties of a substance has a considerable advantage over the usual definition of a strue ture unit as the endpoint of some prescribed scheme of subdivision. In general the subdivision schemes are described as imaginary experiments in which a substance is considered to be subdivided down to some chosen stopping point. However, in most cases the stopping point cannot be described in terms that are consistent with the observable properties of the materials involved and that avoid a circular argument. Furthermore, it is usually not clear how the structure unit defined by subdivision is to be used when interpreting particular phenomena. Thus, is carbon dioxide to be regarded as an assembly of atoms, of molecules, or of electrons and nuclei on the basis of some subdivision scheme? Structure units regarded as generators of properties provide a precise means of dealing logically with each aspect of carbon dioxide or any other substance. A second important aspect of the use of structure units defined as generators is the specification of the WBARBOUR, I. G., "ISSU~S in Science and Religion," PrenticeHall, Inc., New York, 1966, p. 162.
conditions that have to be fulfilled in order to apply the idea of a structure unit in a particular situation. The central condition is that an experiment must reveal some invariant property before it is appropriate to invent a structure unit. Thus, in a system of elements, a compound appears with properties that are invariant with respect to the relative amounts of the elements, and this invariance is the justification for assigning the atom as a structure unit for each element and the formula unit for each compound. Structure units as property generators are logically consistent and closely related to observable phenomena. For these reasons it has particular appeal in teaching. The student can be provided with a pattern that permits him to understand, evaluate, and apply each of the many different structure units which he may encounter in his study of chemistry. Equally important is the possibility that with a general pattern the student can develop his own structure unit appropriate to some new situation that he may discover. One other aspect of the structure unit approach may also he brought forward. The structure unit based on some one or several invariant properties of a system can be part of a still larger pattern. Invariant properties of systems also include such features as the symmetry operations implicit in conservation of mass, of energy, of charge, and of momentum. These various invariant properties stand in contrast to those properties of systems exemplified by volume and entropy that are not invariant. Indeed one can argue that the recognition of invariant relations is one of the major intellectual patterns that characterized scientific investigation. It is probably fair to conclude with a philosophical observation. The idea of a structure unit as a property generator is in the spirit of the instrumentalist appropriate to science.6 That is to say that atoms, molecules, ions, and other structure units are inventions of the mind whose validity is completely tested by their utility in the interpretation of data. For those chemists who subscribe to logical positivism or to realism the appeal will be much less than the attractiveness of proposing that it is really possible to chop up a substance until one has in hand a sample of a simple structure unit. Indeed it may well be that rival interpret* tions of structure unit strategy provide some insight into rival philosophical positions taken by chemists either consciously or unconsciously. The ideas described here were developed whiie the author was directing a UNESCO Pilot Project for Chemistry Teaching in Asia held in Bangkok, Thailand. He is indebted to the participants and consultants in the project who provided much stimulating discussion of the issues involved in the understanding of chemical phenomena. Laurence E. Strong Earlham College Richmond, lndiano
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