ANALOGIES in TEACHING FRESHMAN CHEMISTRY* JOHN R. LEWIS University of Utah, Salt Lake City, Utah
This @per points out the place of analogies in teaching freshman chemistry. A number of analogies, used i n the classroom and i n textbooks, are given as illustrations. The objections to the use of analogies and the advantages which are derived from their use are dis'cussed. The conclusion i s that analogies should be used because: (1) many students, i n freshman classes, are not properly pre@red for the conventwnal presentation of the subject matter; and (2) since chemistry i s a growing science, it is advisable to use analogies until the more rigorous mathematical presentation can be absorbed by students.
CLASSROOM ANALOGIES
The analogies given under this heading have been selected from a collection made by the author and used in his classes. They are grouped under the topics in which they are used in the classroom.
Structure of Matter The Dalton Atom.-The Dalton atomic theory states that elements are made up of small individual units called atoms. To account for certain properties of matter, such as the slight compressibility of liquids and solids, the atoms were likened to "small, hard lead shot" arranged in a compact manner which resist any force RE analogies useful in teaching chemistry? Do tending to bring them closer together. The expression students come to our freshmen chemistry classes "small, hard lead shot" is within theexperienceof most with backgrounds such that instructors need students and consequently they are able to visualize not depend on the analogy to help "put over" abstract atoms. The Cumplex Atom.-The past few years have given ideas? There is general agreement among teachers us a preponderance of evidence in support of a complex that the average student learns new facts and grasps abstract concefitions more readily if they are presented to atom. The old Dalton atomic picture has given way him in terms of his past experiences. The purpose of to the pictures of Lewis, Langmuir, Bohr, and the many this paper is to point out the place of the analogy in other investigators who are working in this field. For students this new atom is likened to the solar system teaching by this formula. and is spoken of as "a miniature solar system." Just NATURE OF ANALOGIES as the earth revolves about the sun, the nucleus of the In general, the word analogy implies a resemblance solar system, so the planetary electrons revolve about of relations; agreement or likeness between things in the nucleus of the atom. And now we believe that as some circumstances or effects when the things are other- the earth turns on its axis, so too does the:electron spin wise different. "Resemblance and similarity are ex- along its orbital way. Energy Leuels in Atoms.-To explain the more recent ternal or superficial, and may involve no deeper relapicture of the atom, President Compton of the Massation; as, the resemblance of a cloud to a distant mounchusetts Institute of Technology1 uses an interesting tain." On the other hand an analogy is "a resemblance that may he reasoned from, as that from the analogy to account for the energy levels of the electrons likeness in certain respects we may infer that other and in atoms. An atom is likened to a factory.building in which a great deal of work is being done. Men are perhaps deeper relations exist." hammering and moving objects from one place to anWhat is a chemical analogy? Wherein does i'f differ other and as a result of such disturbances, small pebfrom chemical illustrations or comparisons? A chemibles, which are resting on the steps of the fire-escape cal analogy, strictly speaking, is one drawn from the on the outside of the building, are shaken down from subject matter of everyday experience to explain chemistep to step. The pebbles bear the same relation to cal theories and problems. In this paper, however, the building that the planetary electrons bear to the the writer does not wish to confine himself strictly to nucleus of the atom. The steps on the fire-escape are those examples which can only he classed as analogies. "the energy levels" which may be occupied by the It seems more desirable to include border-line cases ,~ * e'ecuons (peDoles). which may be classed as comparisons or illustrations or as combinations of all three. 1 COMPTON, RARL T., "The battle of h e alchemists," Elm.
A
3
-
..
-
* Part of this paper was presented at the Salt Lake City meet-
ing of the American Association for the Advancement of Science, Pacific Division, June, 1933.
. ~ % ~ . ~ - \
Eng., 52, 7&80 (Feb., 1933). * Readers who are interested in the use of analogies in picturing the modern atom will be delighted with Dr. Compton's article from which the above analogy was taken.
627
The Nature of Molecules.-Molecules can be divided into simpler units (decomposed) but in so doing the properties which characterize them will be lost. Students grasp this point more readily if told about the car of wheat or corn; divisions and subdivisions are made until a single kernel remains. If this is cut in two, pulverized or destroyed in some other manner, the grain loses certain important properties. For example, it will not germinate. Relationship of Substances, Molecules, and Atoms.To show the relationship of substances, molecules, and atoms one writerZ says that as words are made up of syllables which are made up of letters, so also substances are made up of molecules which are made up of atoms. Extending this to include electrons we may say that as words are made up of syllables which are made up of letters which are made up of cumes and straight lines, so also substances are made up of molecules which are made up of atmns which are made up of electrons around nuclei. The Structure of Benzene.-Years ago the structure of benzeue was unknown to chemists. The percentage composition and molecular weight of the substance pointed t o the formula CeHsbut the quadrivalence of carbon could not be satisfied if the structural formula was written in the conventional manner. Then came KekuM's dream-analogy. He saw a chain of carbon atoms dancing before his eyes, and as they danced they seemed to become a snake. The snake seized hold of its own tail. The chain of carbon atoms had become a closed ring. The ring theory of the structure of benzene, which grew out of this analogy, has been of naramount imnortance in the develoomeut of organic chemistry. Catalysis A catalyst is an agent which changes the rate of a reaction but which a t the end may be recovered, apparently unchanged, and used again. The rBle of catalysts in chemical reactions may be made clear to students by suitable analogies. The following have been used with success. The Workmen Analogy.-A number of workmen were filling a coal car. While the foreman was absent the coal went into the car a t the rate of three shovelfuls per ten minutes, per man. With the foreman present, the coal went into the car a t the rate of fifteen shovelfuls per five minutes, per man. The goreman said nothing, but his presence served to stimulate the rate of filling the car much the same as a catalyst changes the rate of a chemical reaction. The Policeman Analogy.-A traffic policeman may be considered to be a kind of catalyst since he regulates the speed of traffic without actually driving all the cars on the street. Oil Analogy.-Ostwald likened the behavior of a catalyst to the action of oil on the bearings of amachine. The machine operates more smoothly but the oil is unchauaed. aM A R ~ L L. ,C., "The story of human progress," The Macmillan Co., New York City, 1927, 548 pp.
Chemical Equilibrium Equilibrium is established when the forward and reverse reactions take place with the same velocity. At any given moment there will be the same number of molecules of each substance present as a t any other moment although the same individual molecules may not be present during each period of observation. Students understand this dynamic equilibrium more readily if one or two well chosen analogies are used. Wild Horse Analogy.*-Given 100 horses and 100 men in a small enclosure. The men try to ride the horses, but due to the wildness of the horses many are thrown. These remount, however, to take the pIace of others who are subsequently thrown. This process continues until a t any given moment, when equilibrium is established, 50 horses have no riders. If one wishes to show the effect of increasing the concentration of one of the reactants on the final equilibrium of a chemical reaction, the above analogy can be modified to show that if 200 men are brought into the enclosure to ride the 100 horses, a new equilibrium point will be established in which there will be a t any given moment, let us say, 25 unmounted horses. In other words the increased number (concentration) of men has resulted in increasing the number of mounted horses. The Bridge Analogy.-Two cities, located on opposite banks of a river, are connected by a bridge. People are continually crossing from one side to the other. If the number passing in opposite directions, per unit time, is the same, the total number of people in each city will remain constant. That is, a state of equilibrium is maintained. The Solubility-Product Principle The solubility-product principle states that the product of the concentrations of the cations and anions of difficultly soluble salts must exceed a certain minimum value before a precipitate can form. It can be shown that the concentrations of the two ions need not be the same so long as their product is. greater than the minimum value which is spoken of as the "solubility-product constant." The Fish Analogy.-To explain the solubility-product principle more fully, the analogy of the fishermen and the fish has been told to students ,with considerable success. It is somewhat as follows., Imagine a secluded lake filled with trout just a day or so before the official fishing season opens. A small party of game wardens and their friends arrive a t the lake to prepare for the season's business. Naturally they take their fishing-tackle along in order that they may participate in the summer's activities. The fish are plentiful and hungry and the wardens are anxious to try their new fishing equipment, which they do. Every man catches a generous supply of trout. The "concentration" of men is low but the "concentration" of fish is high so the solubility-product constant is exceeded and a pre-
* From the general chemistry lecture notes of Dr. J. H. Walton of The University of Wisconsin.
cipitate is formed (i. e., a fish on the fisherman's hook). Now imagine the same lake several days later, after the season is well under way. There are many fishermen angling for the numerous fish left in the lake. Many fish are caught because under these conditions the solubility product is again exceeded. Finally, imagine the scene a t the lake late in the season. A few fishermen are left trying to catch the two or three fish which have escaped the thousands of hungry fishermen who have visited the lake during the summer. Try as they will, they cannot catch a fish. The solubility product has not been exceeded. TEXTBOOK ANALOGIES
In reviewing a number of the leading texts in general chemistry, the writer has checked the analogies which have come to his attention. In the paragraphs which follow are examples of analopies - which have been selected from the& texts. First Text.-The f i s t edition of Richardson's "General Chemistry"3 contains a number of interesting analogies. On page 85 is one used in explaining the laws of chemical combination. The author asks the student to imagine an absurd grocer who stores away the commodities which he sells in packages of fixed weight, packages which he refuses to break and sell in smaller or larger units. Another interesting analogy is given by Richardson on paxe 202 to explain chemical equilibrium. He assumes-two diierent kinds of individuals called blacks and whites confined in a field. Both kinds are wandering a t random within the enclosue. When a black meets a white a bair is formed which remains together for a time, i. e.,-until they tire of'the compani&ship and separate. Here we have a condition of equilibrium in which a t any given time there are a certain number of pairs of the blacks and whites. Richardson, on page 208, uses another form of this analogy in which he has two groups of individuals lined up and throwing baseballs a t each other. On one side are young, vigorous men while on the other are old men with "glass arms." At f i s t the young men get the better of the older ones, hut as the young men use up their "ammunition" and the old men warm up, a state of equilibrium is established in which the number of balls going in either direction is the same. Second Text.-Holmes, in the revised' edition of "General Chemistry4 uses the analogy of the fiaancial condition of a student to explain chemical equilihrium. On page 80 the author shows that the student begins the year with a cash reserve for emergencies, a regular allowance from home, and the expectation of necessary expenditures. By considering income and outgo as analogous to two opposing chemical reactions and the cash reserve as an amount that may grow, decrease, or remain fixed (constant), a successful parallel is obtained.
Third Text.-In explaining the number of atoms of each kind in a given type of molecule, Deming, in his new "Introductory College Chemistrf"' gives an interesting analogy. Students'are asked to imagine that automobiles are too small to be examined individually, but that the quantity statistics of a certain factory are available which show that for each million steering wheels built into its cars, six million spark plugs are needed, four million wheels, and two million headlights. The conclusion then is that each car possesses a minimum of one steering wheel, six spark plugs, four wheels, and two headlights. Fourth Text.-Mellor's "Modern Inorganic Chemi s t ~ contains ~ " ~ -a number of analogies. On page 138 the author points out that one substance can accommodate another much in the same way that "a scuttle of coal might a t the same time accommodate a bucket of A .,.
D.,UU.
22
Sound-Film Analogy.-The talking film on the kinetic theory of gases made a t The University of Chicago under the direction of Dr. H. I. Schlesinger, draws an analogy between the bombardment of a target, by lead bullets from a machine gun, and the bombardment of the walls of a vessel by gas molecules. In either case, a pressure is created. The pressure exerted by the lead shot on the target is recorded by a pressure gage which can he observed by those who see the demonstration. OBJECTIONS TO THE USE OF ANALOGIES
The common raised by to the use of analogies are summarized in the following para-
---,.. *
gapus.
Analogies should not he used too frequently, especially if the students have proper background for the subject matter. The too frequent use of analogies under these conditions may make them amusing or humorous rather than instructive. It is quite probable that such analogies will lack dignity. The second charge which one may make against the use of analogies is that teachers may .overload them. Analogies are not identities. Often many absurd assumptions must he made hy teachers before the analogy can be applied. An overloaded analogy is quite likely to lack dignity and, what is more serious, imply relations which do not exist. This brings us to the third and, in the opi&on of the writer, the most serious objection to the use of analogies. Reactions produced in the students' minds may be entirely foreign to the ones the teacher wished to obtain. For example, after giving a class of elementary students the a n a l o p about the car of corn to illustrate the nature of molecules, one student asked whether or not the instructor thought some of the corn found in the ruins
-
6 DEMWG, H. G., "Introductory college chemistry," John Wiley & Sons, Inc., New York City, 1933, 590 pp. 8 MBLLOR, J. W., "Modern inorganic chemistry," Longmans, Green & Co.. New York City, 1930, 1103 pp. *The excellent editorial on "Classroom analogies" in the March, 1933, JOURNAL oa CHEMICAL EDUCATION should be readby those interested in analogies.
of the cliff dwellings of the southwest would germinate. Apparently that student had taken a trip into the old southwest during part of the class-period.
The writer believes these books are very satisfactory for students with suitable backgrounds. It is unnecessary for college teachers to use analogies extensively on groups of selected students. The facts ADVANTAGES OF ANALOGIES are, however, that a great many of our freshman chemOne advantage of analogies has already been sug- istry classes are mixtures of students who have had gested in the @st paragraph of this paper; namely, that with those who have not had chemistry in high school. students grasp new facts and abstract conceptions if For such classes there will remain a definite need of they are presented in terms of the students' own experi- the analogy in the chemical diet. If chemistry were not a growing science, it is conences. An analogy draws on the students' past exceivable that future students would come to our nniperiences and is, therefore, a valuable tool in teaching. versity classes with such broad experience and excellent Analogies are useful where students do not have the training that analogies would be seldom needed. With proper background to follow the conventional methods used by some teachers. Mixed classes, i. e., those a "dead" chemistry we could soon give our high-school which are made up of students who have and those instructors such definite ideas concerning the kinetic who have not had chemistry in high school, furnish an theory, isotopes, atomic numbers, and the other subexample. Those students with no previous chemistry jects which now form a part of the high-school course, can be helped along hy the use of suitable analogies. that they would be able to impart their knowledge Analogies serve as excellent substitutes for mathe- rather effectively to their students. These students matical concepts which are used in introducing many would come to the university so well equipped for the theories. Frequently the analogy is retained and used average freshman chemistry course that analogies along with the mathematical formula, the one reenforc- would rarely he necessary. But chemistry is a growing science. The researches ing the other. For example, the kinetic theory, which and new theories of today become the subject matter of is an analogy, is taught to students not only by means of mathematical formulas but also by means of simpler our freshman classes tomorrow. Just yesterday few of us knew anything about the "energy levels" of the analogies. atoms. Today a discussion of energy levels in atoms In the hands of skilful teachers, the undesirable forms an important part of many of our courses. Yesconsequences of analogies, pointed out in the previous terday, if we thought of atoms, we had a mental picsection, can be reduced to a minimum. The skilful ture of electrons hanging on the corners of cubes. teacher does not use analogies too frequently, nor does Today we have discarded the cubes but have, in their he use those of questionable value. His analogies are chosen after be has had an opportunity to determine place, another picture which serves us better. But we are prepared, and expecting, to discard our present the background of his class. By observing these prepicture as soon as a more accurate representation can cautions, he is less likely to stimulate irrelevant rehe found. actions in the minds of his students. It is quite possible that, in the near future, we shall be teaching quantum mechanics to our freshmen. If GENERAL DISCUSSION we do, it will be necessary to make use of analogies as Of the many textbooks examined for analogies, one we now use them in teaching atomic structure. We or two stand out as exceptions. These contained very shall do as Dr. Charles P. Steinrpetz did when he few analogies of the type illustrated above. In this wrote his book "Four Lectures on Relativity and group should be mentioned Hildebrand's "Principles Space."'"n the preface he states that "the relativity of Chemistry"'and Schlesinger's "General Chemi~try."~ theory is intrinsically mathematical and it is impossible Parenthetically, i t should also be mentioned that Rich- to give a rigidly correct and complete exposition of it ardson's revised "General Cbemi~try"~ does not con- without the extensive use of mathematics. The best tain the analogies which were, in the opinion of the that can be done, therefore, in explaining the theory of writer, an interesting feature of the first edition. relativity to the layman, and to the'engineer who is * ' H ~ ~ ~ B RJ.AH.,N "Principles D, of chemistry," 3rd ed.. The not an expert mathematician, is to give by analogy, example, and comparison a general conception of the Macmillan Co., New York City, 1932, 328 pp;, 8 SCWLESINGBR, H. I., %enera1 chemistry, rev. ed., Long- theory and its fascinating deductions and conclusions."
mans, Green & Co., New York City, 1930, 847 pp. RICHARDSON, L. B., "General chemistry," rev. ed., Henry Holt & Co., New York City, 1932, 779 pp.
'0 STEEYMETZ, C. P., "Four lectures on relativity and space," McGraw-Hill Book Co., Inc., New York City, 1923, 126 pp.
Our attention has been called to an unfortunate transposition of figures which occurred on page 523 of Mr. Kraissl's article on "A History of the Chemical Apparatus Industry" in the September number. The date of introduction of Nonsol glassware was 1902-not
1920.
