The Conceptual Knowledge of Beginning Chemistry Graduate Students

1 Have Found You an Argument The Conceptual Knowledge of Beginning Chemistry Graduate Students Twenty years ago а paper entitled "The Grim Silence of Facts" was puЬlished in the Journal (1). It began as follows. While grading а beginning graduate inorganic examination some time ago, I was startled to discover that the student believed silver chloride to Ье а pale green gas. . .. А little later the student launched into а long, p\ausiЬle explanation as to why silver chlo­ ride was а pale green gas. This paper stimulated an on-going discussion of the proper balance between the theoretical principles we expect stu­ dents to understand and the factual knowledge on which they are built. lt might now Ье time to examine the concep­ tual knowledge that chemistry majors construct during their undergraduate experience. For the Jast three years а conceptual knowledge exam has been given to entering graduate students at Purdue during the orientation program for new teaching assistants. The number of questions on the exam and the wording of these questions has gradually changed, but responses to these questions have now been obtained for а sample of up to 132 graduate students. Some of the questions and the responses they elicited are described below. А complete Hst of the questions and the answers he would give to these questions can Ье obtained Ьу writing the author. What Are the BubЫes ln Bolllng Water? Osborne and Cosgrove found that the majority of second­ ary-school students believe that the bubЬJes in boiling water are made up of either "heat", "air", or "oxygen and hydro­ gen" (2). The first question examined the extent to which graduate students in chemistry give similar answers. It was phrased as follows: "Assume that а beaker of water on а hot plate has been boiling for an hour. Within the liquid, bubЫes can Ье seen rising to the surface. What are the bubЫes made of?" Slightly more than 70% of the graduate students answered that the bubЫes contain water vapor, steam, or nюlecules of water. Almost 20%, however, suggested that these bubЬles consisted of air or oxygen and 5% indicated that they con­ tained а mixture of Н 2 and 0 2 gas. Many students followed the advice of Samuel Johnson, who was quoted as saying: "1 have found you an argument; 1 am not oЫiged to find you an understanding" (З). Others, however, tried to explain their answers. The following are typical explanations of the assumption that boiling water contains bubЫes of air. These are air bubЫes.With increasing temperature, the solubllity of air in water decreases and since at room temperature there is always some air dissolved in water, it gets pushed out of solution. Or: Most of the containers have smaJI packets of air trapped inside. And so when the water is boiling this air gets heated and the hot air rises up which is seen in the form of bubЫes. What Js the Relatlonshlp belween Temperature and Heat? There is an extensive literature devoted to the analysis of student's concepts of heat and temperature (4-8). The fol­ Jowing item was used to probe the hypothesis that students' misconcepts about these topics are resistant to jnstruction; "One way of raising the temperature of an object is to heat it. Does this mean that adding heat to an object always raises its temperature?" More than 80% of the sample said "no". This means, however, that slightly less than 20% said "yes". Some of the explanations indicated significant confusion about the con­ cepts of heat and temperature. То add heat is Like giving energy-and sometimes you сап give energy to an object but it won't give it back; this is an endothermic reaction.When an object is heated and the temperature raises, it means that the reaction is exothermic. Others used thermodynamic principles to reach jncorrect conclusions. q = nСЛТ heat = mass Х specific heat Х ЛТеmр. Therefore Л Т = heat/mass Х specific heat.If heat is added to an object then q is positive, mass is positive, and the specific heat is positive. Therefore ЛТ must Ье positive and the temperature rises. Or: Уes, at constant volume the internai energy is equal to C,.dT. Therefore, dT = dU/C,., at constant pressure it is dT = dH/dT, which implies that the greater the change in U or Н, the greater the change in Т. The following quotation summarizes the most common ex­ planation of why the answer to this question is "no". No, as in the case of boiling water.One may continue to add heat, but the temperature of the water doesn't continue to increase above the boiling point. The excess heat energy is converted into kinetic energy and water molecules vaporize as they escape the surface of the water. 1s Heat Conserved? То further probe the students' conception of heat, they were reminded that mass and energy are both conserved and then asked: "1s heat conserved?" The majority (60%) said "no". But 40% said "yes". The most common explanation was: "Heat is а form of energy and is therefore conserved." The next most common was: "Heat is а form of energy and therefore is not conserved." Two examples of another com­ mon explanation are given below. Heat is conserved. When something is cooled, it heats something else up.То get heat in the first place though, you may have to use energy. Heat is just one form of energy. And: Yes, heat is transferred from а system to its surroundings and vice versa. The amount lost Ьу one system equals the amount gained Ьу the surroundings. What Happens to the Welght of an lron Bar When 11 Rusts? It is not surprising that many secondary-school students believe that nails lose weight when they rust (9). In spite of the expectation that BS chemists would not make the same mistake, the following question was used on the conceptual knowledge exam: "What would happen to the weight of an iron bar when the iron rusts? Does it increase, decrease, or remain the same?" As expected, most (81 %) of the graduate students conclud­ ed that the weight of the bar would increase, as long as the rust was not scrapped off the bar. Approximately 10%, how­ ever, argued that the weight would decrease for reasons other than the loss of rust. Another 6% concluded that the weight of the bar would remain the same. А typical explanation for the assumption that the weight of the bar would increase is given below. Or: The weight of the salt on the ice surface generates heat to melt some of the ice which then dissolves the salt to give а liquid which has а lower freezing point than water. And: When you put salt (or anything really) on the ice, it disrupts the crystal structure of the ice. The water molecules can no longer get into а nice perfect array, and so the ice becomes а liquid. As were explanations based on chemical reactions. Placing salt on the ice will encourage or initiate the formation of an aqueous base, NaOH, thereby causing the one bond between oxygen and hydrogen to break and resulting in the formation of NaOH + НС!. rxn: NaCI + Н20 -. NaOH + НС! The weight increases assuming none of the rust falls off the bar. This is due to the formation of iron oxides. Explanations for the decrease in the weight of the iron bar are more interesting. It decreases-the iron oxide that is forming is less dense than iron. Or: As iron rusts, its weight decreases. Thus mass lost shows up as energy (i.e., if you had а closed system you could measure the change in energy. The energy would increase as the mass de­ creased.) Explanations for why the weight remains the same are equally interesting. Remains the same. А chemical reaction neither creates nor de­ stroys matter.It changes it. Oxidation causes the rusting. It does not create or destroy the iron, it changes its form. And: It would Ье the same, since the metal is only being oxidized. А small percentage of students were not аЫе to answer this question. Only one explained why: The weight would change according to the difference in the densi­ ties of Fe(s) and Feз02(s). How Does Salt Melt lce? Many of us who teach chemistry are asked practical ques­ tions, such as: "How does salt melt ice?" Because the prima­ ry goal of our ТА orientation program is to help beginning graduate students learn how to function as teaching assis­ tants, the following item was used on the comceptual knowl­ edge exam. "In the winter, some people scatter salt on icy driveways. Explain how placing salt on the surface of ice сап melt the ice." The most common answers were based on simple colliga­ tive property explanations: salt lowers the freezing point of water or the melting point of ice. 10% of the students who invoked а colligative property explanation, however, con­ cluded that salt raises the freezing point/melting point of water/ice. Other explanations were based on thermodynamic argu­ ments, such as the idea that salt dissolving in water is an exothermic process. The salt that is added goes into solution in some of the water that is present. Due to this, а certain amount of heat of solution is released. This helps in melting the ice. Mechanical explanations were also popular. The weight of the salt on the surface of the ice disrupts the lattice structure and the ice melts-this is analogous to the Ыades of ice skates . ... J А limited number of answers to this item provided а method for getting the salt into the crystal, so that colligative proper­ ty explanations might succeed. The salt lowers the melting point of water. Even though the salt is scattered on the ice, as cars drive on it or even when people walk on it, the pressure of their weight melts а slight amount and the salt works to melt it. During the day, sunlight warms the ice enough to bring it to its melting point when salt is in the mixture. Ionic substances lower the aЬility of water molecules to Ьind to one another, lowering the melting point. How Does а Barometer Work? Many years of observing teaching assistants led to the hypothesis that the following item would Ье а useful addi­ tion to the conceptual knowledge exam. "А barometer can Ье built from а long, thin tube of glass that is sealed at one end. The tube is filled with mercury and then inverted into а small pool of mercury. Explain how this barometer works." А significant number of students were unaЫe to produce an answer. One of the most popular explanations might Ье described as the "one-force model". There is no force pushing down on the mercury column inside the tube, but the mercury in the pan has the force of atmospheric pressure pressing down on it. The downward force on the pool, causes а column of mercury to Ье supported, the height of which depends on the pressure exerted on the pool. Some students invoked а model which assumes that а gas is trapped at the top of the tube of mercury. (Student drew а figure that indicated that there is "trapped gas" at the top of the tube.) As pressure from the atmosphere in­ creases, the pressure on the Hg should force mercury higher up the column until increased pressure from the compressed trapped gases balances the outside pressure. Lower outside pressure will lead to а falling Hg level inside the tube as the trapped gas will expand to yield а lower internal pressure. Explanations, such as the following, which were based on а dynamic equilibrium between opposing forces were unfortu­ nately rare. Because the open end of the tube is inverted into the mercury end of the dish, no air is allowed into the upper end of the tube. Therefore, only the weight of the Hg column (no air in the tube) will press against the pool of Hg.This weight will balance against the atmospheric pressure pressing on the pool of mercury. Or: The atmosphere exerts а pressure on the pool of water [sic], which then gets pushed up the tube until the pressure exerted do\vn Ьу the column of mercury is the same as the pressure exerted up. How Does а Hot-Alr Balloon Work? Several years ago, the following question was used on an hour exam in а general chemistry course for science and engineering majors. The distribution of answers was almost random; the fraction of the student population choosing each answer was essentially the same. Which statement best explains why а hot-air balloon rises when the air in the balloon is heated? (а) As the temperature of the gas increases, the average kinetic energy of the gas molecules increases, and the col\i5ion5 between these ga5 molecu\e5 and the wall5 of the balloon make the bal­ \oon ri5e. (Ь) А5 the temperature of the gas increa5es, the pre5sure of the ga5 increa5e5, pushing up on the balloon. (с) А5 the temperature of the ga5 increases, the gas expands, some of the gas escapes from the bottom of the balloon, and the decrease in the density of the ga5 in the balloon lifts the balloon. (d) А5 the temperature of the ga5 increa5e5, the volume of the balloon expands, causing the balloon to rise. (е) А5 the temperature of the ga5 increa5e5, hot air ri5e5 inside the balloon, and this \ifts the balloon. When the same question was given to the graduate students, the distribution of answers was no longer isotropic. Each answer was chosen, however, Ьу а significant fraction of the total sample who completed this item: А(8), В(6), С(40), D(8), and Е(18). How Does а Pressure Cooker Work? The following item was used to probe the students' abllity to extend their knowledge of chemistry to real-world exam­ ples. "Long before we had microwave ovens, people used pressure cookers to increase the speed at which food cooks. Explain how а pressure cooker works." One of the most popular answers was based on the ideal gas law. Several examples are quoted below. We know Р 1 Т 1 = Р2Т2. So if the pre5sure is douЫed, the tempera­ ture shouJd Ье douЬled, increased heat lead5 to quicker cooking. Or: Pre5sure cooker5 are based on the principle that Р а: Т, i.e., pressure is directly proportional to temperature. When volume kept constant thus if you increase the pre5sure the temperature also increase5 and it take5 le5s time to cook. Other answers invoked pressure as а direct means of cooking food faster. Food cooks faster becau5e the pres5ure i5 high. This mean5 that there are more impacts of molecule5 per 5urface area, which in turn generates more heat. Or: Cooking i5 actually а way of denaturing the protein5 in food. Temperature i5 а way of physically denaturing, but 50 is pre55Ure. So therefore temperature and pressure work together to cook the food. А popular explanation was based оп the assumption that а pressure cooker is а closed system, which is inherently more efficient. If we increase the pre5sure under which food is cooked, we have more col!i5ion5 of heated air with the food, heating it fa5ter. On an open 5tove, heat е5саре5 into the 5urrounding5, without affecting the food more than once. Other explanations invoked complex thermodynamic mod­ els, which invariaЬ!y led to the wrong prediction. = dP/dT -ДН/ дV, therefore dP is inversely proportional to dT, when Р increase5, Тьр decrease5. Or: Ciausius-Clapyron equation: дН < О alway5 in this са5е, 50 а5 the pressure increa5es, the temperature decrease5, thus the food cooks fa5ter. А remarkaЬ!y small fraction of the explanations included arguments such as the following: Д5 the pre5sure inside the sealed cooker builds, а5 а result of the vaporization of water, the boiling point of water i5 increa5ed, thereby increa5ing the temperature at which the food cook5hotter temperature, less time. Why Does Sodlum React wlth Chlorlne? The following item was used to probe the source of stu­ dent's misconcepts. "Everyone knows that sodium metal reacts with chlorine gas to form sodium chloride. Explain why. In other words, what is the driving force behind this reaction?" The first year this item was used, essentially all of the answers were based on simple thermodynamic principles, such as: "Because of а decrease in the Gibb's free energy of the system." During the next two years, the students were encouraged to Jook for explanations that helped us under­ stand why the free energy decreases. А significant fraction of the sample was no longer аЫе to answer the question, or invoked statements of the obvious, such as: "Because Na and С! are very active," or "NaCI is а very staЫe material." Ву far the rnost common explanation was based оп the assumption that the octet rule drives chemical reactions. Chlorine wants to obtain another e\ectron to achieve the most staЫe configuration where eight e_lectrons are pre5ent in the out• ermo5t molecular orЬital. Sodium donate5 an electron to chlorine and, thereby, allows both the chlorine and sodium atoms to achieve the eight electron configuration. Or: This happens because every element wants to оЬеу the octet rule and as 5uch, when Na and CI are brought together Na donates its single outermost electron to become more staЫe and С! gladly accept5 this single electron from Na and in the process NaCI is formed. And: The driving force i5 for sodium and chlorine to have а filled octet. А filled octet corre5pond5 to а more staЫe energy state than either sodium or chlorine exhiЬit. Thus sodium donates an elec• tron to chlorine which give both а filled octet. In spite of the fact that the net transfer of an electron from sodium to chlorine to produce Na + and CJ- ions would Ье an endothermic process, а significant fraction of the students proposed arguments such as the following. Sodiuш metal is very unstaЫe, it wants to give up electrons badly to become Na + , which i5 much more staЫe. Chlorine ga5 readily accepts the electrons and become5 с1-. This notion was so robust it led to errors in the remembered magnitudes of electron affinities and ionization energies. The electron affinity for Cl is greater than the energy required to pull an electron off of Na. Therefore С! can remove an electron from 50dium and the two re5uJting ion5 form an ionic 5alt. А small, but significant fraction of the population invoked the lattice energy of NaCl as the driving force behind this reaction. No student, however, invoked the combination of the electron affinity of chlorine coupled with the lattice energy of NaCl as more than compensating for the energy required to produce а Na+ ion and the energy required to break the Cl-Cl bond. Why Do Both lcebergs and Steel Shlps Float? Research оп misconceptions of density (10, 11) led us to investigate the students' responses to the following item. "Ice is less dense than water, but steel is almost eight times as dense as water. Explain why both the Titanic and the iceberg it hit were аЫе to float оп water." One student admitted: "l've been searching for а good explanation for this one for а long time." А surprisingly large fraction of the sample population invoked miscellaneous buoyancy explanations, such as: The Titanic was equipped with flotation device which allowed the ship to have buoyance. Other relatively innovative explanations were given, There is а force between the iceberg and Titanic-and this one plus the fact that ice is less dense than water prevent the Titanic from dropping. Or: Ship is also propelled Ьу an engine-when it took in water it sank. And: The Titanic was made from titanium, not steel. А popular explanation was based оп surface tension: "The surface tension of water supported the boat." An equally popular explanation invoked the surface area of the ship. Steel (of the Titanic) is more dense than water, however, its weight is distributed over а large area. Or: The weight of the ship is spread over such а large surface area that it is suspended оп top of the water. It is also а shape that doesn't allow water оп the top of the ship. А remarkaЬly small fraction of the population proposed explanations based оп the idea that the average density of а ship filled with air might Ье less than that of the water it would displace. Anything less dense than water floats оп it, so the ice floats. The Titanic is also less dense than water even though it is made of steel because the steel contains an air-filled area. So in essence it is like а steel balloon, and the steel balloon is less dense water. 2. Misconcepts are resistant to instruction. The research being done to identify the concepts students build during their first exposure to chemistry is important for all of us because the misconcepts they build are so resistant to instruction that а significant fraction of the population retains them even after the 500 h of laboratory and 400 h of lectures that characterize the undergraduate experience in chemistry mandat­ ed Ьу the ACS Committee оп Professional Training. 3. Knowledge is not the same as understanding. Many of the responses we have observed сап Ье explained Ьу assuming that students all too often possess knowledge without understanding. 4. Misconcepts are often instructor-driven. Student misconcepts about physics соте from prior experi­ ence with the world (13-16). They know, for example, that they must арр!у а constant force to keep an object (such as а car) in motion, regardless of what they are told Ьу our physics instructor. In Ьiology, there are media-driven misconcepts, such as the com­ mon notion that humans and dinosaurs coexisted. (Remember the Fred Flintstone cartoons?) In chemistry, there are two additional sources of misconcepts. Some result from the language we use. We use terms (such as "heat capacity") or phrases (such as ''heat flows") that were meaningful in the context of the accepted theory at the time they were proposed, in spite of the fact that this theory is по longer accepted. The language often remains constant as science evolves, while the meaning of the terms changes until they be­ come misleading. Other misconcepts in chemistry are instructor-driven. Some result from the way we simplify ideas so they сап Ье Jearned for the first time. Explanations that help students make sense of the chemistry we expect them to learn for the first time are often remembered in place of the more correct, and far more explicit, discussions to which students are introduced at later points in their careers. Misconcepts are also created when students are not explicitly told-or are unaЫe to understand-points that are obvious to their instructors. The following equations, for exam­ ple, are both used as statements of the first Jaw of thermodynam­ ics. дЕ= Both equations are legitimate, but the first describes the fact that the energy of the universe is constant, дE�шiverse =О whereas the second describes how the energy of а system сап change. ЛE,ystein = q Concluslon The student responses are consistent with-but Ьу means test the validity of-the following assertions. о дE=q+w по 1. Knowledge is constructed in the mind of the learner (J 2). Students construct knowledge about the concepts we expect them to learn from lectures, laboratory experiments, textbooks, homework assignments, and so оп. During this process they test the validity of the knowledge they construct within the domain in which it is defined. They have difficulty, however, applying their knowledge to areas where they have not been actively encouraged to apply it. All too often, this means they cannot extend their knowledge beyond the limits of the classroom into the real world. Evidence for the domain-specific character of chemical knowl­ edge is easy to oЬtain. Ask students in organic chemistry to explain why acetylene is reactive. They will frequently invoke the С=С triple bond. Then ask students taking inorganic chemistry why nitrogen is virtually inert. They will attribute it to the N=N triple bond. Because we seldom ask students to extend their knowledge beyond the domain in which it is constructed, it is the rare student who recognizes the dissonance generated Ьу assum­ ing that the same argument can Ье used to justify diammetrically opposing behavior for systems that have the same number of valence electrons. +w Finally, instructor-driven misconcepts сап Ье generated uninten­ tionally when the limits of assumptions are not explicitly described. How many of us, for example, do calorimetry experiments in which we ask students to assume that the heat given off in а chemical reaction is equal to the heat absorbed Ьу the water in which the reaction is run or Ьу the water bath that surrounds the reaction? It is possiЫe that this experiment reinforces the idea that heat is "con­ served". That heat cannot Ье either created or destroyed. Llterature Clted 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Davenport, D. А. J. Chem. Educ. 1970,47,271. Osborne, R.; Cosgrove, М. J. Res. 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