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JAMES0.SCHRECK Univenitq Nonhern Colorado Greeley,CO 60639
The "Bean Lab" A Simple Introduction to Equilibrium, Paul D. Dickinson Catlin Gabel School, 8825 S.W. Barnes Road, Portland, OR 97225 Walt Erhardt Battle Creek Area Mathematics & Science Center, 354 North 27th Street Battle Creek, MI 49015
The equilibrium of the reaction Fe3 + SCN- = FeSCPt often is used in laboratory experiments to teach that equilibrium constants do exist and that they are constant and can be calculated. Teaching high school chemistry, we learned that there are several areas where students encounter obstacles when they carry out this lab designed to conceptualize the study of equilibrium. These factors include: 1.Confusion about the directionsfar findingfinalconcentrations in each reaction vessel and the mathematics involved. (Vhy do I have to subtract these?") 2. Diff~eulties with the highly abstract idea of a constant relationship among concentrations at equilibrium. 3. Difficultiesunderstanding that it is the rates ofthe readions that are equal at equilibrium, not the concentrations of the reactants and products.
An activity that has proven helpful to us to overcome these difficulties is the equilibrium "bean lab". It provides a concrete model of equilibrium from which students may move to more abstract aspects of the concept. The purpose of the activity is to (1)learn to recognize an equilibrium situation, and (2) learn to define the equilibrium in terms of microscopic properties and molecular properties.
930
Journal of Chemical Education
Procedure Each group is provided with a suitable reaction vessel (one that students can reach into easily with their hands such as a plastic pail or 600-mL beaker), and a specific number of each of four types of beans. We specify 30 each of small red beans (R), great northern (white) beans (W), pinto beans (P), and blackeyed peas (B). These beans are all about the same size, are difficult to distinguish by feel, and are easy to find in most supermarkets. The beans are all placed in the reaction vessel. This provides an initial concentration of each type to start a "reaction". Students also will require about 20 additional beans of each type for their "extra" pile to be used later. The "reaction" proceeds when students randomly withdraw from the vessel the minimum number of beans necessary for either a forward or reverse reaction to occur. For example, if the reaction R + P = 2W + B is assigned to be studied, a minimum of three beans must be withdrawn during each trial in order to allow for either a forward or reverse reaction to occur. If the student were to withdraw two pinto beans and one white one, neither the proper combination of reactants nor the proper combination of products have taken part in this "collision", so the collision is said to be unsuccessful, andno reaction occurs. The beans are placed back in the reaction vessel, stirred thoroughly
with the fmgers (or a stirring rod), and another three are withdrawn. If two whites and a blackeyed pea were now withdrawn, a successful wllision occurs, and a reverse reaction takes place. The three "reacting" beans are removed from the vessel and the products of their reaction, a red bean and a pinto bean, are added to the vessel instead. A sample data table might, so far, look like this: + 16 1 R + 1P = 2W Equation: Trial
Reaction
0 1
NR
2
c
R
P
W
B
30
30
30
30
31
31
28
29 etc.
In a successful forward reaction, one red, one pinto, and one white might be withdrawn from the vessel. In such a collision, only the red and the pinto would react. The third bean, the white one, would be returned unreacted to the reaction vessel along with the two white beans and the blackeyed pea producedin the"reactionX.I t should benoted at this point that there are factors other than collision frequency that govern reaction rates. The orientation of molecules in soace (esoeciallv for the more comdex colli. . sion required for the reverse"reaction), and the activation enerw are also imoortant. A discussion of how the model coulzbe altered toiake these variables into wnsideration might prove interesting. To keep the model simple though it should be emphasized that we will assume that whenever the reactants collide in the appropriate ratios they react successfully. As more trials are undertaken and more "wllisions" take place, the number of white beans and blackeyed peas will increase. This is because onlv two of the three beans must be correctly withdrawn for-a forward reaction to occur; whereas. all three of the beans must be wrrectly withdrawn for a reverse reaction to occur. Thus, the "rate" of the forward reaction will predominate at first. Soon, however, the wncentrations of the white beans and blackeyed peas will increase to the point where it is more probable that thev will be withdrawn and reverse reactions will be&n to t& place more frequently. Eventually the higher ckcentrations of the "products" will offset the fact that only two out of the three beans must be withdrawn correctly for a forward reaction to occur. and the rates of the forward and reverse reactions will b&ome equal (that is, a t equilibrium). Once each student has completed 20 successful reactions, not trials. vou mav ask. "Has the reaction reached e~uilibrium y e t F ~ist p&sibl'e that it has. However, it is Lest to have students continue until the distribution of forward and reverse reactions is even. This can easily be evidenced by notine whether the numbers of each kind of bean have bkcome Fairly consistent and are merely alternating between two or three values. There are usually about 20 to 23 red beans left in the reaction vessel, although the laws of probability allow some exceptions to this general rule. We have found that, usually, 120-150 trials, not reactions, are sufficient to reach this point. Students have no trouble
completing this in 45-50 minutes if they are prepared ahead of time and arrange their "extra" pile of beans into individual piles of reactants and products that may be picked up and exchanged quickly. We suggest that students should proceed until ahout half of their lait 10 reactions are forward, and half are reverse reactions. This helps to insure that their early arrival at an apparent equihbrium is not a fluke of probability. We ask students -~~~ ~to exolain ~ - the- difference ~ ~ in the ratio offorward to reverse reactions a t the beginning of the experiment and the end of the exoeriment. Durine the eatherine of data. the teacher shouid be careful to watch-for stud& whd have a ~rewnceived(incorrect) notion of what "will" havpen anri attempt to manipulate each trial to produce the expected results. A mixture similar to the starting mixture of 30 beans of each tvve mav be disolaved in a beaker or a eraduated cylinder next." to eac6 student's "equilibriumr mixture. There is a visible difference in the overall "wlor" of the two mixtures owing to the shift away from the darker red and into beans toward the lighter white beans and blackeyed peas. This "macroscopic" difference is similar to color changes when real solutions are mixed and come to equilibrium. Students might be asked to explain this color difference and asked if the color would become more different if the reaction were allowed to continue. This helps to accomplish one of the two stated purposes of the lab, "to explain in terms of macroscopic qualities". ~~
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Summary The use of the '%bean lab," either in lieu of or in addition to the use of an actual laboratory experiment, has been helpful in teaching students of varied conceptual abilities. It has been particularly helpful with students who are still largely concrete in their approach to chemistry. We have prepared questions that make it possible for students to think about and discuss changes in equilibrium wnditions in terms of a visible model. When asked what would happen to the number of each kind of bean if 10 additional red beans were added after the system had reached "equilibrium," nearly all of our students predict that the chance of collisions between red and pinto beans would increase and more white beans and blackeyed peas would be produced. Thev also see that for evew two white beans and blackeved peas produced, one of thimnew"red beans and one ofthe remaining pinto beans must be subtracted. This sets the stage for Le Chgtelier's Principle and for the subtraction step done later during the thiocyanato-iron ion laboratory. Our students have been able to transfer ideas gained durim the bean lab to other visible models and to chemical equations. They can see that reactants and products are part ofthe same system, rather than theleft and right sides of an equation, separate from one another. The addition of one kind of bean has an explainable and predictable effect on the concentration of other beans in their reaction vessel. This is an important aspect of any good model and, in this case. it orovides a n oooortunitv to discuss whether there is some sirt of matheGtica1 reiationship among the numbers of each kind of bean at equilibrium. After usine the bean lab it is easy to develop a set of questions that &etch students from this concrete model toward more abstract aspects of the study of equilibrium.
Volume 68 Number 11 November 1991
931
