In the Classroom edited by
applications and analogies
Ron DeLorenzo Middle Georgia College Cochran, GA 31014
The Painting–Sponging Analogy for Chemical Equilibrium Andoni Garritz* Facultad de Quimica, UNAM, Mexico, D.F. 04510 High school and freshman undergraduate students have great conceptual difficulties understanding chemical equilibrium. A large number of misconceptions have been reported (1–5). Two ordinary ways exist for teaching chemical equilibrium: the “thermodynamic” (6–9) and the “rate” (2, 10) approaches. The latter is used in most textbooks. This manuscript presents an analogy of the second kind to quantitatively represent chemical equilibrium by the length of a line that is painted and removed at competing rates. In the classroom, this analogy has had a good influence on students’ learning processes. It is similar to the mechanical analogy (11, 12) of filling and transferring glasses of water from one fish tank to another.
walking rates (“rp” and “rnp”) and efficiencies (“pe” and “npe”) of the painter and the nonpainter, to appreciate the different final length of the road line. Note 1. This program was suggested by Hal Harris, one of the re-
One of the inhabitants of Paintersland decides to paint a line down the middle of a 100-meter road connecting his town with Nonpaintersland, the town of experts on paintremoving. The awkward painter starts the line, but the paint bucket is left in town at the point where the line begins. Therefore, each time the brush is dry he must walk back to the bucket to re-wet it. Then he walks once again to the line end and continues his painting. Meanwhile, a nonpainter of the other town takes a sponge with paint remover in it, walks to the freshly painted line, and begins to remove it, thus partially undoing the painter’s action. Each time his sponge is dry he, too, has to walk back to his town to the bucket of paint remover, re-wet his sponge, return once again to the line, and continue to remove it. What is the end of the story? How does the line distance change with time? (See Figure 1.) Thinking of this analogy, students always accept that the equilibrium point of the line length is reached when speeds of painting and sponging are the same. If painter and nonpainter have equivalent skills and walking speeds, the line stops growing half way between the two towns. But if the painter is faster and more efficient than the nonpainter the line goes farther (or the other way around if the nonpainter is quicker and more skillful). The notion of chemical equilibrium as a dynamic state is well understood with this analogy. Figure 2 represents the line distance as the process advances. The result is similar to the product concentration in a real approach to chemical equilibrium, starting from the reactants. The general shape of the figure is a consequence of the painter (and nonpainter) returning to their towns after each segment of the line is painted (or removed), and that is why it resembles a real product concentration graph of a reaction tending to equilibrium. The algorithm to obtain Figure 2 is the QuickBasic routine1 of program 1 (see Appendix). Students should be encouraged to experiment with the model by changing the parameters so that the line begins “completely painted” (length = 100), with the same equilibrium result, or by modifying the
Antonio Ceron
The Analogy
Figure 1. The painting–sponging analogy for chemical equilibrium. Painter and nonpainter in action. viewers of this manuscript. The original one was presented in a spreadsheet. I would like to acknowledge this contribution.
Literature Cited 1. Johnstone, A. H.; MacDonald, J. J.; Webb, G. Educ. Chem. 1977, 14, 169–171. 2. Hackling, M. H.; Garnett, P. J. Aust. Sci. Tech. J. 1986, 31, 8–13. 3. Burgguist, W.; Heikkinen, H. J. Chem. Educ. 1990, 67, 1000–1003. 4. Gordus, A. A. J. Chem. Educ. 1991, 68, 138–140, 215–217, 291, 292, 397–399, 566–568, 656–658, 759–761, 927–930. 5. Banerjee, A. C. Int. J. Sci. Educ. 1991, 13, 487–494. 6. Dickerson, R. E.; Gray, H. B.; Darensbourg, M. Y. Chemical Principles, 4th ed.; Benjamin: New York, 1984. 7. Atkins, P. W. Physical Chemistry, 5th ed.; W. H. Freeman & Co., New York, 1994. 8. David, C. W. J. Chem. Educ. 1988, 65, 407–409. 9. Harris, W. F. J. Chem. Educ. 1982, 59, 1034–1036. 10. Garritz, A.; Chamizo, J. A. Quimica; Addison-Wesley: Wilmington, DE, 1994. 11. Sorum, C. H. J. Chem. Educ. 1948, 25, 489. 12. Laurita, W. J. Chem. Educ. 1990, 67, 598.
Appendix Program 1: QuickBasic routine. I used the Microsoft QBASIC software. A line can be added before “NEXT i” to save the set of road line lengths into a file in order to get the graph using a separate program.
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Journal of Chemical Education • Vol. 74 No. 5 May 1997
In the Classroom 80
sp = 1 snp = -1 pe = 1 npe = 0.5
70
Line length (m)
60 50 40 30 20 10 0 0
5,000
10,000 Time (s)
15,000
Figure 2. Graph of the results of program 1 for the road line length. The walking speed of the painter is 1 m/s and that of the nonpainter is 0.7 m/s. The painter manages to paint 1 m of the line with one brush content, while the nonpainter’s sponge can remove only 0.5 m each time. The equilibrium point is achieved around 74 m from Paintersland.
d = 100 rp = 1 rnp = .7
‘Distance between towns (m) ‘Rate of painter walking (m/s) ‘Rate of nonpainter walking (m/s)
‘Sign of the painter initial direction ‘Sign of the nonpainter initial direction ‘Meters painted with each brush content ‘Meters erased with each solvent content in the sponge ‘Line length (m) ‘Painter initial position (m) ‘Nonpainter initial position (m) ‘Time elapsed (s)
length = 0 p=0 np = d FOR i = 1 TO 15000 p = p + sp * rp np = np + snp * rnp IF p>= length THEN length = length + pe sp = sp * (-1) END IF IF p
