Article pubs.acs.org/jchemeduc
Student Understanding of Liquid−Vapor Phase Equilibrium Andrew Boudreaux* and Craig Campbell Department of Physics and Astronomy, Western Washington University, Bellingham, Washington 98225-9164, United States ABSTRACT: Student understanding of the equilibrium coexistence of a liquid and its vapor was the subject of an extended investigation. Written assessment questions were administered to undergraduates enrolled in introductory physics and chemistry courses. Responses have been analyzed to document conceptual and reasoning difficulties in sufficient detail to be of practical use to instructors. Even after instruction on the relevant material, many students fail to recognize that for one-component systems in which a liquid and its vapor coexist in equilibrium, the pressure is controlled solely by the temperature. Although most students seem to realize that vaporization and condensation both take place, few are able to construct a coherent, step-by-step explanation for how dynamic phase equilibrium is established. Implications for instruction are discussed. KEYWORDS: First-Year Undergraduate/General, Chemical Education Research, Misconceptions/Discrepant Events, Equilibrium, Phases/Phase Transitions/Diagrams, Physics Education Research FEATURE: Chemical Education Research
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These students treated the vapor as an ideal gas in a closed container (i.e., fixed n), rather than focusing on liquid−vapor equilibrium. In addition, more than half of the students indicated that vapor pressure increases with the amount of liquid, perhaps because the larger amount of liquid “evaporates more”. A second study10 probed student understanding of the effects of adding or removing vapor particles from a system in which a liquid maintains equilibrium with its vapor. More than half of the students expressed a belief that adding or removing vapor will cause the vapor pressure to change. A study of chemical engineering students in South Africa11 found that many believed a temperature gradient necessary for condensation or vaporization to occur. This suggests the potential for difficulties understanding the constant temperature processes that govern dynamic phase equilibrium. Taken together, these studies suggest the presence of underlying difficulties with phase equilibrium. Few students spontaneously recognize that a closed liquid−vapor system tends to reestablish equilibrium when perturbed. Students appear to recognize that because vapor is present, the ideal gas law should apply. Many, however, fail to take into account the fundamental property of a one-component, liquid−vapor system: in phase equilibrium, the pressure is controlled solely by the temperature. Additional research shows that even advanced chemistry students exhibit conceptual difficulties with phase equilibrium.12 The present study seeks to add to what is known about student thinking about phase equilibrium. A primary goal is to support the development of instructional strategies for use in introductory courses. We document the specific steps in reasoning that students use on questions involving vaporization, condensation, and phase equilibrium.
his paper describes the identification of conceptual and reasoning difficulties that university students encounter when studying liquid−vapor phase equilibrium. Most science majors take introductory chemistry and physics, and phase equilibrium lies squarely in the overlap of these disciplines. Phase equilibrium forms the basis for the study of advanced topics in thermodynamics, such as the Clausius−Clapeyron equation. In addition, a basic understanding of phase change and phase equilibrium is necessary in other fields, such as atmospheric science. Phases of matter are taught at a wide range of instructional levels, and experienced instructors recognize that the topic poses considerable challenge for students. Research findings compiled by Driver et al.1 indicate that many young students believe when a wet object dries, the water simply disappears or is absorbed into the container. Most of these same students simultaneously understand that boiling water is a source of water vapor. In later grades, students often struggle to recognize that temperature remains constant during a phase transition. An increasing body of research documents the understanding of postsecondary students of topics in thermal physics, including the behavior of gases.2−6 Recently, several studies have reported on student misconceptions surrounding vaporization, vapor pressure, and the equilibrium between a liquid and its vapor. Azizoglu et al.7 found that about one in five Turkish preservice teachers thought that equilibrium vapor pressure depends on the volume of the container the liquid is in, and about one in two believed that, in a closed container, an increase in liquid content would cause a pressure increase due to the inverse relationship between pressure and volume described by the ideal gas law. This study confirmed the findings of Lin and Cheng,8 who found that students can memorize formulas and algorithms but often use them inappropriately. Canpolat et al.9 also studying the ideas of preservice teachers in Turkey, found that more than half held a misconception that vapor pressure varies inversely with the volume of the vapor. © 2012 American Chemical Society and Division of Chemical Education, Inc.
Published: April 24, 2012 707
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pressure cooker as an ideal gas in a sealed container (e.g., “It is a closed container...it works like an ideal gas.”). Results from the Pressure Cooker Task suggested to us that students tend to apply the ideal gas law indiscriminately, and have difficulty interpreting the macroscopic parameters that appear in the ideal gas law. We considered the possibility that students have difficulty identifying the relevant subsystems when analyzing the equilibrium of a liquid and its vapor, or that they struggle to match the values of pressure, volume, temperature, and number of moles to the appropriate subsystem (i.e., the liquid or the vapor). Finally, we wondered whether students understood and recognized the need to apply the fundamental idea that equilibrium between a liquid and its vapor in a rigid, closed container occurs at specific pairs of pressure and temperature values. Results from our preliminary investigation led to the following questions for research: 1. To what extent are students able to use the macroscopic parameters P, V, n, and T to characterize a system consisting of a liquid and its vapor? 2. To what extent can students apply the conditions of phase equilibrium to the liquid and vapor subsystems? 3. What specific difficulties do students encounter?
CONTEXT FOR RESEARCH Our study involved undergraduate students enrolled in the general chemistry and introductory calculus-based physics courses at Western Washington University, a comprehensive, Master’s degree-granting institution. These students typically major in chemistry, physics, mathematics, or engineering technology. Each course covers states of matter and phase changes, gas laws, the kinetic theory of gases, and thermodynamics. Our investigation focused on student understanding of phase equilibrium in the context of closed liquid−vapor systems involving only a single component. When studying such systems, students are expected to understand that temperature alone controls the pressure.
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PRELIMINARY RESEARCH: THE PRESSURE COOKER TASK Many introductory chemistry and physics texts pose tasks that involve a pressure cooker.13 Bodner, however, has found that even chemistry graduate students have substantial difficulty using basic principles to explain how a pressure cooker works.12 While many students recognize that an increase in pressure will cause an increase in the boiling point of water, the underlying mechanisms are often poorly understood. We tasked a group of 57 students in introductory calculusbased physics to explain in everyday language how a pressure cooker works. Our aim was to elicit specific types of student reasoning that we might probe further. The students had received traditional lecture instruction on phase change and phase equilibrium prior to completing the task on a course exam. The following quote is the most sophisticated response we received: The temperature in the pressure cooker is able to rise above 100 °C because the pressure is higher [than atmospheric pressure] which allows for the water to reach a higher temperature. The same effect can be observed at elevation; there is less pressure so lower boiling point. This response does not provide a mechanism by which the pressure inside the cooker changes. The student fails to describe the one-to-one relationship between the pressure and temperature of a liquid and its vapor that are in equilibrium inside a rigid, closed container. We are thus unable to determine whether the student recognizes that the increase in pressure is due to a net phase change from liquid to vapor inside the cooker. The statement does, however, relate a change in boiling point to a change in pressure and contains no explicit errors. If it is assumed that this answer indicates understanding of the underlying mechanisms, then a count of similar responses provides an upper bound for the number of students who understand phase equilibrium in this context. Just over onequarter of the students gave a response similar to the one presented above. Many students made explicit reference to the ideal gas law. For example: As pressure increases within the cooker, volume remains the same. This causes the temperature to rise proportionally using the equation PV = nRT where V, n, and R are constants. As P increases, to keep the same values on both sides, T must rise as well. This statement incorrectly assumes that the amount of water vapor is constant. In general, students did not construct arguments based on phase equilibrium or on the behavior of small particles, but instead seemed to treat the contents of the
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RESEARCH METHODS To address these questions, we designed a set of research tasks. The tasks were administered in written form on exams and quizzes in the introductory chemistry and physics courses after students had received instruction on the relevant topics; the tasks required students to apply concepts to novel situations in order to make qualitative comparisons. In all cases, students were asked to explain their reasoning. Below we describe each task, provide a rationale for the task’s design, and outline the reasoning we expected for a correct response. The Pressure Comparison Task
We considered employing isobaric systems for the research tasks. In such systems, when equilibrium between a liquid and its vapor is maintained, P−V work may be done. Loverude et al.2 and Meltzer14 have shown that students have difficulty applying the concept of work to ideal gas processes. We realized that asking students to analyze processes that involve both liquid−vapor equilibrium and P−V work might yield fragmented responses. We thus began with tasks involving systems with variable pressure but fixed volume. In the Pressure Comparison Task, students consider two pots of water. Each is purged of air by vigorous boiling, then sealed and simultaneously removed from the heat source. Students compare the pressures in the pots after they have been sealed a long time. To develop a robust picture of student reasoning, we administered multiple versions of the task. In one, the pots are prepared in rooms with different ambient temperatures, while in other versions, the pots are in rooms of equal temperature. We refer to these as the different T and same T versions, respectively. Furthermore, in the different T version, the pots were prepared at the same ambient pressure, while in the same T version, the pots were prepared at different ambient pressures. In these versions of the task, the pots are of the same size, but are filled to different levels with liquid water; thus, the volume available to the vapor is different in the two pots. The different T and same T versions of the Pressure Comparison Task are shown in Figure 1 and Figure 2, respectively. 708
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Figure 1. Different T version of the Pressure Comparison Task. Figure 3. Changing V version of the Pressure Comparison Task.
unchanged, the pressure inside the cylinder is the same before and after the piston is moved. The three versions of the Pressure Comparison Task described above are summarized in Table 1. Table 1. Different Versions of the Pressure Comparison Taska Task Version
Controlled Variables
Prompt
Different T Compare pressure in pots 1 (Pext) and 2 after cooling Same T
Compare pressure in pots 1 T and 2 after cooling
Figure 2. Same T version of the Pressure Comparison Task. Changing V Compare pressure in cylinder before and after piston is pushed in
To answer correctly, a student should recognize that each pot will come to thermal equilibrium with its surroundings, and that the final pressure inside each vessel will equal the equilibrium vapor pressure of water. Because temperature alone controls the equilibrium vapor pressure, students should recognize that the higher temperature pot must have greater pressure in the different T version and that the pressures must be the same in the same T version. The tasks above involve the net phase change that occurs when the system moves from one P, T equilibrium state to another. It is possible that phase changes associated with compression or expansion at constant P and T would trigger different types of student reasoning. We thus designed a third version of the Pressure Comparison Task. In the changing V version, the volume of a single, sealed cylinder containing “liquid X” and its vapor is increased or decreased slowly by pushing in or pulling out a piston. During this process, thermal equilibrium with the environment is presumed to be maintained at all times; the temperature remains constant because a slow compression or expansion allows heat exchange with the surroundings. The piston is fixed in place with a pin at the beginning and end of the process; students are asked to compare the pressure inside the container before and after the volume change. This version is shown in Figure 3. The changing V version of the Pressure Comparison Task is analogous to the same T version in that students consider pressures that occur at the same temperature but different volumes. Thus, in the changing V version, because temperature controls equilibrium vapor pressure, and temperature is
T, (vol. of liquid, Pext)
Manipulated Variables T, (vol. of liquid, vol. available to vapor) (vol. of liquid, vol. available to vapor, Pext) (vol. available to vapor)
a
Students compare pressures inside sealed vessels that contain liquid and vapor. A number of variables are presented; students must recognize that for a given substance, temperature alone controls the pressure. Pext refers to the ambient pressure at which the vessels are prepared; parentheses are used to indicate variables that do not affect the pressure.
The Oven Task
On the Pressure Comparison Task, students must select a vapor subsystem and characterize it appropriately using the ideal gas law variables. Student responses indicated a lack of facility with particle−model explanations for phase equilibrium. We thus developed an inquiry-based physics lab to address the observed difficulties. Use of the lab in course instruction served as a context to further investigate student thinking. This paper does not discuss our laboratory curriculum in detail or make claims about the effects on student learning, but instead focuses on the additional insights into student reasoning that were gained. In one part of the lab, students complete the Oven Task, a pencil-and-paper thought experiment. Students consider a sealed, rigid container with liquid water and water vapor in equilibrium at room temperature. The container is placed in a warm oven: Toven is given as 45 °C while Troom is 20 °C. Students are told that over time equilibrium is reestablished and are asked to list the steps in the cause−effect chain through which this occurs. The first step is provided, and students are 709
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discussed subsets of student responses together to reach consensus on a framework for categorizing reasoning. A single researcher then applied this framework to all responses in a given data set, setting aside responses difficult to categorize. These problematic responses were subsequently discussed, resulting either in a consensus categorization or, in some cases, modifications to the framework and subsequent reanalysis. Our investigation proceeded in two phases. In the first phase, responses to the Pressure Comparison Task were analyzed in order to explore student understanding of the macroscopic conditions under which a liquid and its vapor coexist in equilibrium. Seven common themes in student reasoning emerged. The second phase focused on analysis of responses to the Oven Task, and resulted in a pair of additional themes that characterize student understanding of the microscopic processes that govern the dynamics of the transition from one equilibrium point to another. While themes in student reasoning are presented separately in the discussion below, they were interrelated, with individual responses often containing evidence of multiple difficulties. Furthermore, conceptual reasoning and mathematical difficulties were generally intertwined, and could not be completely separated. We thus do not quantify the prevalence of specific difficulties. A guiding criterion for reporting a given category, however, was that it occurred in at least 10% of student responses. In reporting student difficulties, we do not necessarily imply that student ideas are stable and coherent, as a “misconceptions model” of student reasoning would suggest. It may be that students generate responses on the spot through the activation of more primitive, commonsense notions associated with a “knowledge in pieces” perspective. (Use of each of these two perspectives in an investigation of student understanding of special relativity is described by Scherr.15) Rather than collecting evidence of student learning with an express purpose of supporting one view or the other, we take an empirical approach with a primary aim of characterizing student thinking in sufficient detail to provide practical guidance to instructors.
prompted to include the following terms in their response: temperature, pressure, rate of vaporization, rate of condensation, moles of vapor, and volume of vapor. A correct response requires recognizing that the temperature alone controls the vaporization rate while the pressure alone controls the condensation rate. The increase in vaporization rate at the higher temperature of the oven leads to an increase in the amount of vapor in the same volume, which in turn increases the pressure. This provides negative feedback on net phase change by boosting the condensation rate, allowing the system to stabilize at a new combination of pressure and temperature. Box 1 shows the steps that we expected students to produce. Box 1. The Cause−Effect Steps That Students Were Expected To Formulate in the Oven Task 1. The temperature increases, so the vaporization rate increases. [This was given to students.] 2. The vaporization rate increases, so the amount of vapor increases. 3. The amount of vapor increases, so the pressure of the vapor increases (because the volume available to the vapor is essentially constant). 4. The pressure increases, so the condensation rate increases. 5. The condensation rate increases until its value equals that of the vaporization rate. Equilibrium is reached. Administration of Tasks
The Pressure Comparison Task was administered as an ungraded written quiz or on course examinations in the introductory calculus-based physics course and the general chemistry course. Data were collected from 511 students in eight different course sections involving four different lecture instructors. In each case, students had received instruction on liquid−vapor phase equilibrium and the concept of vapor pressure. The instruction took place over 5−30 min of lecture, and included assigned textbook reading. Each student in the study responded to only one of the three versions of the task. Students completed the Oven Task as part of a required lab in the calculus-based physics course. Written responses were collected from 88 students in one lecture section of the course. Students were encouraged to discuss their ideas with their laboratory partners before writing their answers, and a teaching assistant was present to offer assistance. When students completed the task, they had received traditional instruction on phase equilibrium, including the idea that temperature and pressure govern the rates of vaporization and condensation, respectively. In addition, they had considered the effect on pressure of changing the amount of gas in a rigid container held at fixed temperature.
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RESULTS AND DISCUSSION
Phase One: Investigation of Student Understanding of the Conditions under Which a Liquid and Its Vapor Coexist in Equilibrium
The Pressure Comparison Task was designed to elicit student ideas about macroscopic variables and the empirical relationship between pressure and temperature in liquid−vapor systems. Table 2 presents correct response rates on different Table 2. Pressure Comparison Task Correct Response Ratesa Students Answering Correctly, % (N)
Methods of Analysis
On the Pressure Comparison Task, the percentage of students selecting the correct comparison was calculated as a measure of the overall difficulty that the task posed to students. On the Oven Task, a corresponding percentage was determined for the students who provided a correct and complete set of steps. Results from qualitative analysis form the bulk of the discussion below. Student explanations were examined for evidence of specific conceptual and reasoning difficulties. Two researchers
Task Version
Calculus-Based Physics
General Chemistry
Different T Same T Changing V
70 (167) 23 (53) 29 (61)
25 (189) 24 (41)
a
The task was administered after students had received instruction on liquid−vapor phase equilibrium
versions of the task in the general chemistry and introductory physics courses. In cases in which the same version of the task was administered in multiple sections of the same course, results were similar, and have thus been averaged. 710
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Correct response rates for the changing V and same T versions are comparable, suggesting that neither the specific origin of a difference in volume, nor the identity of the substance (i.e., water vs “substance X”) had an effect on student performance. The correct response rates reported in Table 2 do not take reasoning into account; a response was counted as correct even if the explanation was incomplete or, in some cases, partially flawed. For example, the following student response on the different T version was counted as correct: The pressure in each pot will be proportional to the ratio of the equilibrium temperature to the initial temperature since the volume is unchanged. Therefore, Pot 1 will have a greater pressure since it is at a greater temperature. This student recognized correctly that the container with the greater temperature has the greater final pressure. However, he included an incorrect rationale involving the temperature change of each container, rather than a comparison of the final equilibrium temperatures. We chose a minimally restrictive criterion in order to overestimate the percentage of students who understand liquid−vapor phase equilibrium. These correct response rates thus serve as an upper bound for student understanding; true comprehension may be lower. The fraction of students who answered correctly on the same T and changing V versions of the task was similar in both the chemistry and physics courses; about one-quarter in each of the four cases. This similarity suggests that the two populations have similar conceptual and reasoning difficulties with regard to phase equilibrium, and that these two versions of the task are of comparable difficulty. The success rate on the different T version was nearly triple that on the other versions, about 70%, suggesting that the different T version is less challenging for students. Below we present student responses on the three versions of the Pressure Comparison Task as evidence of specific difficulties. Difficulties Relating Pvapor to Psystem. To succeed on the Pressure Comparison Task, one must interpret the concept of pressure appropriately. We expected students to associate the pressure in the vessel with the equilibrium vapor pressure of the liquid contained by the vessel, as in the following correct student response: “Vapor pressure increases with T... and vapor pressure is the only factor contributing to the pressure in the pot.” Many students, however, had difficulty when characterizing the pressure of the system. Some students, as this comment indicates, seemed to regard the vapor pressure as one contribution to the total pressure: “Ptotal = Pair + PH2O from Dalton’s law.” It is unclear what “PH2O” specifically denotes; possibilities include the pressure of the vapor, the hydrostatic pressure of the liquid, or their sum. This response raises the possibility that the student did not recognize that the conditions described in the task imply that the pressure of the system is the equilibrium vapor pressure. The preparation procedures specified in the task constitute an operational definition of the concept of equilibrium vapor pressure. The student above failed to apply such an operational definition, limiting his ability to apply this concept in a specific physical situation. Failure To Recognize That Temperature Alone Controls Equilibrium Vapor Pressure. Many student responses indicated difficulty with a fundamental aspect of single-component liquid−vapor systems: in equilibrium, the temperature alone controls the pressure of the vapor. Failure to
apply this relationship between temperature and pressure was widespread among all groups of students involved in the study. On the changing V version of the task, students should recognize that because liquid is always present, net vaporization or condensation must occur in conjunction with the volume change in order to hold pressure constant. The following correct response exemplifies such reasoning: [Pressure] will remain the same, which is equal to the vapor pressure at 300 K, because the pressure initially decreases [as the volume increases], but the liquid releases more vapor to keep the pressure constant at 300 K. This student seems to consider both the effect of a volume change on the pressure of a gas, and the one-to-one relationship of pressure and temperature for a liquid−vapor system. The student reconciles these two ideas by explaining that the number of particles of vapor can change in this situation. Overall, only one-quarter of the students answering the changing V and same T versions of the task realized that the pressures must be the same. On the same T version, one student justified an incorrect pressure comparison by explaining, “Both pots have equal temperature now so the space above the water in the pot at the ski lodge causes less pressure.” Although the student explicitly recognizes that the vessels have the same temperature, he indicates incorrectly that their pressures are different. He does not apply the rule that temperature controls pressure in liquid−vapor systems, instead concluding that different volumes will lead to different pressures. Indiscriminate Application of the Ideal Gas Law. Some students based their pressure comparison on the ideal gas equation. Many who took this approach seemed to neglect completely the implications of phase equilibrium for the pressure and temperature of the system. If students try to apply the ideal gas law in the Pressure Comparison Task, they should realize that lack of information about the amount of vapor leads to an impasse, requiring another approach to be adopted. We found, however, that students tended to make assumptions about the number of moles of vapor in order to continue using the ideal gas law. The following response is a typical example: The pots have come to thermal equilibrium with the room, therefore the temperatures are the same. But pot 1 has a greater volume of vapor, therefore the pressure is lower, assuming n is the same also. The student has identified the information relevant for solving the problem: that the space above the liquid water is filled with water vapor, and that the two vessels have the same temperature. The student does not, however, go on to discuss the implications of phase equilibrium. Instead, he justifies the use of the ideal gas law to compare the pressures by putting forth an erroneous assumption that the two vessels contain the same amount of water vapor. This type of incorrect reasoning is similar to results from the Pressure Cooker task presented earlier. Students who gave answers similar to the above manipulated the ideal gas law, treating the problem as if it were algorithmic rather than conceptual. A lack of conceptual knowledge namely, the failure to recognize that a priori assumptions about the amount of vapor cannot be madeseemed to prevent students from realizing that the ideal gas law is insufficient to solve the problem. Thus, mathematical competence does not necessarily lead to conceptual understanding, a finding consistent with the work of Pickering.16 Tendency To Interpret n as the Total Number of Moles. Many of the students who completed the changing V 711
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only an ideal gas without any liquid. Students tended to focus on single relationships in the ideal gas law (e.g., the direct relationship between pressure and temperature), while neglecting the effect of other variables. As shown in Table 2, student performance on the different T version of the Pressure Comparison Task was significantly higher than on the same T version. This discrepancy can be accounted for by the concept of salience. It may be that a difference in the value of a variable is a highly salient feature for students. If a variable has the same value in two different situations (or is thought to by a student), then a student may ignore this variable when formulating an answer. Consider the following response (same T version): PV = nRT, so P = R/V, and P1V1 = P2V2. As the volume increases, the pressure decreases. The pressure inside pot B is greater than the pressure inside pot A because there is less volume for gas in container B. P = constant*1/V. This student not only treats n and T as fixed between the two pots, but also crosses these variables out, rewriting the equation without them. This is consistent with a notion that fixed variables may be ignored as unimportant, and may account for the apparent failure of the student to appreciate the central importance of temperature in determining the pressure. The different T version may draw student attention to the role of temperature due to the high salience of the difference in temperature of the two pots, accounting for the higher correct response rate.
version of the Pressure Comparison Task stated that the amount of water vapor remains constant during the volume change. We considered the possibility that the students were interpreting n to be the total number of moles of water molecules inside the vessel (i.e., vapor and liquid), rather than water vapor alone. To investigate, we administered a modified form of the task. In one section of the chemistry course (N = 89), we asked students explicitly whether they agreed or disagreed with the following statement: The number of moles, n, in the ideal gas law (PV = nRT) refers to the total number of moles of water molecules (i.e., the sum of the liquid and vapor moles). Remarkably, about one-half of the students incorrectly agreed with this statement. However, even this large fraction may underestimate the prevalence of the difficulty interpreting n; some students who answer correctly when asked explicitly may not spontaneously recognize the need to carefully define variables and systems when analyzing a physical process. Tendency To Assume That Two Different Pots Have the Same Amount of Vapor. Of the students who properly identified the variable n in the ideal gas equation as pertaining only to the vapor phase, many still insisted that the two pots have the same value for n. Consider the following response (same T version): The number of moles (n) only refers to the vapor moles...the ideal gas law cannot be applied to liquids. P = nRT/V; the number of moles of gas will remain the same as in [the other pot]. However the volume occupied by the gas is greater so the pressure will be less. This student clearly states that n does not vary between the two pots, even while admitting that n refers only to the gas. This student also stated, As the water is cooling, more and more water vapor will return to its liquid state; the number of moles of gas will decrease. Here she recognizes that particle exchange can occur between the liquid and vapor phases, yet does not seem to realize that this is a mechanism by which the two pots can have differing amounts of vapor. Her response is consistent with an inappropriate reduction of the ideal gas equation to Boyle’s law (P1V1 = P2V2). This finding is similar to those of Azizoglu.7 Belief That the Volume of Liquid Controls Amount of Vapor. Another student who admitted that n refers only to the vapor went on to state: The pressure would be less because there is an increase in the volume that can be occupied by the water vapor and there is less water to produce water vapor [emphasis added]. Many other students indicated that the amount of vapor is related to the amount of liquid water, with more liquid water implying more vapor. Canpolat also found that students sometimes relate vapor pressure to the amount of liquid present.10 Salience of Differing Variables. It is possible that the above responses are symptomatic of a larger difficulty attending to multiple mechanisms or relationships. The inverse relationship between the pressure and volume of a gas, as described by Boyle’s Law, may have a high salience for students taking introductory chemistry and physics. The ideal gas equation is emphasized in these courses, so it is perhaps not surprising that students spontaneously seek to apply this tool in solving problems. It may be that once students apply a gas law relationship to the water vapor, their consideration of the implications of the liquid−vapor equilibrium is inhibited. Kautz et al.5 presented evidence for a similar phenomenon on tasks involving
Phase Two: Student Understanding of the Dynamics of the Transition from One Equilibrium Point to Another
On the Pressure Comparison Tasks, very few students applied concepts of phase equilibrium or reasoned about particle exchange. The persistence of students in using algorithms rather than applying concepts of phase equilibrium prompted us to wonder whether students lacked content knowledge and facility with the mechanistic reasoning surrounding phase equilibrium. In Phase Two of our investigation, we analyzed student responses to the Oven Task to explore the following additional questions for research: 4. To what extent can students apply mechanistic reasoning about vaporization and condensation to explain how dynamic phase equilibrium is established? 5. What specific difficulties do they encounter? When responding to the Oven Task, some students seemed to combine steps 2 and 3 from Box 1, linking an increase in the rate of vaporization directly to an increase in pressure with no explicit statement that the amount of vapor increases. Other students stated that the rates of vaporization and condensation are equal, but failed to explicitly identify this as the condition for phase equilibrium. These types of incomplete responses were nevertheless counted as correct. As judged by these criteria, 38 out of 88 students in the class responded correctly. Thus, despite instruction on the relevant material, scaffolding that provided the key words, and group assistance, fewer than half of the students adequately explained the mechanisms underlying dynamic phase equilibrium. Many responses were incomplete beyond the level described above. For example, one student added only the following to the given, initial step: “This new amount of vapor drives up the gas pressure, increasing the rate of condensation.” While this statement contains no explicit errors, key steps are omitted. The student does not explain that the increase in the rate of 712
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encountered in introductory chemistry and physics courses. This is consistent with the work of Gussarsky and Gorodetsky,17 who found that 12th-grade students in Israel tend to confuse “everyday” meanings of equilibrium, such as physically balancing an object, with “scientific” meanings, as in chemical equilibrium. Some students indicated that when the sealed container is perturbed by being placed into the oven, it will ultimately return to its original equilibrium state, rather than a new equilibrium at an elevated pressure and temperature: As vapor pressure increases the rate of condensation increases in order to bring the vapor pressure back down to equilibrium. The vapor pressure will only decrease as a result of maintaining equilibrium. This response is consistent with a belief that a liquid−vapor system has a single, fixed equilibrium state. The students who completed the Oven Task had taken a previous course on mechanics. In this course, they considered a variety of mechanical systems involving simple harmonic motion, each of which exhibits a single equilibrium position. It is possible that some students inappropriately extended features of this type of equilibrium to the novel phase equilibrium context of the Oven Task.
vaporization causes an increase in the amount of vapor. While this may be implied, the crucial statement that the volume is fixed is also missing, and thus, the conclusion that the pressure increases is not fully justified. Responses of this type were not counted as correct. Other responses contained sequencing errors suggesting difficulties with cause−effect relationships, or incorrect statements indicating general misunderstandings of the nature of phase equilibrium. Below we present examples as evidence of specific difficulties. Difficulties with Cause−Effect Relationships. Many students failed to place causally related processes in the correct order. For example, one student explained, “As temperature approaches 45 °C, rate of condensation also increases. Pressure will also increase as a result.” Although the rate of condensation and the pressure both increase, the student has placed these in the incorrect causal order. The condensation rate increases as a result of the increase in pressure, rather than vice versa. Other students made no statements of causality whatsoever: “As the temperature approaches 45 °C, rate of condensation also increases as well as pressure.” This language suggests that the student has merely recognized that the processes are correlated, with no indication that he understands the underlying causal mechanisms. The student may have simply memorized that increases in temperature, the rate of condensation, and the pressure often occur together in liquid−vapor systems. Other responses were more ambiguous: “As the molecules evaporate more quickly, the pressure increases, and the moles of vapor increases.” This student may have reversed the cause and effect order of the changes in amount of vapor and pressure, or may have failed to recognize that these changes are causally linked. “The moles of vapor increases”, as a cause, should precede “the pressure increases” as an associated effect. The student’s use of the linking word “and” suggests awareness only of correlation, rather than causality. Some students linked causally unrelated phenomena: “Step 3: Since the rate of vapor and rate of condensation are proportional to temperature, they will both be equal.” Here the student incorrectly links the rate of condensation to temperature. He further assumes (incorrectly) that two quantities both proportional to a third will equal one another. Difficulties with the Concept of Equilibrium. In a closed system consisting of a liquid and its vapor, phase equilibrium refers to the condition in which the relative amounts of liquid and vapor are stable, and occurs when the rate of condensation and the rate of vaporization are equal. While many students seemed to recognize that this condition applies, there was a tendency to mingle this with other meanings associated with the term equilibrium. One student explained: Pressure will level off when evaporation and condensation are equal, as well as temperature being in equilibrium. Moles of vapor increase as well as volume of vapor because the level of water would decrease slightly until pressure, condensation, temperature, and evaporation are in equilibrium. The language is, at best, imprecise; the student refers indiscriminately to temperature, pressure, condensation, and evaporation as being “in equilibrium”. Another student seemed to confuse the conditions for phase equilibrium with those necessary for mechanical equilibrium: “Once the rate of condensation is equal to the rate of evaporation there is no net force, resulting in a state of equilibrium.” The student may be confusing different types of equilibrium
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CONCLUSIONS Even after receiving instruction, students in introductory, university-level chemistry and physics courses experience substantial difficulty understanding the conditions under which a liquid and its vapor coexist in equilibrium. On tasks that require students to apply these conditions to a system that undergoes a change in temperature or a change in volume, many students treat the amount of vapor as a fixed quantity. Students who spontaneously discuss the conditions of phase equilibrium exhibit a number of additional difficulties. Many students: • Define the system (or subsystem) inappropriately • Do not recognize that vapor pressure is controlled solely by temperature • Tend to focus on variables that differ from one situation to another, regardless of whether or not those variables influence the vapor pressure • Fail to adequately distinguish between multiple usages of technical terms such as equilibrium • Struggle to construct a coherent “story” of how equilibrium is established through the processes of vaporization and condensation
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IMPLICATIONS FOR TEACHING It is well established in the science education literature that students’ prior ideas must be taken into account if instruction is to succeed.18 We thus put forward the following suggestions for instruction on liquid−vapor phase equilibrium. First, students should be guided to articulate for themselves the conditions under which a liquid and its vapor will come to equilibrium. (Arons has written on the importance of the verbal articulation of concepts.19) This should include a statement of the observations necessary to confirm that equilibrium has been established, namely, that the relative amounts of liquid and vapor are not changing over time. In addition to this, students should be guided to construct the mechanistic, causal chain of reasoning that explains phase equilibrium. That is, students should “tell the story” of how equilibrium between a liquid and its vapor is established. Our results suggest that the majority of 713
dx.doi.org/10.1021/ed2000473 | J. Chem. Educ. 2012, 89, 707−714
Journal of Chemical Education
Article
(10) Canpolat, N. Int. J. Sci. Educ. 2006, 28, 1757−1770. (11) Gopal, H.; Kleinsmidt, J.; Case, J. Int. J. Sci. Educ. 2004, 26, 1597−1620. (12) Bodner, G. J. Chem. Educ. 1991, 68, 385−388. (13) Giancoli, D. Physics for Scientists and Engineers, 4th ed.; Prentice Hall: Upper Saddle River, NJ, 2008; p 493. (14) Meltzer, D. Am. J. Phys. 2004, 72, 1432−1446. (15) Scherr, R. Am. J. Phys. 2007, 75, 272−280. (16) Pickering, M. J. Chem. Educ. 1990, 67, 254−255. (17) Gussarsky, E.; Gorodetsky, M. J. Res. Sci. Teach. 1990, 27, 197− 204. (18) Donovan, M.; Bransford, J.; Pellegrino, J., Eds.; How People Learn: Bridging Research and Practice; National Academy Press: Washington, DC, 1999. (19) Arons, A. A Guide to Introductory Physics Teaching; Wiley & Sons: New York, 1990; pp 15−17.
students at this level will require scaffolding when building this explanatory story. Students should be presented with opportunities to apply this reasoning to different situations (e.g., an isothermal volume change or a constant volume cooling process). We suggest that students be given opportunities to distinguish related (yet distinct) meanings of the technical terms pressure and equilibrium. When students first encounter situations in which “pressure” is used to describe liquid−vapor systems, students should articulate the difference between this “new” pressure and previous uses of the term (e.g., the hydrostatic pressure in a container of water). Students should further be asked to reflect on how the fundamental definition of pressure applies to both the hydrostatic and liquid−vapor contexts. Similarly, students should be asked to distinguish between the various “types” of equilibrium: thermal, mechanical, phase, chemical, and so forth. To develop a more flexible understanding of the behavior of gases, students should be given opportunities to consider gas systems that can undergo changes in the amount of vapor. Standard textbook problems on the ideal gas law most often involve a fixed number of moles, but many systems in chemistry or physics have variable molar quantity. In addition to systems in which phase equilibrium occurs, there are other situations in which students may encounter changes in the number of particles in the system (e.g., a chemical reaction involving consumption or evolution of a gas as a reactant or product). Because such “real-world” situations occur, students should have practice applying the ideal gas law to analyze them. Particularly relevant to liquid−vapor systems is the change in the amount of vapor associated with either a change in volume or a change in temperature. Students should be given tasks in which they must compare systems that have different vapor volumes or temperatures, yet the same pressure.
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AUTHOR INFORMATION
Corresponding Author
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ACKNOWLEDGMENTS The Washington State NASA Space Grant program provided support for this work. The authors are grateful to Mark Peyron, Sergei Smirnov, Andreas Riemann, and James Stewart for administering research tasks in their chemistry and physics courses, and to Emily Borda and Steve Gammon for providing valuable feedback on the manuscript.
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REFERENCES
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