applications and analogies
edited by RON DELORENZO Middle Georgia College Cochran, GA31014
A Student's Travels, Close Dancina, Bathtubs, and the Shopping ~ a l More c ~ n a l o ~ i eins~eaching Introductory Chemistry Geoff Ravner-Canham Sir ~llfredkrenfeCol ege Corner Brook. Newio-no ana. Canaaa A2H 6P9
Although analogies have their limitations ( I ) ,they have been found to be verv useful in relatine chemical conceots to the everyday lives'of students (2,3). Tn this article, I A l l describe four analoeies that can be used for discussion in introductory chemiitry classes. A Student's Travels The probability model of the atom is one of the most abstract topics in the chemistry curriculum. I t seems to have no relevance to students. Yet I point out to students how their locations vary with time just as those of electrons. To illustrate this, students are asked to consider their location a t intervals throughout the week. Figure l shows the probability plot of a student who lives away from home in a boarding house, goes to a nightclub periodically, and travels home on weekends
.. .
f.: + Boarding House
.
0:
t
Home
.
C Nightclub
Figure 1. Probability plot of the location ot a typical student during a week. Like the electron-density plot for a n electron, there i s a high probability of finding the student in certain locations, such a s i n the college. I n fact, there is a reasonably high probability of the student being in four locations: a t the college, a t the boardinghouse, a t the nightclub, or a t home. There is a very low probability of finding the student between those four locations. The analogy can approach the ideal if one considers a student who commutes from home and lacks any social life. Aplot of this student's location with time would resemble that of a p-orbital, that is, the student would be a t college or a t home, but there would be little chance of finding h i m h e r i n between (Fig. 2). This is analogous to the p-orbital, where there is a high probability of finding the elec-
I
Figure 2. Probability plot of the location of a student who only con mutes from home to college.
tron within one or other lobe of the orbital, but a zero probability of finding the electron in the nodal plane separating the two orbital lobes. A student who lives on campus and who attends only College social events will have a single-focus probability plot. This would closely resemble a two-dimensional version of the s-orbital electron-density plot. This device can be turned into a project where students are required to plot their location throughout the day (or week) a t periodic intervals. Close Dancing A number of texts appear to confuse the three types of atomic radii: ionic. covalent. and van der Waals. This confusion is apparknt in the plots of atomic radii that show the noble eases to be much lareer than the oreceeding halogen ( 4 );hen, in fact, the covalent radius bf a halogen i s being compared with the van der Waals radius of the noble gas. lh illustrate the difference between the covalent and van der Waals radius, I use the analogy of close dancing. The dancing pair are pressed closely against one another-just as the two atoms i n a covalent bond are pressed together with their electron clouds overlapping (Fig. 3). The distance from the center of one individual to the contact point is less than the normal radius of the individual. However, when two couples brush past one another, the contact distance represents the maximum radius of that individual, that is, the van der Waals radius. Bathtubs The importance of intermolecular forces often is overlooked (5). One reason why the topic is covered so fleetingly lies with the difficulty of explaining London (dispersion) forces. However, many of us have lain in a bathtub and, by appropriate movements, caused t h e water to
F I ~ L I3LThe ' danclng coLples anaogy of alomic rao I n rnls L, ro F eye v ew' me conlac! o srance w tnln a co-p e represents tic cova en! rad .s wn e Inn conlscl o.slancn from one co.pls lo anorner represents the van der Waals radius. Volume 71
Number 11 November 1994
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Figure 4. "Electron wate? moving in a single bathtub. "slosh" from one end to the other. This motion provides an excellent analogy for these forces. I ask my students to visualize a nonpolar diatomic molecule as if it were a bathtub full of "electron water" (Fig. 4). The water represents the electron-density plot, while the two nuclei are located on the bottom of the tub. If the electrons are "sloshed" up to one end of the bathtub, that end will become somewhat negative while the other end will become somewhat positive. Yet, an instant later, the electrons will "slosh" up to the other end of the tub, reversing the charge arrangement. On average, though, the electrons would have a level surface in the tub. Then I ask the students to visualize two bathtubs in a row. If the electrons in one tub "slosh" away from the second tub, the electrons in that tub will be attracted to the exposed nucleus in the first t u b t h e London (dispersion) force (Fig. 5). The following instant, the electrons have flowed to the other end of the tub, giving the same attraction but of opposite polarity (Fig. 6). Once again, though, the average electron "level" would be flat.
Figure 5. "Electronwater" in a pair of bathtubs.
The Shopping Mall The equilibrium rvocess is another diff~cultconcept for students to grasp. L two-floor shopping mall provides a useful analogy in this case. Assume access from the parking lot is restricted to the lower floor. When the mall opens in the morninp, shoppers flood in. Some of the shoppers travel up the rscalnt& hut initially none come down. 'fhus, only the forward "reaction" can take place at this timc. As theshoppers complete their purchases upstairs, the number descending the escalator increases. The reverse "reaction" is starting to occur. Finally, the point is reached at which the rate of people going up matches the rate of people coming down-the equilibrium situation (Fig. 7).
Figure 7. Shoppers in a bi-level shopping mall. The analogy can be modified by the suggestion that there is a biz discount store on the upper floor. and thus the actual n k b e r of shoppers upst& may be much greater than the number downstairs. In this case, one can refer to the concentration of shoppers, that is, the numher of shoppers per square meter, as being higher on the upper floor. I t is only the mte of ascent and descent that becomes equalized. This is quite a strong advantage of the analogy. It avoids the misconception that, in an equilibrium, the proportions of reactants and products must be the same. To finish, students can be asked to identify the limitations of the analogy. The most obvious one is that, as the day goes on, the flow of shoppers reverses, so that the rate of descent starts to exceed the rate of ascent on the escalators. Equilibria, however, do not spontaneously revert to the starting conditions. As pointed out by Webb ( I ) , the identification of such limitations by students gives the instructor an appreciation of whether the analogy itself has been understood. Acknowledgment
Figure 6. "Electron water" moving in the opposite direction. The analogy is particularly useful because the variables of the bathtub model match the variables of the intermolecular forces. Thus, students recognize that the "sloshing" is more effective the longer the tub and the more "electron water" in the tub. Indeed, the London (dispersion) forces are stronger when the molecules are longer and when the molecules possess more electrons.
Julian Dust is thanked for helpful comments on the manuscript. Literature Cited 1. Webb, M.J.SehoolSci Moth
1885.85,MW50.
2. Laot,A. M.J C k m . Edue 198%60,748-750.
3. Last,A M.J
C k m . Edvr
1985.62.1015-1016.
4. Huheey, J. E. J. Chrm Edue 1968,45,791-792.
6. Rayner-Csnham, G. W Chemlkch 1992,22,32%332.
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Journal of Chemical Education
