RON
edited by: DELORENZO
Middle Georgia College Cochran. Georgia 31014
Some Analogies for Teaching Rates/Equilibrium Davld J. Olney Lexington H. S. Lexington, MA 02173
Muny high school teachers have found that theconcepts of reaction ratesand dynamicequilibrium are itosay theleast!) truut~lrsnmeto students. Heing able to ~ u p p l vsome analogies that appeal to their e \ ~ r y d n yexperience and or imaginations oftentimes helus in their understanding. " This article will present in capsule form several analogies developed by the author over his many years in the chemistry classroom that seem to be effective. Before starting. -. we will note that manv teachers have their own favorite veriions of these, or will add their awn twists to them tosuit their teaching stvles. That's understandable.. . and acceptable! We'll also ;dmit that there is a potential danger to using analogies. The author commends a teacher friend who early in the school year holds up a globe and asks "List 15 ways in which this thing does not accurately portray planet Earth." Perhaps a similar probe could be done of these stories. But we shall leave that exercise to you and your knowledgeable students. ~~~
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The Bee Hive (for Establishing Equlllbrlum) Story #I. Some schools maintain in an outside window of a science room a 2-ft X 2-ft X &in. elass-walled box containing a working beehive. A short transparent piece of tubyng throueh the window casinaallows the bees to enter and leave the hive a t will. A queei and perhaps 100 other bees are provided by a supply house to start the colony, and the beginnings of a honeycomb are provided within the box. Once the hive is in full operation, one can observe the comings and goings of bees (some of them especially marked) during a 15-hour period. At dawn all the bees are inside: no movement through the tube. Shortly after dawn, there is one-way traffic to the outside. A bit later a few bees return, but even more leave. By mid-morning equal numbers of bees come and go through the tube per unit time. The population of bees in the hive achieves a steady state (say 75 out of 100 total). An afternoon storm causes inward rate to increase temporarily; the population inside rises a bit, then a new steady-state is achieved. As night approaches, more return than leave until all are back in the box. I t is suggested that one observer (A) can watch just the connecting tube and count bees comine and aoina per 10 minutes. inother observer (B) can simply tall; bees-inside the hive at the start of each half-hour. At middav, observer B might think the tube was somehow closed off because the population inside remains quite steady. However, observer A assures himher that bees are indeed moving, but in equal numbers (per unit time) both ways. Story #2. The Fishbowl One can scarcely improve on the visual demonstration of population equilibrium among goldfish in a closed system achieved in the Chem Study film entitled Chemical Equilibrium.' If any high school teacher has not seen this film (and we learned at one . nonular . summer institute that about 33% had not!), you are urged to do so. One can only admire the 696
Journal of Chemical Education
patient photography needed to capture the goldfish swimming to achieve population equilibrium! Story #3. The Boy in the Well (for Actlvatlon Energles) Imagine a countryside with a most unusual topography. I t has very flat plains, with extinct volcanic cones (with extremely smooth sides!) pushing up now and again. On top of one such hill lived a family with a young boy, who all too often was left alone for several hours at a stretch. On one such day, he was playing with a tennis ball. It got awav from him, and in his efforts to chase it he and the ball tumbled into an empty well on the hilltop. He was not hadly hurt as he tumbled to its hotrim but now faced the dilemma of getting out! He first tried scaling the well's slippery walls but always lost his grip and fell back. He next reasoned he could tunnel out to the side of the hill and roll down to the town below from there. He started in with his trusty jackknife, but after several minutes of scraping it became obvious the task was too much. Then came the moment of inspiration! He whipped out a magic marker and wrote on the tennis ball "HELP, I'M STUCK IN T H E WELL ON T H E TOP OF T H E HILL". He reasoned that the ball would naturally roll downhill from his point of higher elevation and with luck would be spotted by someone down there. Of course, merely dropping the ball from shoulder height didn't help much; the well's bottom and sides prevented further motion. He toyed with the idea of scratching out a tunnel to the side big enough for just the ball, but rejected it as impractical. Clearly the trick was to get the ball u p and out. His first effort sent it 9 feet in the air. I t bit a wall of the 12-foot deep well, and returned to his hands. A stronger effort got it 15 feet into the air, (and so above the well-head) but it went straight up-and then straight back down. But finally an input of energy on his part (and some english on the ball) got it clear of the well. I t did indeed roll down the hillside was picked up by a child down there, helicopters were summoned, and the boy was rescued. A happy ending! The analogy to chemical systems often driving to achieve a state of minimum potential energy, but with activation barriers to overcome, is easily made. And perhaps with the right catalyst, he could have made that tunnel! Story #4. The Dance Hall (for Le Chateller's Prlnclple) Welcome to Chem County's favorite dance hall. It features unusual construction features. The front doors open to a seating gallery, complete with water cooler and fans. T o get onto the dance floor, the c o u ~ l emust s pass through a revolving door, and dancing must be done aicouples. On one particular night, 80 boys and 60 girls arrive as singletons. After a bit, the dance floor gets filled to its capacity of 45 couples and equilibrium is established. However, it's dynamic as individuals pass through the revolving door. Now consider various scenarios that might "disturb" this equilibrium: I The film Chemical EquMlbrium was originally produced as part of the Chemical Education Material Study under an NSF grant. It can be rented or purchased from a variety of commercial sources at present.
1. Some extra couples sneak out a rear door adjacent to the dance
floor. 2. Some couples sneak in that unlocked door. 3. Some extra singleton bays arrive through the front door, anxious to dance. 4. The air conditioning breaks down everywhere in the hall. 5. The air conditioning goes berserk, coaling the entire hall to an uncomfortable level. 6. The revolving door isailed, allowing TWICE as many people per minute to pass through. It's not difficult for students to predict the shift in the "point of equilibrium" each such disturhance sets into motion. Immediately I present the reaction PCl,(g)
+ Cldg) = PCls(d
which is exothermic by 93 kJ/mol. Suppose that it's a t equilibrium with 0.35, 0.15, and 0.45 mol/L, respectively. We pose for discussions such "what-if' questions as the effect of
1. somehow removing PCI5 from the container,
2. inserting extra PCIs, 3. inserting extra PCls, 4. raising the temperature of the entire container, 5. lowering the temperature of the container,and 6. inserting a catalyst into the system (at equilibrium)
Note the close analogy to the six disturbances in the dance hall. In a nonquantitative manner, one can predict the changes in concentrationsof the threechemicals likely toensue. It all helps to make graphic the meaning of "shifting the point of equilibrium to the right". The author has searched in vain for a plausible disturhance to the dance hall akin to increasing the pressure on the system by lowering the volume. Perhaps the reader will invent one! The author is convinced that analogies like these do aid in making the comings and goings of mulnculei (so vivid in the mindsof instructors!^ more undcritandablefor ourstudents, by involving their imaginations as well.
Volume 65
Number 8 August 1988
697
