The Complexity of Teaching and Learning ... - ACS Publications

Research: Science and Education

Chemical Education Research

The Complexity of Teaching and Learning Chemical Equilibrium Louise Tyson and David F. Treagust* Science & Mathematics Education Centre, Curtin University of Technology, GPO Box U1987, Perth, Western Australia 6001, Australia Robert B. Bucat Department of Chemistry, University of Western Australia, Perth, Western Australia 6010

Research into students’ conceptions of the nature of chemical equilibrium has been underway since the 1960s. A number of studies have identified common alternative conceptions held by students at the secondary and tertiary level (1–5). These studies have made a number of recommendations for those engaged in teaching this difficult topic. Hackling and Garnett (6 ) suggest that greater emphasis on the quantitative aspects of equilibrium may help students gain a clearer picture of the relationship between the concentrations of reactants and products in equilibrium systems. Wheeler and Kass (1) recommend greater differentiation in the range of examples presented to students when discussing Le Châtelier’s principle. They also suggest that concentrationversus-time graphs may help students to visualize what is happening when a change is made to a system at equilibrium and that a greater emphasis on a laboratory approach may benefit students by providing concrete situations. Jordaan (7) suggested that when using Le Châtelier’s principle to predict the effect of changes to equilibrium mixtures, these disturbances can be viewed as being due to one of only two factors: a change in temperature or a change in concentration of one of the species in the mixture relative to the others. Despite this large body of research and numerous recommendations, the same alternative conceptions are found consistently in our classrooms today (8). It is not enough to simply alert students to the common errors made in examinations and tests because research has shown that their ideas are extremely resistant to change (9). Teachers need to be able to monitor students’ understanding of scientific principles so that they may develop their teaching strategies to accommodate their students’ current ideas. *Email: [email protected].

554

Background One problem for classroom teachers is that the methods traditionally used to identify students’ alternative conceptions are extremely time consuming. These include the use of interviews, word association tasks, and concept mapping. The typical high school chemistry teacher spends an average of 220 minutes per week with an upper secondary class that consists of 20 students; this amounts to about 11 minutes for each student in the class, not including marking outside of hours. A two-tier test methodology (10) has been developed to provide teachers with an easily administered and evaluated pencil-and-paper test designed to identify students’ alternative conceptions. A two-tier test consists of items with a multiplechoice answer followed by a selection of reasons in multiple choice format. This was a three-year study involving the development, use, and evaluation of a two-tier test to explore students’ understanding of chemical equilibrium, and a case study at an independent girls’ school. During the case study, one of us (L.T.) was involved in making daily observations of the lessons taught under the topic of chemical equilibrium, and in interviewing three students at least three times a week during the course of the topic and on their completion of the topic test. The purpose of these interviews was to trace the evolution of the students’ ideas relating to chemical equilibrium and to identify issues that hindered the development of their understanding of this concept. This study revealed three issues that were particularly relevant for those teaching the topic of chemical equilibrium. First, analysis of responses in the reason section of the two-tier test indicated that students used multiple explanations when predicting the effect of changes to equilibrium mixtures. In some contexts, such as the addition of a solid to an equilibrium

Journal of Chemical Education • Vol. 76 No. 4 April 1999 • JChemEd.chem.wisc.edu


mixture, a student would use the equilibrium law but a general preference for Le Châtelier’s principle was evident. As a result, we decided to examine the relative usefulness of each of these explanations. Second, the use and interpretation of language emerged as an important issue in the teaching and learning of the topic of chemical equilibrium. It was evident that students, teachers, and textbook authors often did not share the same meaning for words commonly used in connection with this topic. Finally, the highly sophisticated nature of the content of this topic was found to have important implications for its teaching.

Rates of Reaction If we consider the effect of the addition of hydrogen gas by applying collision theory to the problem, then the increased number of H2 particles would lead to a greater number of collisions between particles of hydrogen and nitrogen gas, with the result that the rate of the forward reaction is greater than the rate of the reverse reaction until equilibrium is reestablished. This would lead to a higher concentration of ammonia gas in the reaction mixture at the new equilibrium. At the new equilibrium, both the forward and reverse rate of reaction will be faster than the initial equilibrium.

The Usefulness of Different Levels of Explanation

Comments and Critique of Different Explanations Based on Classroom Research

Three levels of explanation can be used at the secondary level to predict what will occur when reaction mixtures that are at equilibrium are disturbed: Le Châtelier’s principle, the equilibrium law, and an analysis of reaction rates using collision theory. These explanations can be used independently to make predictions about the effect of changes to equilibrium mixtures, but if a student attempts to understand the effect then some consideration of rates of reaction in addition to Le Châtelier or the equilibrium law will be required. The reaction between hydrogen and nitrogen gases to form ammonia gas can be used to illustrate these three approaches. Let us consider a system at equilibrium in a container of fixed volume, as represented by the following chemical equation N2(g) + 3H2(g)

2NH3(g) + heat

and examine the effect of adding additional H2 gas on the concentration of NH3 gas.

Le Châtelier’s Principle According to Le Châtelier’s principle, the system would be considered to oppose the change made to it, responding to reduce the concentration of H2 gas. The forward rate of reaction would be greater than the reverse rate of reaction until equilibrium was reestablished. This would lead to an increase in concentration of NH3 in the reaction mixture at the new equilibrium. Equilibrium Law The equilibrium law relates the concentrations of reactants and products at equilibrium. It may be expressed in the following manner: At a particular temperature, all reaction mixtures in which the reaction represented by the general equation aA + bB

xX + yY

is at equilibrium have the same value of the ratio [X]x[Y]y Keq = ––––––– [A]a [B]b The numerical value of this ratio is called the equilibrium constant, Keq. The ratio between product and reactant concentrations under any conditions is called the reaction quotient, Q. If additional hydrogen gas is added to the reaction mixture described above then the value of the ratio of product and reactant concentrations will decrease, Q < K. The forward reaction rate will increase, resulting in an increase in the concentration of ammonia and decrease in the concentration of nitrogen and hydrogen until equilibrium is established and Q = K.

All three approaches to the problem lead to the same answer in this case; that is, an increase in the concentration of ammonia when the new equilibrium is established. A typical series of lessons on the topic of chemical equilibrium will involve a combination of these approaches. The question of the relative usefulness of these three explanatory frameworks arises. Is one more useful than the other? Teachers in Western Australia have expressed a preference for using Le Châtelier’s principle when teaching students how to predict the effect of changes to equilibrium mixtures (11). Eighty-seven percent of teachers surveyed indicated that they prefer Le Châtelier’s principle because it is “easy to explain”, “more logical”, “a straightforward rule”, and “less difficult”. This is in spite of the research criticism that it has limited generalizability because Le Châtelier did not delineate the limits of applicability of the principle (12–14). It appears that chemistry teachers feel they can adequately set the boundary conditions for Le Châtelier’s principle for their students. Experienced teachers are aware of the problems of using Le Châtelier’s principle for questions involving a change in total pressure or the addition of an inert gas, and they alert their students to this trap. However, the addition of solids and water to equilibrium mixtures did cause problems for students when using Le Châtelier’s principle. Students using Le Châtelier are likely to respond that an equilibrium mixture will counteract change when a solid or liquid is added to it (although in some instances the addition of a solid will not disturb an equilibrium mixture) because they view it as a simple algorithm. Le Châtelier’s principle does not provide any plausible reason to suppose that the equilibrium mixture will not be disturbed. Some students learn an additional rule— “that solids do not affect equilibrium mixtures”—to help themselves overcome this problem. This leads some students to the incorrect assumption that you “cannot alter the amount of a solid in an equilibrium mixture”. Students using the equilibrium law are more likely to find it plausible that the addition of a solid will not affect an equilibrium mixture because solids are not included in the equilibrium constant expression. However, it was observed that these students also are likely to develop the misconception that “you cannot alter the amount of a solid in an equilibrium mixture”. For a student using collision theory to make sense of the addition of a solid, the situation was no clearer. Collision theory does state that the amount of a solid will not influence the rate of a chemical reaction, and from this perspective it appears straightforward that the addition of a solid should not increase the number of collisions between reacting particles

JChemEd.chem.wisc.edu • Vol. 76 No. 4 April 1999 • Journal of Chemical Education

555


and the equilibrium mixture should remain undisturbed. However, collision theory does state that particle size influences the rate at which a reaction proceeds, and this can cause problems for students whose normal practice is to add granulated and powered solids to reaction vessels in the laboratory. Students reason that if they add a solid to an equilibrium mixture there will be more collisions between particular reacting species and that this should cause an increase in the concentration of certain species in the mixture. During an interview, the following question was presented to a student: Limestone decomposes to form lime and carbon dioxide according to the following equation CaCO 3(s) + heat CaO(s) + CO2(g) What will happen to the concentration of CO2 if solid lime is added to the equilibrium mixture ?

The student responded that the concentration of CO2 would decrease owing to increased collisions between lime and carbon dioxide. When the interviewer replied that the addition of a solid would not disrupt the equilibrium mixture because solids were not included in the equilibrium constant expression, the student responded “what if powdered lime had been added?”—and the interviewer was at a loss for words. The addition of solids to equilibrium mixtures was not as unambiguous as had previously been thought. The addition of water to an equilibrium mixture also produced problems for those who stated a preference for Le Châtelier’s principle. Using the principle does not prevent students from obtaining the correct answer but does preclude their arrival at a scientifically acceptable explanation for the observed phenomena. The following item appeared in the final version of the two-tier test produced for chemical equilibrium. 5. Consider the following reversible reaction that is in a state of equilibrium in a solution which is blue in color Co(H 2O)62+(aq) + 4Cl{ (aq) pink

CoCl4 2{(aq) + 6H2O(,) blue

What will be observed if water is added to this system? (1)* the solution turns pink (2) the solution becomes more blue (3) the solution remains unchanged Reason (1) to counter the increase in amount of water present the system will form more Co(H2 O)62+(aq) (2) liquids are not included in the expression for K and hence the ratio of products to reactants will not be disturbed (3)* the ratio of concentration of products compared to reactants as expressed by Q will decrease and more Co(H2O) 62+(aq) will form (4) the forward reaction has a higher mole ratio than the backward (5)* to counter the decreased concentration of Cl{(aq) the system will form more Co(H2O)62+ (aq) *Scientifically acceptable response.

Seventy-five percent of students correctly predicted what would happen, but the reasoning used by many of them was not scientifically correct. When asked why the equilibrium mixture turned pink, a typical response given by students and teachers was “in order to oppose the change the system will try to reduce the amount of water present.” This explanation is technically incorrect in that it is not the extra water that 556

disturbed the equilibrium. The effect of adding water is perhaps most easily explained using the equilibrium constant expression. The reaction quotient for the above reaction is [CoCl42{(aq)] Q = –––––––––––––––––––––––– [Co(H2O)62+(aq)][Cl{(aq)]4 For the purpose of illustration, if we assume that the concentration of each species in the reaction mixture at equilibrium is 1 mol L{1, then the value of Keq will be 1. If we double the volume of the reaction mixture by adding water, the concentration of each species in the mixture will be 0.5 mol L{1 and the value of Q becomes 16. The reaction mixture is no longer at equilibrium. In order to reestablish the value of the equilibrium constant, the rate of the forward reaction will decrease less than the rate of the reverse reaction, reducing the concentration of [CoCl42{(aq)] and increasing the concentration of [Co(H2O) 62+(aq)] and [Cl{(aq)]. A search for a chemical equation that includes water as a species participating in the reaction in which the addition of water will not disturb the equilibrium mixture has not yet been successful, and so the usefulness of Le Châtelier’s principle is not challenged in this instance. The analysis of the two-tier test results in this study suggests that Jordaan’s (1993) recommendation to focus on the change in concentration of each species in the equilibrium mixture when using Le Châtelier’s principle should be extended to the other two explanations used by students. The following item in the two-tier test was incorrectly answered by 98% of the first-year university students surveyed and 85% of the secondary school students surveyed in the pilot study. These students selected 1 as their answer and reason 1 was the most popular among these students. 8. If you have a 0.5 M solution of sodium dichromate (Na 2Cr 2O 7) in which the following equilibrium is established CrO42{(aq) + 2H+(aq) Cr2O 72{(aq) + H2O(,) yellow

orange

and you add 10 mL of 0.5 M solution of sodium dichromate to the original solution what would you observe? (1) the solution becomes yellow (2) the solution becomes deeper orange (3)* the solution remains unchanged Reason (1) to counteract the increased amount of Cr2O72{(aq) the system will form more CrO 42{(aq) (2) there will be more collisions between particles of Cr2O72{(aq) and H2O(,) (3) because of increase in Cr2O7 2{, Q will be greater than K (4)* there is no change in concentration of any species (5)* the value of the ratio expressed by Q is unchanged (6) because of increased volume there will be fewer collisions between particles *Scientifically acceptable response.

Students appear to have used an algorithmic approach to this problem and certainly did not consider whether there was a change in concentration of one species relative to the other. Their success rate on this problem would be likely to increase if they used this approach or alternatively if they attempted to visualize what was happening in the problem.



The Interpretation of Commonly Used Terms When discussing changes to reaction mixtures that are at equilibrium, there are some phrases that are commonly used in communication among teachers, students, textbook authors, and examiners. Language has traditionally been viewed as a conduit that is a means of transmitting knowledge from the mind of the teacher to the mind of the learner. A post-constructivist perspective of learning suggests that those involved in the processes of teaching and learning have come to view language as symbolic. It requires interpretation as learners construct their own meanings for words. Bergquist and Heikkinen (15) identified words associated with chemical equilibrium that also have common language meanings, which present different visual images to those who use them. One well-documented common misconception relating to chemical equilibrium is that the concentrations of all species in the reaction mixture are equal at equilibrium. This is not surprising, because we know students bring prior knowledge of the word equilibrium to the classroom. When you ask students to describe their understanding of the word prior to instruction they will often reply that all things are equal. The experienced chemistry teacher is mindful of this and employs strategies in the classroom to address the problem, such as drawing a concentration-versus-time graph for a system that is at equilibrium or using an analogy such as the liquid transfer model (16 ) to simulate a chemical reaction. The meaning of the word equilibrium may be carefully discussed in the classroom, but there are other words that are not given the attention that they deserve.

Closed System Frequently, when introducing the equilibrium topic, a reaction in a closed container is described and then the terminology of “closed system” is quickly introduced. Students are expected to interpret the words closed system to be equally applicable to a sealed vial containing NO2 and N2O4 or an open beaker of aqueous sodium chloride. If the teacher emphasizes the meaning of these words through the use of multiple examples, then problems associated with the interpretation of the terms can be resolved, as indicated in the interview response of a secondary student: I was a bit unsure about equilibrium in physical systems. How it wasn’t closed in the beaker if you’re dissolving something in water, but then it was not looking at the water and the air you were looking at the salt and the water. That was just a bit confusing at first because we had been told that it had to be closed but then I realized that it was actually a closed system.

However, while the student was struggling with the term closed system, the concepts of physical and chemical reversible processes and the equilibrium law were being introduced. As teachers, we need to be aware of the intellectual demands placed on our students early in the equilibrium topic, not just by the nature of the content but also by the terminology used to describe that content.

Equilibrium Position and Shift to Left/Right The phrase equilibrium position, or equilibrium balance, was found to be subject to misinterpretation by students and teachers. The following item appeared in an early version of the two-tier test.

Consider a saturated solution of calcium hydroxide in contact with solid calcium hydroxide Ca(OH)2(s) Ca2+(aq) + 2OH{(aq) If water is added to this system which is at equilibrium the equilibrium position will (a) shift to the left (b) shift to the right (c) remain unchanged (d) not be able to be predicted

The term equilibrium position was given at least three different interpretations by students and teachers when they answered this question. For many who answered “c”, the phrase was assumed to be interchangeable with the equilibrium constant, and a typical reason for their choice was “The equilibrium position is the same as concentrations are the same although more will dissolve.” Others assumed that the meaning was related to the rate of the chemical reaction or the time taken to reach equilibrium. One student who answered “b” gave the following reason for the choice: “Because as more water is applied the solution would be less concentrated making the equilibrium occur later.” Yet another student chose “a” as the correct answer with the reason that “It will take longer for the reactant to reach equilibrium because the concentration of Ca(OH)2 will decrease by adding H2O.” Clearly the terms shift to the left and shift to the right mean different things to different people; one student even replied “Didn’t know what meant by shift left and right.” Another group of students interpreted the phrase “equilibrium position” to mean the rate of the forward reaction relative to the backward reaction. These students typically chose “b” with the typical reason that “When water is added [Ca2+] and [OH{] decrease and the reverse reaction decreased while forward reaction rate remained constant. Thus more Ca(OH)2 dissolves.” Owing to these and other similar problems with misinterpretation of language, we decided to frame test questions around the change in concentration of one of the species in a reaction mixture and delete these terms from all test items. This trend also is evident in more recent chemistry textbooks and in the university entrance examinations for chemistry in Western Australia, although these terms are still used in many of the revision materials used by students when studying for their examinations. The examples described above are not an exhaustive list of terms that have problems of interpretation associated with them. The terms reactants and products reinforce student notions that reactions proceed in one direction only. Teachers and students need to work together throughout the equilibrium topic to negotiate shared meanings for common terms and perhaps decide that some terms cause too many problems and should be omitted. The Specific Nature of the Content White (17) has suggested that the properties of specific science content should have implications for the teaching of that content. The content of chemical equilibrium is abstract, has a high degree of linkage with other content areas in chemistry, and is highly sophisticated in that the interpretation required of terminology and concepts is very specific. It is possible that teachers and students tend to overlook the specific nature of content in this topic and that this causes them to oversimplify their interpretation of certain problems.

JChemEd.chem.wisc.edu • Vol. 76 No. 4 April 1999 • Journal of Chemical Education

557


In this study one area identified as a source of students’ difficulties was the subtle differences between physical and chemical systems that are at equilibrium. In particular, the concept of saturation for physical and chemical systems caused problems. Many teachers and textbooks use a reversible physical system such as the dissolution of sodium chloride in water to introduce the equilibrium concept. It is often used as a starting point because students have considerable experience with this type of reaction both at home and at school. However, the students’ experience and understanding of this type of reaction is in direct conflict with how they are expected to interpret the reaction in terms of an equilibrium mixture. This is illustrated by the following excerpt from a student interview in this study. STUDENT: So that’s unsaturated. INTERVIEWER: Okay. STUDENT: And then for saturated it would have two arrows. But is that just because there is solid left?…and it’s dissolving the…I don’t understand why it should reform though. INTERVIEWER: Yes…why it should go back? STUDENT: So I don’t understand…for that…why…for a saturated one, why there should be a double arrow?

In terms of predicting changes to equilibrium mixtures, there are differences in physical and chemical systems that are not explained in textbooks and may be only rarely discussed by teachers. For the dissolution of sodium chloride at a particular temperature, there is a point of saturation at which no more solid will dissolve and a maximum concentration of chloride and sodium ions is reached. For this type of physical system the addition of a solid will not affect the equilibrium mixture and most students appear comfortable with this. However, in a chemical system which is at equilibrium there is not a maximum concentration of any species reached at any particular temperature; there is not a point of “saturation”. Students appear to transfer the notion of saturation to chemical systems—which is perhaps not surprising, given that they were introduced to equilibrium mixtures by using physical systems as examples. The conception that “solids do not disturb equilibrium” in some instances arises from the students’ confusion about whether the solid will dissolve and therefore affect the concentration of one species relative to the other. The following conversation took place with an A-grade student after her final test on the topic of chemical equilibrium. INTERVIEWER: I dissolve lead sulfate in water to form lead ions and sulfate ions. What will happen if I add solid lead sulfate to this? It is at equilibrium initially. STUDENT: Nothing will happen. INTERVIEWER: Why? STUDENT: Because you can’t dissolve any more. If you’ve got solid already it means there’s already excess that hasn’t dissolved, so increasing the excess isn’t going to change the amount that’s dissolved. INTERVIEWER: Good. What will happen if I add solid lead sulfate to this system which is at equilibrium? PbSO 4(s) + H+(aq) Pb2+(aq) + HSO4 {(aq) STUDENT. It will…that’s different because it’s not…you’re not looking at something with an excess of it. You are in a way, but not the same sort of thing. It will increase the forward reaction. Will it? I’m not sure. I’m confused now. I don’t know. I just don’t know about that one. 558

In this study, it was observed that the students who had specifically compared and contrasted the similarities and differences between physical and chemical systems had less difficulty making predictions about how solids would affect equilibrium mixtures. Recommendations A number of recommendations for teachers have emerged from this study. The first is related to the different explanations that are used to predict the effect of changes to equilibrium mixtures. Not all students who were most successful in making these predictions used Le Châtelier’s principle or the equilibrium law. It does not appear that one explanation is better than the other. Certainly the problems associated with Le Châtelier’s principle can be minimized by adopting the recommendations of Jordaan (7) and focusing on change in temperature and relative concentration as the two central factors responsible for disturbing equilibrium mixtures. It appears that students use a multifaceted approach, and their choice of explanation depends on the context of the problem. As teachers, we need to value each of these explanations and appreciate that each of them expands our students’ understanding of the equilibrium concept. Language emerged as a key factor in the development of students’ understanding of chemical equilibrium; we need to be alert to terms that are subject to misinterpretation by our students. It may be that we should not use terms such as equilibrium position or equilibrium balance and should frame questions in terms of “what happens to the concentration” of a particular species in the equilibrium mixture. We also need to be aware that the content of chemical equilibrium is highly specific and that in attempting to simplify the content for our students we may cause them to make general assumptions about equilibrium mixtures that are not valid. This was the case with physical and chemical equilibrium systems when students assumed that the addition of solids would affect these two types of systems in a similar manner. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11.

12. 13. 14. 15. 16. 17.

Wheeler, A. E.; Kass, H. Sci. Educ. 1978, 62, 223–232. Gussarsky, E.; Gorodetsky, M. J. Res. Sci. Teach. 1988, 25, 319–333. Hackling, M. W.; Garnett, P. J. Eur. J. Sci. Educ. 1985, 7, 205–214. Maskill, R.; Cachapuz, A. F. C. Int. J. Sci. Educ. 1989, 11, 57–69. Bradley, J. D.; Gerrans, G. C.; Long, G. C. South Afr. J. Chem. Educ. 1990, 10, 3–12. Hackling, M. W.; Garnett, P. J. Aust. Sci. Teach. J. 1986, 27, 27–32. Jordaan, F. Aust. J. Chem. Educ. 1993, Nov, 9–15. Tyson, L. M.; Treagust, D. F.; Bucat, R. B. Development of a Two-Tier Test To Examine Students’ Understanding of Chemical Equilibrium; Paper presented at the National Association for Research into Science Teaching, St. Louis, MO, 1996; Abstracts p 194. Driver, R. Int. J. Sci. Educ. 1989, 11, 481–490. Treagust, D. F. Int. J. Sci. Educ. 1988, 10, 159–169. Tyson, L. M. The Relationship between Preferred Explanations and the Nature of Science Content: Chemistry; Paper presented to National Association for Research into Science Teaching, St. Louis, MO, 1996; Abstracts p 193. Allsop, R. T.; George, N. H. Educ. Chem. 1984, March, 54–56. Gold, J.; Gold, V. Chem. Br. 1984, 20, 802–806. Bridgart, G. J.; Kemp, H. R. Aust. Sci. Teach. J. 1985, 31, 60–62. Bergquist, W.; Heikkinen, H. J. Chem. Educ. 1990, 67, 1000–1003. Russell, J. J. Chem. Educ. 1988, 65, 871–872. White, R. T. In The Content of Science: A Constructivist Approach to Its Teaching and Learning; Fensham, P. J.; Gunstone, R. F.; White, R. T., Eds.; Falmer: London, 1994; pp 255–262.


The Complexity of Teaching and Learning ... - ACS Publications

Recommend Documents