Student Ideas Regarding Chemical Equilibrium What Written Test Answers Do Not Reveal Wilbur Bergquist and Henry Heikkinen U. Northern Colorado, Greeley, CO 80639 Student mastery of new material is believed to depend upon their ability t o integrate the new information with existing knowledge (1-6). Bodner's (1)summary of the constructivist view stresses that the learner strives to organize information in terms of nrevious exneriences. Piaeet viewed learning as a process of "equilibratibn" as studenis attempt to relate new information to their existing knowledge through processes of assimilation and accommodation. Resnick (3) . . defines learnine as an active process. occurrine as a result of mental constructions by the learner. All these viewpoints stress that knowledge and meaning are actively constructed in the mind of thelearner. A wrinkle in the constructivist approach is that prior beliefs can interfere witb new 1earni;g by causing rejection or, a t least, a restructuring of the new material to fit current ideas (I, 7,8). Moreover, intuitive ("common sense") conceptions resist change, since many intuitive ideas are often in direct conflict with the new material (9).Learners a m e a r to accept selectively those events that support theirconceptions &bile ignoring, even rejecting, those observations that conflict. I t becomes very important that chemical educators attempt to identify the nature and depth of their students' "commonsense" ideas rather than assuming that working examples and defining new vocabulary will lead students to the same degree of understanding that they have gradually come to possess. Education should be thought of as producing. &nge in a student's conreptirms rather than simply occul muloting new information within the student's memory. Examinations can help determine which concepts and skill3 students already possess. Two qualities expected of any accepted assessment method are that (1) student responses are valid-that is, that they accurately reflect the student's current level of understanding, and (2) changes in test performance reflect changes that have taken in students' minds. Unfortunately, correlations between understanding of concepts and written test performance are not as high as most educators might wish (IO,14). High test scores may mask basic student misunderstanding of major concepts. Manv standardized chemistrv examinations focus on computational skills and recall of definitions (11-13). Questions that require students to synthesize information and apply concepts are not very common in such examinations. T o demonstrate masterv of chemical eauilibrium concepts, for example, students &e typically asked to solve compuiational problems; correct results are accepted as an indication that students "understand" equilibrium correctly. Such a belief is risky since many equilibrium computations are readilvsolved hv the annlication of an aleorithm memorized through repeatld ddrLhThus,correct responses do not necessarily reveal whether a student understands chemical equilibrium but only indicate that the student can compute eauilibrium constants or calculate eauilibrium concentrations. Chemlcal Equlllbrlum Mlsconceptlons Equilibrium, considered one of the more difficult chemical concepts to teach, involves a high level of student misun1000
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derstanding (10, l k l 8 ) . Yet equilibrium is fundamental to student understanding of other chemical topics such as acid and base behavior, oxidation/reduction reactions, and solubility. Mastery of the concepts associated witb equilibrium facilitates themasterv of these other chemical conceots. Since high marks on an examination are generally interpreted by students as an indication that they understand the material, it is likely that such students will assimilate any misunderstandings of chemical equilibrium into their reasoning patterns and thus propagate additional misunderstandines about other chemical topics. Bereauist (15). for example, found that students often selected ihk correct &Itiple-choice answer on an examination dealine with chemical equilibrium without a corresponding 1e;el of understanding for the underlying concepts. Manv students assumed that concentrations fluctuate as equilidrium is established and that addition of more reactant changes only the product concentrations. An additional misunderstanding that emerged was the belief that the volume of a eas samole could be different from the volume of the flask containing it. Garnett and Hackling (16Yprobed student confusion regarding rates of forw&d reaitions as physical conditions changed. The most common misunderstanding was that the rate increased as a function of time-or "as the reaction got going" . . (p . 8). Students also believed that the forward and reverse reactions alternate and exist as distinctly separate events when equilibrium is attained. In addition, Garnett and Hackling found that many students interpreted Le Chatelier's principle as implying it would be possible for a change in conditions to increase the rate of the favored reaction but decrease the rate of the opposing reaction. Wheeler and Kass (10) found students failed to distinguish between how fast a reaction proceeds (rate) and how far the reaction goes (extent). Many students believe that even though equiiihrium reactions are reversible they still go to completion, while other students think that the forward reaction goes to completion before the reverse reaction commences ( 1 6 , l n . In probing the quantitative aspects of equilihrium systems, Gage (18) found that students knew they had to compensate for changes in concentration of one reactant but could not correctly adjust all species involved in the reaction. Students often acted on the belief that the concentrations of reactants must equal the concentrations of products at equilibrium. In addition, thesestudies identified apeneral inab:llity of students to distinguish between mass &d concentration. Common student misunderstandings of chemical equilibrium identified in research to date can be summarized within four general areas of difficulty: 1. Studentsshow confusion regarding amounts (moles)and concen-
trations (molarities)by a. attempting to compute roncenrrarions when given rnolarity. b. expressing an unrrnainty when ro use volume. c. assumingsroichiom~tric mole ratios apply among product and reactant concentrations at equilibrium. d. assuming molar amounts are equal even when one is in excess.
Students show confusionover the appearance and disappearance of material by a. assuming concentrations fluctuate as equilibrium is estsblished. b. assuming a reaction is reversible yet goes to completion. e. assuming thst the forward reaction must be completed before the reverse one starts. d. assuming that addition of more reactant changes only the product concentrations. Students show confusion over the meaning of K, by a. describing it as varying- in value while at constant temperature. b. assuming that the value changes with amounts of reactants or products. Students show confusion aver the use of Le Chatelier's principle by a. attempting to adjust a system that is already at equilibrium. b. attemptinc . .to change concentration of the added reactant only. e. attempting to change concentration values of all species mesent ereeot the added reactant. d. expressing uncertainty how a temperature, volume, or pres. sure change (including the addition of a nonreactrng gas) will alter the equilibrium concentrations. ~
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tntervlew Examples ol Equlllbrlum Mlsunderstandlngs The following second-semester general college chemistry student responses were obtained during the think-aloud interviews conducted by Bergquist (15). They help illustrate some of the common student misunderstandings of chemical equilibrium listed above. Oscillating or Pendulumllke Behavior Interviewed students often described equilibrium as occurring either as an oscillating set of reactions or as exhibitine ~endulumlikebehavior. The general description of this oscillating process was that the foiward reaction, which generates nroducts, goes to completion before a second reaction, which iegeneratis the original reactants, starts. This viewpoint was expressed by Student H. (In the following dialogues, student responses are indicated by "S"; interviewer comments are marked by "I".)
tion of the initial amounts had already occurred. One individual. areuine that since no chance in the established eauilibriuk v2uesuis possible, thought6 mol remained. Misunderstandings regarding appearance and disappearance of material tended to cluster around one of three general beliefs regarding limiting reagents;
1. that one reactant can be totally consumed upon addition of another reactant. The fact that we added more 12, consumes all of the Hz? Correct. So there is no Ht left? There is no Hz left. that equilibrium is attained when one or both of the original reactants are totally consumed. S: Sav if hvdroeen ~~, , .. was the limitinc" reactant and vou added more iodine, you're not going todoa thing because there's not enough . . .possibly your hydrogen is already used up.
I: S: I: S: 2. ~
3. that equilibrium was being controlled by a limiting reagent. S: So I can't really say that it has increased or not unless I know that the iodine is the limiting readant. If it is, then it will increase, so I'm just guessing here that it is. But if it wasn't the limiting reactant and the other was, then it will stay the same. I: In other words, if the HZis the limiter, more addition of Is would have no effect? S: Yes.
Confusion over Concentration Two-thirds of students interviewed displayed little differentiation between amount and concentration. The most common error was the use of concentration as an expression
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S: Because equilibrium is not instantaneous. I: Is or is not? S: Is not instantaneous. So it would take a second. On addition it would go toward product and then decrease to come back. Others, like Student D, describe equilibrium as a pendulumlike event with back-and-forth shifting in concentrations as reagent amounts fluctuate.
S: This isgoing to shift over this way. And thisisgoing to move that.
It increases, decreases, increases, decreases . .. this is going to decrease. . . which increases this and decreases this. I: until it stops? S: Until it reaches equilibrium. This same student also felt that the oscillation hetween the forward reaction and the reverse reaction occurred a t different rates. S. There's a gradual shift this way, but there is a gradual shift back thst way. But not at the same rate.
Aooearance and Disanoearance of Materials .. .. Students showed poor understanding of changes that occur to a svstem a t eauilibrium if the concentration of a n original reactant is increased. Many students incorrectly descrihed the amount of iodine present after reestablish2HI system (table). ment of equilibrium in the Hz 12 Several of these students gave the wrong answer of 0.08 mol (the original 0.06 mol plus the additional 0.02 mol). Others incorrectly responded with a value of 0.02 mol, indicating that no further reaction was possible since total consump-
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Equal molar amounts of the gases H2and I2 were mixed in an empty 4.00-L flask.The flask and its contents were maintained at a constant 527 ' C for four days. Measurements were made on the third day and again on the fourth day; both showed that 0.060 mol of H. gas,0.060 mol of I* gas, and 0.240 mol of HI gas were all present. 1. At Me end of
me fourth dav
(a) the volume ot Me flask was(b) me concentration 01 the & gar was (c) me concentration of the I t gas was
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(d) me concentration of the HI gas was .2. At me stan of me experiment the moies of i2 present were .3. At Me start of the experiment the moies of HI present were .On the fifth day, an additional 0.020 mol of the gas 11 was added to the flask described at the end of the fourthday above (0.060 mol Hs. 0.060 mol IS, and 0.240 mol HI). The flask and its contents were held at a constant 527 'C for another six days. (Thus a total of 10 days have passed since the start of the experiment.) 1. At Me end of the temh day (a) the concentration of the IS gas was .[ans: 1.92 mol/L based on solvlng the quadratic; however. the expression (8 mol) - (x mol)]/4Lwas also accepted.] (b) me concentration of the Hz was .2. Compared to day four, on me ninth day (a) the concenbation of 12 d. decreased only a. increased,then decreased e. increased only b. decreased,then increased I. I am unsure c. stayed the same (b) Me concentration at H2 d. decreased only a. increased,then decreased e. increased only b. decreased,then increased I. i am unsure c. stayed the same (c) the concentration of HI d. decreased only a. lncreased,then decreased e. increased only b. decreased,then increased I. I am unsure c. stayed the same 3. Draw your image of this flask and contents at the end of the 10th day.
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of "how much" material was present. This attitude was clearly expressed by Student K, S: Amount is how much you have of something,and so is concentration.
One student incorrectly believed the concentration of a given aqueous solution would change if transferred to a different-sized vessel. Misuse of Volume The concept of volume was generally misapplied in two ways. One common misunderstanding of volume appeared when students, in discussing the volume of the flask, attempted to describe volume as identical to area. This comment by Student B, S. The volume is like the area, the space. was echoed by Student J, S: Not really, because we were talking of volume. Well, the volume of the flask which is the area, actually is the same.
The second error was describing volume as a measure of amount. as Student C did in discussine - the auantitvof silver salt dissolved, S: Now the total amount dissolved is 100 mL. I: You dissolved 100 mL? S: Well, that's how many you took out.
Typically, the words volume and area were both used to describe the space occupied, while volume was also used as the amount of material present. Student J expressed this dual usage best. S: Say you had the same volume of a gas that you have in this flask, hut it was in a smaller flask, the area will be different, hut the volume of gas in the flask will he the same.
Concentration and volume are apparently difficult concepts for learners, as other recently reported research (19-21) confirms. Confusion over Gas Behavior An unexpected misconception that emerged in this study was the belief that the volume of a gas sample could be different from the volume of the flask that contains it. This belief is clear in the responses of Student G,
S: You don't know how much the volume ofthe flask is. The flask is 4 L. I: But the contents. .. ? S: The contents we don't know. I: So there's a difference between the volume of the flask and volume of the contents? S: Uh-uh [affirmation].
and Student E, S: Volume of the flask, I said, was the same. Because I was thinking of the flask and not what was in the flask. I: Ok. So the contents have their own volume and the container has its own volume? S: Right.
and was best stated by Student F, I: Is there any difference between the volume of the flask and the volume of contents? S: Probably, yes. I: Whv? S: ~ e c i u s there e is nothing that says that all of your contents are going to fill the flask completely.
While Student J also showed a misunderstanding of gas behavior, his responses exposed lack of clarity regarding relationships between gas pressure and volume.
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Journal of Chemical Education
S: Well, the volume of the flask is going to remain the same, while
the volume inside the flask could increase or decrease depending upon the pressure that the gas was under. I: So the volume of the flask is defined by the structuralcontainer? S: Right. I: But the material in the flask, its volume could fluctuate? S: Right.
In addition, Student J expressed a sense of uncertainty due to the invisible, somewhat abstract nature of gases. S: Hecause when you're making ~olutions,you're starting with the watw,or thesolvent, and youadd theadute. So that's why I'm a little hit unclear with gases, I guess. I: You can visualize things dissolving and precipitating back out? S: Yah. I: But you have a hard time visualizing what a gas is doing? S: Don't you? [laughs]Yah, well, yah I do. Because, you know, gases you really don't see, you just, I guess, imagine what is going on. It's sort of a concept in your mind.
lmplicatlon8 for lnstructlon The literature on student conceptions, through frequent use of the term "misconception," suggests that students have in some way fallen short of the mark. Perhaps both inatructional methods and a lack of awareness of ootential conceptual pitfalls are responsible for creating some of the difficulty students have in understanding chemical equilibrium. One source of misunderstanding might be the traditional instructional language associated with Le Cbatelier's principle that suggests that a system a t equilibrium shifts to compensate partially for an applied stress. I t is possible that some students use this "stress-then-shift" logic to support their beliefs that equilibrium reactions oscillate. That is, students might correctly invoke Le Chatelier's principle t o predict appropriate shifts in concentrations hut then infer, incorrectly, that these resulting changes in concentration cause a second-eeneration stress on the svstem resultina in a compensating &ift back toward the original values. There is also a "common" lanaume Statements - oroblem. . of equilibrium concepts conta; everyday terms such as shift, equal, stress, and balanced. Such vocabulary can generate very different visual images, based on personal experiences (22,23). We must be aware of the differences between the technical use of certain words in science and everyday usage of the same terms. Since eeneral chemistrv students have had little - - - - ~most ~ conscious interaction with systems a t equilibrium (even thoueh their verv lives deoend on such eauilibria). i t is hard to imagine that-previousinformal expeiiences could have shaoed manv of these naive conceotions. Some misconceotions regarding equilibrium might be the result of instruction that emohasizes "correct" conceDts without hiahlighting common~conceptualerrors that liad students aitra;. I t seems aoorooriate to look critically a t the common instrucchemistry in search tional meihods and materials of of oossible sources of difficulty for students in understanding equilihrium. A thread linking some of these misconceptions appears to be that many students are unable to grasp the proportional aspects of concepts such as concentration (molb). Since nronortional loeic is critical to manv chemical conceots, esp e c h l y equilib;ium (24,25), one p&sible implication i Bthe need to down-play the common emphasis on "unit analysis" in favor of more practice with proportional reasoning. Another contribution of common instructional methods to equilibrium misconceptions may be found in student reliance on limiting reactant problems as a model for thinking about equilibrium systems (15). Perhaps the common approach of implying for the first half of the course that reactions "eo to com~letion"creates the feeline that a reaction l*sLonly as long'as material is availahle. perhaps continued ~
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focus on the "nroduct side" and the "reactant side" of chemical equations contributes to the belief that reactions proceed only in one directionat a time. In a survey of six general chemistry textbooks with a 1989 copyright date (2631),the earliest indication that reactions are "reversible" was found in a fifth chapter during a discussion of weak and strong acids. The first introduction to a system at equilibrium was usually in terms of vapor pressurk, which tended to occur around chapter 10. Although the concept of a limiting reagent is critical in predicting yields of chemical reaction, earlier acknowledgment that many reactions are reversible, that theoretical yields are based on the assumption of 100%conversion of reactant, and that all species involved in the reaction can exist simultaneously in the reaction vessel might help students avoid some of the more common misconceptions associated with chemical equilibrium. Again in the six texts surveyed, equilibrium as a specific topic was withheld until either chapter 13or 14. By contrast, the concept of a limiting reactant was introduced much earlier, ranging from chapter 2 to chapter 5. Finally, it is important to monitor how the technical vocabulary of chemistry is used by students rather than focusing on how well they can define words. The use of "area" as "v&me" and "concentration" as "amount" noted in this study are examples of the possible mismatch of definitions and students' actual usage. Conclusions Although current instructional methods may appear effective in transmitting the mathematical skills associated with equilibrium, such instruction often fails to develop student understanding of the supporting concepts. This discontinuity hetween the level of student understanding of concepts and their written test performance should be a primary
concern for those interested in promoting concept building with students. Providing students opportunities to verbalize their understanding of a concept is critical if deep-seated student misunderstandings are to be identified, diagnosed, and addressed. Literature Clted I . Bdner. G. M. J. Chem. Edue. 1986.63.873-878. ~~. c,,~,s r ~ , < h 0 ! IW..~I,II." II?O :. Hr
