Research: Science and Education
Simulations for Teaching Chemical Equilibrium Penelope A. Huddle* and Margie W. White Department of Chemistry, University of the Witwatersrand, P O Wits, 2050 Johannesburg, South Africa; *
[email protected] Fiona Rogers St Mary’s School for Girls, Waverley, Johannesburg, South Africa
Analogies are not new to science; they have been used through the ages by both scientists and students to help them understand theoretical concepts (1). However, in recent years renewed attention has been given to the role of analogies in science teaching (2) and it has been suggested (3) that the goal of science education research should be to invent analogies and evaluate their effectiveness in science lessons. These analogies may be verbal or may involve actual physical experiences, diagrams, simulation experiments, and even computer-assisted activities. Ausubel (4 ) was the first to suggest that students need to relate new knowledge into existing mental structures for meaningful learning to occur and for students to be able to apply the knowledge to other situations. Concrete examples are easier to integrate into existing knowledge than abstract ones and, if carefully chosen and presented, can enhance the intelligibility and plausibility of explanations (5). Certain topics in chemistry are highly theoretical and give learners great difficulty (6 ). Thus, the teaching of chemistry lends itself to the use of analogies to explain abstract concepts (7, 8) where the analogies are generally recognized to generate meaning through a constructivist pathway (9). Not surprisingly, findings by researchers (7, 10) show that analogies may be more effective for students of lower formal reasoning and are less useful for more capable students who have probably already reached the formal operational stage of development (11). Results of studies in the classroom (7 ) show that the use of analogies is infrequent and less effective than it might be but that a competent teacher can systematically integrate analogies into her classroom practice (12). Chemical equilibrium is rated as the most difficult concept for students to comprehend (13, 14 ) and one of the more difficult sections of physical science to teach (15–17 ). It is therefore not surprising that it is a topic in which teachers frequently use analogies and in which analogies are often cited in textbooks (7 ). The analogies themselves may lead to or reinforce alternate conceptions (18). For example, the often used analogy of water flowing in and out of a sink to show the constant dynamic properties of a steady-state open system (7 ) does not accurately mimic chemical equilibrium. In fact, it may reinforce the documented alternate conception in equilibrium (13) that the forward reaction goes to completion before the reverse reaction commences. Harrison and Treagust (18) emphasize the need for a systematic approach when using analogies and the need to map out similarities and differences between the analogy and target (the science concept being studied) to prevent further alternate conceptions from arising in the minds of students during the use of an analogy. An in-depth study carried out at the University of the Witwatersrand (Wits), Johannesburg, South Africa, revealed 920
that our first-year students espouse most of the common alternate conceptions in chemical equilibrium (19). Studies by Bradley with student teachers in South Africa showed that these alternate conceptions were not remedied by three years of study of chemistry at a tertiary institution (20). Bradley’s work reinforces studies by Driver (21) and Novak (22), who found that students’ ideas are extremely resistant to change. This emphasized our need to find a simple yet effective analogy for equilibrium, one that would address most of the known alternate conceptions (13, 15, 23–26 ) in this topic. A series of simulations was chosen, an adaptation of the Equilibrium Games of Lees (27 ) used to show partitioning of a substance between two phases. In several ways the simulations mimic the microscopic events that lead to and then maintain a dynamic equilibrium. More importantly, the graphs drawn at the end of the simulation experiments are similar to concentration-versus-time graphs obtained for real reactions on approach to equilibrium (cf. ref 28). This allows easy mapping of the analogy to the target. The simulations can be extended to incorporate aspects of Le Châtelier’s principle and demonstrate the constancy of the equilibrium constant at constant temperature (a feature of chemical equilibrium that our students have been slow to grasp). Also of importance, especially in South Africa and other developing countries, is the fact that the requirements for the Game are so simple that even the most poorly equipped schools and colleges should have access to them. We set about designing the simulations and then testing them on various audiences to determine whether any improvement in understanding of the concept had occurred. Pilot Study—Methodology From 1993 to 1996 the simulations were piloted on four very different audiences: Grade 12 school pupils, student teachers, experienced teachers, and college lecturers. Each trial of the simulations (referred to subsequently as the “Equilibrium Games”) led to minor modifications of the original Games. In this paper we present the final form of the Games in a systematic manner as recommended by Harrison and Treagust (18).
Step 1. Introduction of the Target Concept to Be Learned Explanations about equilibrium are kept to a minimum. Students are simply told that not all chemical reactions go to completion. In fact, for many reactions in a closed system, as the concentration of product molecules increases, they begin to collide with each other and re-form reactant molecules. Comparison is made of energy profile diagrams for reactions that go to completion (and have very different activation energies, E f and E r, for the forward and reverse reactions, respectively) and those for reactions that reach an equilibrium (where E f and Er are similar in value).
Journal of Chemical Education • Vol. 77 No. 7 July 2000 • JChemEd.chem.wisc.edu
Research: Science and Education
Step 2. Introduction of the Analogy The students are given two sheets of graph paper, 49 cards (ca. 3 × 4 cm, colored on one side and white on the other; or a set of playing cards!), and a large shallow box (about 60 × 300 × 5 cm) to represent volume. An explanation of how the unmodified Equilibrium Games work has been given elsewhere (29). The refined version is outlined briefly here. Students work in pairs—one “reacting” the colored (reactant) cards and the other “reacting” the white (product) cards. To begin, a specified number of cards are placed colored-side up in the box. Game 1 Students are told that a certain fraction of the colored cards (e.g., 1⁄4) have sufficient energy to change to a white card and a different (larger) fraction of the white cards (e.g., 1 ⁄3) have sufficient energy to change back to a colored card. For each cycle, one student randomly turns over 1 of every 4 colored cards at the same time as the other student turns over 1 of every 3 white cards. In a case where the number of cards of a certain color is not exactly divisible by 3 or 4, the number of complete sets divisible by that number is taken. The number of colored and white cards visible at the end of each cycle is recorded in a table (Table 1a) against the number of the cycle. Students also record in the table the number of colored and white cards turned over in each cycle and determine the change in the total number of white and colored cards from
the end of one cycle to the next. They are told that each cycle represents a certain time interval (10 s, 1 h, etc.). This process is repeated until a stage is reached where the number of colored cards turned over in a cycle is equal to the number of white cards turned over and the students decide to stop playing the Game. (If 49 cards were used as in the example above, “equilibrium” would be reached after 5 cycles; see Table 1a.) Students now plot a graph of concentration (number of “reactants” and “products”) on the y-axis versus “time” (the cycle number) on the x-axis (Graph 1). Different-colored pens are used to plot on the same set of axes the number of colored and white cards present at the end of each cycle. In Game 1 the fraction of colored cards turned over is smaller than the fraction of white cards turned over; this is an example of an equilibrium with Kc < 1. The Graph 1 that is obtained is identical to that given in textbooks for real equilibria where Kc < 1 (e.g., ref 28). The number of cards turned over in each cycle (see Table 1, “rf” or “rr” column), is related to the number of molecules reacting in a finite time; that is, it is related to the rate of the forward (rf) or reverse (rr) reaction. Thus, students can actually see the rate of the forward reaction decreasing and the rate of the reverse reaction increasing as equilibrium is approached, until at equilibrium rf = rr . (This is not possible in “real” reactions!). Students also note that the net rate of the forward reaction (∆[R]/∆t) is negative and increases to zero while the
Table 1a. Game 1, Starting with 49 Reactant Cards
Table 1b. Game 2, Starting with 49 Product Cards
Cycle No.
Reactants
Products
1
⁄4 = 25% react
Net Rate ∆[R] /∆t
0
49
—
1
49 – 12 + 0
—
2
37 – 9 + 4
(37 – 49) = –12
3
32 – 8 + 5
(32 – 37) = –5
4
29 – 7 + 6
5
Reactants
Cycle No.
Products
1
⁄3 = 33% react
Net Rate ∆[P] /∆t
rra
—
0
—
—
0
0
—
—
49
—
—
12
0 – 0 + 12
—
0
1
0 – 0 + 16
—
0
49 – 16 + 0
—
16
9
12 – 4 + 9
(12 – 0) = 12 4
2
16 – 4 + 11
16
4
33 – 11 + 4
–16
11
8
17 – 5 + 8
(17 – 12) = 5 5
3
23 – 5 + 8
7
5
26 – 8 + 5
–7
8
–3
7
20 – 6 + 7
3
6
4
26 – 6 + 7
3
6
23 – 7 + 6
–3
7
28 – 7 + 7
–1
7
21 – 7 + 7
1
7
5
27 – 6 + 7
1
6
22 – 7 + 6
–1
7
6
28
0
7
21
0
7
6
28 – 7 + 7
1
7
21 – 7 + 7
–1
7
7
28
0
7
21
0
7
7
28
0
7
21
0
7
8
28
0
7
21
0
7
8
28
0
7
21
0
7
ar
rfa
= rate of forward reaction = number of colored cards turned over. rr = rate of reverse reaction = number of white cards turned over. Kc = [Reactants]/[Products] = [white cards visible]/[colored cards visible] = 21/28 = 0.75. Boldface numbers designate values at the end of the cycle. f
ar
⁄4 = 25% react 1
Net Rate ∆[P] /∆t
rr a
= rate of forward reaction = number of colored cards turned over. rr = rate of reverse reaction = number of white cards turned over. Kc = [Reactants]/[Products] = [white cards visible]/[colored cards visible] = 21/28 = 0.75. 40
45
30
40
∆[R ] ∆t
20
35
Net Rate
No. of cards (amount of substance)
1
f
50
30 25 20
10 0 0
-20
10 5
5
15
10
20
25
30
35
40
-10
15
0
⁄3 = 33% react
Net Rate a rf ∆[R] /∆t
∆[P ] ∆t
-30 1
2
3
4
5
6
7
8
9
10
Cycle number (Time) Graph 1. Equilibrium Game 1: Kc < 1. (䉬) Products; (䊏) reactants.
-40
Time / s Graph 2. Net rate of (䉬) forward and (䊏) reverse reactions vs time.
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Step 3. Identify the Relevant Features of the Analogy Whether the fraction of colored cards being turned over is greater or less than the fraction of white cards and whether one starts with colored or white cards, there comes a time in the Games when the numbers of the two colors of cards being turned over in a cycle are identical. This can be related to rf = rr, and so the system has come to equilibrium even though exchange of cards is still occurring. This highlights the dynamic nature of an equilibrium situation. Step 4. Map Out the Similarities between the Analogy and the Target Students (or pupils) are asked to note the similarities between the Games and a true equilibrium. One. The rate of the forward reaction slows down with time from mixing reactants until equilibrium is established (cf. ref 24 and Tables 1 and 2, column labeled ∆[R]/∆t). Two. The change in the number of colored (or white) cards in each cycle can be related to the rate of the forward (or reverse) reaction. At equilibrium, rf = rr and the students stop playing the Game; but in a real reaction, the molecules 922
Table 2. Game 3, Expected Results and LeChâtelier's Principle in Action Cycle No.
Reactants 1
⁄2 = 50% react
Net Rate ∆[R] /∆t
0
35
1
35 – 17 + 0
2
18 – 9 + 3
3
Products rf
1
⁄5 = 20% react
Net Rate ∆[P] /∆t
rr
—
—
0
—
—
—
17
0 – 0 + 17
18 – 35 = –17
9
17 – 3 + 9
17 – 0 = 17
3
12 – 6 + 4
12 – 18 = – 6
6
23 – 4 + 6
23 – 17 = 6
4
4
10 – 5 + 5
10 – 12 = –2
5
25 – 5 + 5
25 – 23 = 2
5
5
10
10 – 10 = 0
5
25
25 – 25 = 0
5
6
10
0
5
25
0
5
7
10
0
5
25
0
5
8
10
0
5
25
0
5
9
10
0
5
25
0
5
—
—
0
Add more reactant 0′
10 + 14 = 24 —
—
25
1′
24 – 12 + 5
—
12
25 – 5 + 12 —
5
2′
17 – 8 + 6
17 – 24 = –7
8
32 – 6 + 8
32 – 25 = 7
6
3′
15 – 7 + 6
15 – 17 = –2
7
34 – 6 + 7
43 – 32 = 2
6
4′
14 – 7 + 7
14 – 15 = –1
7
35 – 7 + 7
35 – 34 = 1
7
5′
14
0
7
35
0
7
6′
14
0
7
35
0
7
7′
14
0
7
35
0
7
8′
14
0
7
35
0
7
NOTE: At cycle 9, Kc = 25/10 = 2.5 At cycle 8′, Kc′ = 35/14 = 2.5. Boldface numbers designate values at the end of the cycle.
40 35
No. of cards (amount of substance)
net rate of the reverse reaction (∆[P]/∆t) decreases to zero. This gives rise to Graph 2, which is commonly found in school textbooks but is seldom understood by students. Game 2 Game 1 is repeated keeping the fractions of cards turned over the same as before but now starting with 49 white (product) cards. The values obtained at equilibrium and the equilibrium constant are the same as before (see Table 1b). Game 3 Game 3 is similar to Game 1 but this time the fraction of colored cards turned over in each cycle is greater than the fraction of white cards (e.g., 1⁄2 of colored cards and 1⁄5 of white cards). Using 35 cards, equilibrium is reached after 5 cycles (see Table 2). A graph of “number of cards” versus “number of cycles” is plotted as before (Graph 3). For Game 3, Kc > 1 and in the first part of Graph 3 the two lines intersect before becoming parallel to each other. This graph is similar to concentration-versus-time graphs for real equilibria where Kc > 1 (28). Game 1 or 3 can be extended to illustrate Le Châtelier’s principle. For example, using Game 3, once equilibrium has been established, an additional 14 colored cards are added to the box and the Game is played as before (see Table 2 for data). Students note that when the extra cards are added, the rate of the forward reaction increases considerably before gradually decreasing again, while the rate of the reverse reaction increases further until equilibrium is reestablished and rf = rr again. One could also have added extra white cards (product molecules) to the system at equilibrium and played the Game until equilibrium was reestablished. Both demonstrate Le Châtelier’s principle in action and can help to dispel the alternate conception that equilibrium oscillates like a pendulum that swings higher or lower when a stress is applied (23). It is also valuable to dispel the idea that equilibrium is a motionless sea-saw hovering at an angle above the ground until a stress is applied (30). The data obtained after the extra cards are added (Cycles 0′–8′) are also plotted on Graph 3 with cycles 10 and 0′ coinciding.
Products
30
Products 25 20 15
Reactants
Reactants
10 5 0 1
2
3
4
5
6
7
8
9
0'
1'
2'
3'
4'
5'
6'
7'
8'
9'
Cycle number (time)
Graph 3. Equilibrium Game 3: Kc > 1. Le Châtelier’s principle demonstrated.
would continue reacting. For reacting molecules, the parallel portion of the graphs will extend indefinitely or until something is altered to upset the equilibrium. Three. The number of colored cards can be related to the amount of reactants and the number of white cards to the amount of product. “Concentrations” can be determined using V for the volume of the box. One can then calculate the equilibrium constant, Kc, for Games 1, 2, and 3. Kc < 1 if the fraction of colored cards (reactants) being turned over (reacting) is less than the fraction of white cards (products) and the position of equilibrium is shifted toward the reactants (as in Game 1 and 2). Kc >1 for the reverse situation where the equilibrium lies towards the products (Game 3). For the fractions cited above, in Games 1 and 2, Kc = 0.75, and in Game 3, Kc = 2.5.
Journal of Chemical Education • Vol. 77 No. 7 July 2000 • JChemEd.chem.wisc.edu
Research: Science and Education
Four. Each cycle can be related to a time interval that may be very short (e.g., 10 s) or very long (e.g., 10 years). Five. The simulations can be mapped smoothly to real equilibria (28) because the graphs from the Games mimic those obtained using actual experimental data for reactions that go to equilibrium. Six. The fractions used (e.g. 1⁄4 and 1⁄3 for Games 1 and 2, 1 ⁄2 and 1⁄5 in Game 3) represent the percentage of molecules at that temperature that have sufficient energy to overcome the activation energy barrier for the reaction. That is, they are thermodynamic quantities related to the Gibbs free energy and they determine the final position of the equilibrium. If the students keep the fractions constant but vary the number of cards used to play a Game—the equilibrium constant does not alter—this reinforces the constancy of Kc at constant temperature. Students may be reminded that the fraction of molecules with sufficient energy to overcome Ea will alter if the temperature alters. They can test this by varying the fractions used in the Games and noting that Kc changes. However, no matter what fractions are chosen, there comes a time when the exchange rates of the two sides of the cards are equal. Seven. One can place a ruler side-on along one side of the box in which the Games are played and gradually push it toward the other side of the box, thus pushing the cards closer together. This mimics an increase in pressure or decrease in volume of the system. The students note that when this is done, both the reactant and product molecules are affected. Also, one can hold an (unlit!) Bunsen burner under the box and ask the students what would happen if the contents of the box were heated. These activities sensitize students to the fact that both the reactant and product molecules increase in temperature when heating occurs. Both of these exercises address the documented alternate conceptions (24 ) that the “left-hand side” and “right-hand side” of a reaction operate independently and that at equilibrium, if conditions are changed, the rate of a favored reaction can be altered without any effect on the reverse reaction. Eight. The stoichiometry of 1:1 for the reaction in the analogy mimics the equilibrium between, for example, the α and β forms of glucose or between the cis and trans forms of 2-butene.
Step 5. Indicate Where the Analogy Breaks Down The major difference between the simulations and the target is that the Games are in two dimensions and collisions between the cards are not a requisite for reaction. Students need to be reminded that in real reactions, containers are 3dimensional and molecules have to collide with a minimum energy before reaction can occur.
Step 6. Draw Conclusions about the Target Concept The following important aspects of chemical equilibrium can now be discussed: (i) equilibrium is a dynamic state; (ii) the forward reaction does not go to completion before the reverse reaction commences; (iii) [reactants] ≠ [products] at equilibrium; and (iv) there is no “left side” and “right side” to an equilibrated state—one of the more powerful aspects of this exercise is that the colored cards (reactants) and white cards (products) are always mixed and the change from reactants to products and vice versa is totally random.
Discussion of the Chemical Equilibrium Simulations The Equilibrium Games address several known alternate misconceptions. Students believe (24) that the rate of the forward reaction increases from the time of mixing until equilibrium is attained. A study of the column rr in Tables 1a, 1b, and 2 shows that the rate of the forward reaction actually decreases with time. Also, a study of the net rate of the reaction (∆[R]/∆t or ∆[P]/∆t columns in the Tables reveals that both forward and reverse reactions are occurring all the time and the forward reaction does not go to completion before the reverse reaction commences (13). Another alternate conception (31) is that the concentration of the reactants is equal to the concentration of the products at equilibrium; in all the Games, at equilibrium, the number of colored cards is not equal to the number of white cards, and so this alternate conception can be dispelled. When Le Châtelier’s principle is demonstrated in Game 3, Graph 3 is extended to obtain a graph similar to that obtained by Gillespie (28). Students note that when a “stress” is applied to a system at equilibrium, the reactions proceed in both directions as before until r r = rf again and equilibrium is reestablished. The Kc′ calculated for this new equilibrium is found to be the same as before. The fact that the equilibrium constant does not change on addition of the extra cards was an important factor in convincing students and their teachers of the constancy of the equilibrium constant. Students were also interested to find that once the equilibrium was reestablished, the number of colored cards (i.e., the amount of reactants) was greater than before the “stress” was applied. Many learners believe that adding more reactant to a system in equilibrium causes a drastic shift in the position of the equilibrium toward the products until virtually no reactants remain. Main Study. Methodology Used to Test the Simulations The modified Equilibrium Games were tested on three sets of subjects in 1997: (1) 45 grade 12 physical science pupils in a private all-girls school in Johannesburg, (ii) 102 College of Science students in a 2-year bridging program at Wits, and (iii) 240 health sciences students doing Chemistry I at Wits. The last class was divided into two sessions for the Games; the first involved only students registered for medicine (MBBCh) and the second included dental (BDS), physiotherapy (Physio), and pharmacy (Pharm) students. The College of Science students are predominately black learners who experienced poor schooling during the apartheid years in South Africa and did not do well enough in their schoolleaving examinations to allow them direct entry into university. Before each set of subjects played the Games, they were given a pretest (Appendix A) involving 5 items on common alternate conceptions in chemical equilibrium. The learners then played Games 1 and 3 as outlined above, including the test of Le Châtelier’s principle. Finally, they drew the graphs. They were required to decide among themselves where the Games were similar to and where they varied from reality. They also had to answer several questions about the Games (see Appendix B), which drew their attention to salient features of equilibrium. The identical questionnaire (Appendix A) was readministered as a posttest to all the subjects 1–6
JChemEd.chem.wisc.edu • Vol. 77 No. 7 July 2000 • Journal of Chemical Education
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Percentage
their ideas (34 ). No matter how effective the CAI program days after they had played the Games. The results for the may prove to be, few black schools and teacher training colpretest and posttest are outlined in Table 3 and Figure 1. leges in southern Africa and other developing countries have A large change from the pretest to the posttest was unlikely access to computers and can afford the computer package confor the school pupils, as they had already been taught chemical taining the Games. The simple requirements of the Equiequilibrium and the teacher had played Game 1 on the board librium Games as presented here make them accessible to the (using magnets on the cards) before they wrote the pretest. poorest school or college. Likewise, the health sciences students had been taught chemiSome bright health sciences students were initially very cal equilibrium when they were at school. The improvement cynical about having to play games at university, but their on the posttest by the school pupils was virtually identical to attitude altered when they saw how their results gave rise to that of the two health sciences classes. Most improvement graphs similar to those obtained for real reactions moving to occurred in the questions about Le Châtelier’s principle. equilibrium. Many of the teachers on whom the Games were However, the results for the College of Science students piloted stated that several confusing concepts of equilibrium were poor both before and after playing the Games. This unwere resolved during the simulations. Similar simulations for derlined the difference in the knowledge and understanding chemical equilibrium have since been reported by Wilson (35) of these bridging students relative to the others involved in and Edmonson and Lewis (33). However, these simulations the research. Also, when comparing choices by individual do not specifically address the main known alternate constudents from the pretest to the posttest, one was struck by ceptions in equilibrium, nor does Wilson relate her Game the similarity of the answers of the school pupils and health back to the target with graphs—the most powerful feature sciences students. However, the College of Science students’ we found in convincing the brighter students of the worth individual choices varied considerably from the pretest to of the Games. the posttest, suggesting that the students may have been Like Dagher (5), we found the exact extent to which these guessing at the answers in both tests. (This is supported by simulations contributed to conceptual change difficult to assess. the fact that the percentage of college students who improved Since changing alternate conceptions is difficult (21, 22), in the posttest was comparable to the percentage who did it is best that students get the basic concepts correct the first worse.) It is possible that these students had found equilibrium time around. We recommend that equilibrium be introduced so confusing when it was first taught at school that they had according to the explanatory practical model of van Driel, closed their minds to it and nothing could be done to alter that perception. Some college students even found the calculation of the data for Table 1 and 2 quite tedious (even though Full Marks Unchanged simple fractions were chosen) and had trouble drawing the Improved Did Worse graphs; this may have been a further demotivating factor for 60 them. Researchers have found that analogies work better for students who think at a lower (less abstract) operational stage 50 (7, 11). Our results do not support this. It is possible that the 40 Equilibrium Games—while concrete—still require abstract reasoning to extrapolate to the target. 30 The Equilibrium Games have recently been adapted for computer and will form part of a package of computer-aided 20 instruction (CAI) programs being marketed by our department (32). The advantage of the package is that any number of 10 reactant and product molecules up to a total of 99 can be present initially. Once the students choose the number of 0 Medics School Pupils BDS, etc. CoS molecules reacting, the data are calculated and the graphs are drawn for them (see Fig. 2). Every cycle of the Game is Figure 1. Chart showing overall difference between pretest and represented on the screen by (i) a “reaction box”, (ii) a concurposttest scores. rent table of results, (iii) a graph for the Game up to that cycle, and (iv) some comTable 3. Students' Answers on Pretest and Posttest ments or questions. We have yet to test the Choice of Answer, Percent of Students by Type of Student efficacy of these computer simulations on Question Medics (MBBCh) BDS/Pharm/Physio College of Science the students; however, preliminary studies suggest that only by first playing the Games A B C D E A B C D E A B C D E manually can students appreciate all that is of1 Pre — 92 — 90 8 80 Post — 97 — 98 7 83 fered on each screen in the CAI program. 2 Pre 34 59 57 32 40 42 Edmonson and Lewis found that computer Post 18 75 44 49 43 35 simulations have much less instructional po3 Pre 17 54 18 17 27 44 29 32 18 tential than that offered by hands-on experiPost 24 59 14 24 53 16 33 39 15 ments (33). Thomas and Schwenz, in their 4 Pre 32 13 42 15 22 40 18 35 16 25 analysis of students’ alternate conceptions in Post 8
