edited by: RON DELORENZO Middle Georgia College Cochran. G e ~ g i a31014
A Bloody Nose, the Hairdresser's Salon. Fnes in an Elevator, and Dancing Couples: The Use of Analogies in Teaching Introductory Chemistry
rem order
Arthur M. Last Slr Willred Gredell Corner Brmk, NsMwndland, Canada A2H EPO
Inilia Rate
The uir oianalugies can play an impnnant role in assisting students in understandina some of the more difficult and11,r abstract concepts in introductory chemistry. In addition, analogies can provide an amusing interlude during a lecture and c& sometimes help a lecturer to interact with his students. The four analogies presented here represent some of those which my students have found both helpful and amusing in recent years. A Bloody Nose Most classes contain at least one student who is always ready ul liven up lectures with some remark or other, and he or she is the natural choice for the hlmdy nose analogy which I use to help illustrate the n>llisiontheory of bimolecular reactions. I usuallv aooroach this tnoic via conventional means1. explaining the three conditions t i a t must he fulfilled in orde; for a reaction between two molecules to take olace: 1) the molecules must collide, 2) the colliding molecul& must have a total energy that is equal to or greater than the activation energy of the reaction, and 3) the colliding molecules must have the correct orientation. Selecting a student who I know will enjoy what is to follow, I then ask the class toconsider the following "reaction:" my fist +the student's head
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a sore fist + s blwdy nme
In order for this reaction to take olace. ohviouslv the fist and the head must make contact (molkule$ must coEde). A gentle tap is unlikelv to cause a hloodv nose or a sore fist. so the idea that the reactants must collide with a certain minimum amount of energy also becomes apparent. Finally, a hlow to the back of the head is unlikely to cause the student's nose to bleed. What is required is a hlow that lands full in the face. In other words, the reactants must collide with the correct orientation. Needless to say, i t is not advisable to actually demonstrate this reaction! The Hairdresser's Salon The topic of reaction kinetics is also the source of my second analogy. When lecturing on gas reactions that take place on the surface of a catalyst, I like to show how, for many such reactions, an increase in pressure (concentration) only results in an increase in rate up to a certain point. Beyond this point, further increases in pressure (or concentration) do not affect the initial rate, and the kinetics of the reaction change from
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Tho9 l e a r n p a m a a collection of descrlptlve applicalianr and a h alogles destgnad to help st m n t s understandsome of me d flocult c m cepts frequently encountered in chernisby. Canhibutions that will produce a greater appreciation and knowledge of political, religiws. ecom i c , historical, and scientific aspects of life are encouraged.
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F i g m 1. An increase in pressure (concentration)anly results in en increaseof rate up to a -in poim, at which renctim changes Iran first ader to zero ader.
first tozero order. (Fig. I). One can point out that many enzyme-catalyzed reactions hehave similarly, and one can give the usual explanation that, in the case of the gas reactiun, the initial rate reaches a maximum when the catalyst is covered with a monolayer of adsorhed moleculm and, in the case of the enryme-ratalymd reartion, the rate reaches a maximum when all the active sites are heing utilizrd at any given instant'..'. The. analogy that I like tu use here is [hat of a hairdresser's salon (or I~arher'sshop) in which there are four rhairs and i,,w assistants (a chair and an assistant being analogous to an aca accept that each assistant works tive site). I ask the class t at exactly the samespeedand that no matter what type of cut the customer rrquires it takes them exactlv fifteen minutes to do the job. If there is one customer in the-shop, he or she is processed in fifteen minutes and the reaction rate is one customer per fifteen minutes. If the number of customers entering the shop is two, three, or four (i.e., the concentration is increased,, the reaction rate would he increased to two customers per fifteen minutes, three customers per fifteen minutes, or four customers per fifteen minutes respectively. However, the salon staff (active sites) are now working a t their maximum capacity. If five customers enter the salon a t the same time ke., a further increase in concentration), only four of them can he served simultaneously and the rate will remain a t four customers per fifteen minutes. The moral of this story is, of course, never to go to the hairdresser without an appointment! Flies In an Elevator The next analogy is one which can he used during a general chemistry course and in an introductory organic course. When discussing the shapes of molecules, I usually find that the shape which students find the most difficult to fully comprehend is the tetrahedral-in spite of the use of molecular models. I usually approach this &pic from the point of view of the atoms surroundinn the central atom being arranged in such a way that they are as far away from one another as 'See for example: Masterton. William L.. and Slowinski, Emil J.. "Chemical Principles." 4th ed.. W. 6 . Saunders. Philadelphia, 1977, p. 393.
Referencein footnote 1. p. 400. Stevens. "Chemical Kinetics." Chapman and Hall. London. 1965,
Ch. 7.
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Journal of Chemical Education
Figure 2. When f a n strangers enter an elevator, lhey each stand as far away horn one another as possible.
Figure 3. A tetrahedron shap may be described by tour flies In a cubic elevator-a11 as far away horn one another as possible.
wssihle. When we come to the case where we have four atoms surrounding the central atom, for example rH4or SiU4.1 mk the students to think of the way in which people behave in elevators. In order for the analogy to work we must picture a cubic elevator rather than the more conventional design. When four strangers enter such an elevator, each person usuallv retreats to one of the corners-that is, they all stand as far away from one another as possihle. (Fig. 2). However, suppose we have four flies in the elevator rather than four people. The four flies get as far apart as possihle from one another by assuming the following positions: fly A goes to the rear top~right-handcorner, fly B to the front top left-hand corner, fly C to the rear bottom left-hand comer, and fly D to the front bottom right-hand corner (see Fig. 3). All of the flies are as far apart from one another as they can he-in fact. each flv is the leneth of the diaeonal of the side of the L"bi &iy f k m the oth:r three flies. 1; addition, the four flies are all eouidistant from the center of the elevator. We have only to imagine the presence of a carhon atom a t the center of the elevator. and to think of the flies as heina hydrogen atoms, and we'have a mental picture of the geometry i f a molecule of methane.
After heing reminded of the fact that one mole of any sub. stance contains Avoaadro's numher 16.02 X I@') of molecules. the idea of a given numher of moles of students quickly ammonia reacting with an equal numher of moles of hydrogen chloride to form that same numher of mules of ammonium chloride. The term theoretical yield can aLw he introduced at this point. The class is then asked to imagine the arrival of a taxi containing iour additional males. Thc rmm now contain* fourteen males and ten females, tjut obviously the maximum number of dancing couples remains at ten. T h e males (ammonia~are in excess and the females (hydrogen chluride) determine the maximum number oicouplrs that can take t u the flaw at any given time. In chemical terms the females have become the limiting reagent. At this point one can introduce the idea of percentage vield-althoueh ,~~~~~ .. I nrefer to defer this until a later date (dance). Suppose that one of the females has a headache and d w s n d feel like dancinr. Whether we have our oririnal - ten males or our subsequent fourteen, the maximum number of couples that we see dancine a t anv . eiven time is now onlv nine-90 percent of the maximum. In a chemical reaction this corresnonds to a 90 nercent vield. Before vroceding any further one c k stress the LpoGce of basing &ichiom&iE calculations upon the amount of limiting reagent present. Thus
Danclna- Couples Teaching basic stoichiometry provides the opportunity for using the final analogy to he described here. After discussing a relatively simple combination reaction in which the reactants comhine in a 1:l ratio, for example NHxg, + HC4,)
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NHd&)
I then nroceed to the limitine reaeent situation and might ask studen~9what they think will h&pen if we mix two n&La of ammonia with one mole of hsdroren chloride. Only rarely are 100% of the students able td tellme that one mole of ammonium chloride will he produced and that one mole of ammonia will remain unreacted. This provides the opportunity to use the first stage of the "Dancing Couples" analogy. I ask stu&nts tr, imagine that the$ are at a party or a small dance and that the males are equivalent tt, ammonia molecules and the females are equivalent to hydrogen chloride molecules. A male and female dancing together represent a molecule of ammonium chloride, and in this locality i t is not socially acceptable for two members of the same sex to dance together. Students realize a t once that if we have ten males and ten females present then the maximum numher of dancing couples is ten. By reminding them of the original analogy the class quickly catches on to the fact that ten molecules of ammonia will react with ten molecules of hydrogen chloride to produce ten molecules of ammonium chloride.
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fourteen males + ten females -ten dancing couples (14 mole NHd (10 mol HCI) (10 mol NHdCl) and if we observe that 14 males + I0 females 8 dancing couples (I4 mol NHa) (I0 mol HCI) (8 mol NHd then our percentage yield is given by: number of couples observed (actual yield) X 1W% theoretical maximum number of couples (theoreticalyield) - 8 couples X 100%= 80% 10 couples
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Havingdealt with a reaction in which the reagents comhine in a 1:l ratio, I then go on to talk about a reaction in which the ratio of the combining reagents is 2 1 . An example would he: C(.l + 2 Si,)
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CSZI,,
In our dancing analogy we now assume that a new dance craze has swept the nation in which one male (carbon atom) is simultaneously partnered by two females (sulfur atoms). Again we go to a small dance and find that if we have ten males Volume 60
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present and twenty females, we can form ten dancing units. The arrival of four additional young men to give a total of fourteen males and twenty females does not increase our yield of ten dancing units since we need two women to partner each man and only twenty women are available. Students are often surprised to see that although there are more females than males present, the women are the limiting reagent and the males are in fact in excess. Upon returning to the reaction
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between carhon and sulfur it is much easier to explain why we first need to determine which of the two substances is the limiting reagent before we do any stoichiometric calculations. It is my helief that the use of analogies, such as those outlined above, brightens up lectures, helps to develop rapport with students, and allows students to visualize chemical phenomena in everyday terms.
