Macroscopic Observations of Dissolving, Insolubility, and Precipitation

Article Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX

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Macroscopic Observations of Dissolving, Insolubility, and Precipitation: General Chemistry and Physical Chemistry Students’ Ideas about Entropy Changes and Spontaneity Timothy N. Abell and Stacey Lowery Bretz* Department of Chemistry and Biochemistry, Miami University, Oxford, Ohio 45056, United States

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S Supporting Information *

ABSTRACT: Learning thermodynamics requires understanding abstract topics such as entropy and spontaneity. Students tend to rely on metaphors and everyday meanings to reason about these topics. This study investigates how students explain dissolution and precipitation using the concepts of entropy and spontaneity. Students from general chemistry, physical chemistry, and biophysical chemistry participated in semistructured interviews. During these interviews, students observed four tasks: an exothermic dissolving process, an endothermic dissolving process, the insolubility of an ionic salt, and a precipitation reaction. Students reasoned about their observations of dissolving, insolubility, and precipitation by describing entropy as the disorder of a chemical system and describing disorder in several different ways. Few students mentioned microstates or the distribution of energy. Students determined which of the four tasks were spontaneous and offered explanations that included reasoning about changes in enthalpy, reasoning about changes in entropy, and/or using concepts from kinetics. Students’ ideas about entropy changes and spontaneity are examined, and the implications for classroom teaching and future research are discussed. KEYWORDS: First-Year Undergraduate/General, Upper-Division Undergraduate, Chemical Education Research, Physical Chemistry, Misconceptions/Discrepant Events, Aqueous Solution Chemistry, Precipitation/Solubility, Solutions/Solvents, Thermodynamics

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INTRODUCTION Thermodynamics is an abstract chemistry topic that students often struggle to comprehend. Students rely on vague metaphors to describe entropy1−8 and incorporate everyday definitions into their scientific reasoning.1,8,9 Students not only find thermodynamic concepts challenging to learn, but furthermore often confuse kinetic concepts with thermodynamic concepts.6,10,11 Research investigating students’ ideas about entropy has found that students most often describe entropy as a measure of disorder, chaos, or randomness.1−6 Haglund and Andersson found that when they gave a list of terms that could be used to explain entropy to their Swedish engineering students, the students considered the term “disorder” to be the least scientific and, yet, the most useful way to explain entropy and reason about changes in entropy.5 Students have defined disorder, as it relates to the entropy of a chemical system, in several different ways, including the movement of particles,2,4 the number of collisions,2 general “mixed-up-ness,”2 the spatial configuration of particles,4 and the freedom of particles.4 Other misconceptions related to entropy have also been reported. Carson and Watson found that when students observed the exothermic neutralization reaction between hydrochloric acid and sodium hydroxide, they concluded that a positive change in entropy caused the decrease in enthalpy.1 © XXXX American Chemical Society and Division of Chemical Education, Inc.

These students ascribed a causal relationship to entropy and enthalpy. Students have also been reported to hold the idea that entropy is conserved. Christensen et al. gave college physics students a multiple choice questionnaire that presented several scenarios in which there was an energy exchange between a system and surroundings.12 After instruction, half of the students responded that entropy was conserved between the system and surroundings. Investigations of students’ ideas about spontaneity and Gibbs free energy have also been published.1,6,9−11,13 Students tend to invoke the common meaning for spontaneous, i.e., defining it as a process that happens without any outside influence,1,9 rather than consider the thermodynamic factors that affect spontaneity. Bain et al. reported that lower-division students tended to use anthropomorphic reasoning to explain spontaneous processes while upper-division students reasoned from the underlying thermodynamic parameters.3 Even when students did consider thermodynamic factors while reasoning about Gibbs free energy, they often equated changes in enthalpy with changes in free Received: December 6, 2018 Revised: February 13, 2019

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DOI: 10.1021/acs.jchemed.8b01007 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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energy; students ignored entropy considerations and concluded that only exothermic processes were spontaneous.3,6 Students have also been reported to identify connections between the magnitude of the Gibbs free energy change and the rate at which the reaction happened.6,10 The students interpreted more negative values for Gibbs free energy changes to mean that reactions occur faster. The confusion between thermodynamic and kinetic concepts hinders a student’s ability to reason about spontaneity, and Sözbilir found that students often used kinetic data to explain thermodynamic phenomena.11 A few studies have explored how upper-division students apply and understand mathematical models associated with thermodynamics in both physics and chemistry.8,14−18 Students struggled to develop mathematical expressions to represent chemical systems or experimental data but were able to describe systems that would be represented by a given equation.14,19 Some of these studies have demonstrated that students have difficulty translating their math knowledge to problems in chemistry and physics.15,16 This may be due to a lack of conceptual understanding of math, not a lack of physics or chemistry knowledge.15,16,18

PARTICIPANTS

There were 32 students enrolled in second-semester general chemistry (n = 19, GC), physical chemistry (n = 7, PC), or biophysical chemistry (n = 6, BPC) who were recruited from a medium size university in the midwestern United States. The GC courses used a textbook23 that introduced the concept of entropy during discussion of the enthalpy changes that accompany dissolving. The PC and BPC courses provided instruction on the thermodynamics of gas phase and biologically relevant aqueous phase processes, respectively. All students were taught and tested about dissolution and precipitation before being interviewed. The students who were interviewed were representative of both the course and university enrollment where the research was conducted. The GC students were all science (nonchemistry) majors, while the PC students and the BPC students were chemistry, biochemistry, or chemical engineering majors. Of the students, 22 participants were white/Caucasian, with 18 students identifying as female and 14 as male. The research was approved by the university’s Institutional Review Board, and all students were informed of their rights as research participants and consented to be interviewed. Each student was assigned a pseudonym in order to report the findings. The students were compensated for their time with a nominal gift card.

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RESEARCH QUESTIONS To date, studies investigating student thinking about entropy have focused primarily on students’ descriptions or definitions of entropy or processes in which entropy increased. Little research has examined students’ reasoning about entropy changes for processes during which the entropy of the system decreases. There are no studies known to the authors that have asked students to reason about entropy changes and Gibbs free energy after observing a nonspontaneous process. Therefore, the research questions that framed this inquiry were the following:

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METHODS Semistructured interviews were conducted by the first author in both fall 2016 and spring 2017. A LiveScribe pen was used to record any student writing or drawing during the interviews in order to document what the students drew while trying to explain their visual and tactile observations.24 Specifically, we were interested in capturing any drawings of particle models, chemical equations, and/or mathematical equations in order to better understand how the students reasoned about the macroscopic observations they made by using symbolic and particulate explanations.25 The interviews were also audio and video recorded. A typical interview lasted approximately 1 h. The interview guide consisted of five phases (Figure 1) and has been previously described in detail.26 (The full interview guide can be found in Supporting Information.) Students were asked follow-up questions to their responses when appropriate. Each interview was transcribed verbatim, and the LiveScribe images generated by the students in the interviews were used to annotate the transcripts. A qualitative software program, NVivo 11,27 was used to manage the data corpus. Both inductive and deductive coding were used to identify and aggregate students’ ideas about spontaneity and changes in entropy across all phases of the interview. The first round of analysis consisted of deductively coding the data based on the topics used to develop the interview guide: dissolving, insolubility, precipitation, enthalpy/temperature change, entropy, and spontaneity. A second round of analysis was done using open, inductive coding within each of the larger, deductive categories across all participants. The inductive coding was intended to explore the students’ explanations based on both observable features and underlying thermodynamic parameters, with interest in identifying meaningful connections made by students to their prior knowledge. Coding was done by the first author. The codes were grouped into categories based upon the students’ explanations and whether a visible change was observed during the phase. To establish trustworthiness, scheduled debriefing sessions were held weekly with the second author and held

1. How do students reason about entropy changes and spontaneity during their observations of exothermic and endothermic dissolution processes and precipitation reactions? 2. How do students reason about entropy and spontaneity after observing a nonspontaneous process?

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THEORETICAL FRAMEWORKS

Novak’s Theory of Meaningful Learning

This research was guided by Novak’s theory of meaningful learning. This theory states that, in order for students to learn meaningfully, they must have relevant prior knowledge, the new material to be learned must be meaningful and relatable to existing prior knowledge, and the students must choose to incorporate the meaningful material into their existing knowledge.20,21 If these conditions are not met, the new knowledge may be merely memorized without forming substantive connections to prior knowledge or by forming incomplete or inaccurate connections.22 The purpose of this study was to investigate what meaningful connections the students have created between their understandings of entropy and spontaneity in the context of making three distinct observations: (1) an ionic compound that dissolves, (2) an ionic compound that does not dissolve, and (3) a precipitation reaction. This study explored the prior knowledge that the students drew upon while trying to explain their sensory observations, both visual and tactile, of three distinct chemical phenomena. B



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Figure 1. Interviews consisted of five phases and four tasks that students were asked to complete. Reprinted with permission from ref 26. Copyright 2018 American Chemical Society and the Division of Chemical Education, Inc.

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monthly with chemistry education research graduate students and another chemistry education research faculty member who were not involved in the data collection. The first phase of the interview explored the prior knowledge of the students. Students were asked to provide explanations for the formation of aqueous ionic solutions and precipitates, to explain why some processes or reactions are spontaneous, and to share their understanding of enthalpy and entropy. Then, students were asked to carry out three distinct tasks. Students were asked to add solid magnesium chloride to a vial of water (phase 2) and solid silver nitrate to a second vial of water (phase 4). These dissolution processes were accompanied by temperature changes easily detected by touching the vials (phase 2, exothermic; phase 4, endothermic). In phase 5, the students were asked to combine the two solutions made in phases 2 and 4 in order to form a precipitate (silver chloride). Again, this reaction was accompanied by a tactile temperature change (exothermic). The salts in phase 2 and phase 4 were chosen because they both dissolve spontaneously; therefore, the entropy of the system increases for both, but the changes in enthalpy differ in their sign. Phase 2 and phase 4 provide opportunities to explore how differences in sensory information (namely, tactile changes where one vial grows warm while the other vial grows cold to the touch) affected students’ explanations and/or their reasoning about entropy changes and/or spontaneity. The task in phase 5 was also chosen because it was a spontaneous process, but unlike phases 2 and 4, the formation of the precipitate was accompanied by a decrease in the entropy of the system. In phase 3, students were asked to add silver chloride to a vial of water. No macroscopic changes were evident, either visually or by touch. This compound was specifically chosen due to its negligible solubility and to investigate students’ ideas about nonspontaneous processes. The students observed the solid sink to the bottom of the vial and were unable to detect any noticeable temperature change. Students were asked to explain each of their visual and tactile observations, or the lack thereof in phase 3, including a particulate level explanation. Students were also asked specific questions regarding both the enthalpy change and the entropy change that accompanied each process and to comment upon the spontaneity of each process. The findings reported herein focus upon the students’ understandings of entropy changes and spontaneity in the context of these observations.

RESULTS AND DISCUSSION

Entropy and Changes in Entropy

Prior Knowledge. When students were asked to explain the concept of entropy in phase 1 of the interview (prior to any of the observational tasks), four categories of student thinking emerged from analyses of the data (Table 1): entropy as Table 1. Students’ Knowledge about Entropy Prior to the Dissolving and Precipitation Tasks (N = 32) Category Disorder or chaos Freedom of motion Microstates Unsure Ability of a compound to dissociate

GC (n = 19)

PC/BPC (n = 13)

Total (N = 32)

11 7 1 5 1

11 6 5 1 0

22 13 6 6 1

proportional to disorder, entropy as the freedom of motion of particles, entropy as the ability of a compound to dissociate, and entropy as the number of available microstates. Some students invoked more than one of these ideas in their explanations. Six students (n = 5 GC, n = 1 PC/BPC) were unable to define entropy or provide any examples of its application. The majority of students (n = 11 GC, n = 11 PC/BPC) initially described entropy as a measure of the disorder or chaos of a system. Each of these students elaborated upon what “disorder” meant with regard to a chemical system when prompted to do so by the interviewer. Consequently, each of these 22 students is also represented in one or more of the other three categories below. Thirteen students (n = 7 GC, n = 6 PC/BPC) associated entropy with the freedom of motion of the particles in the system, focusing specifically on the translational and rotational motion of the ions. Consider Henry’s (BPC) explanation: “So it’s gonna deal with entropy. So for a solid you only have vibrational motion. Uhh but once you dissociate into the liquid then these ions can move around and can translate, they can rotate, they can do all kinds of things. Umm and, and higher entropy is favored...” Like Henry, most of these students talked about the increased freedom of motion in terms of a phase change, either from solid to liquid or liquid to gas. However, none of the students in this category explicitly mentioned energy in their explanations. C



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There were 10 students (n = 3 GC, n = 7 PC/BPC) who connected their observations of dissolving and precipitation to their ideas about entropy as disorder in order to draw a conclusion about the change in entropy of the system. These students described the relative “order” or “disorder” of the system both before and after their observations of dissolving and precipitation. Consider this explanation offered by Gavin (PC) after he observed the precipitation of silver chloride: “So in this case the entropy or disorder is decreasing because silver and the chloride are forming a solid. So there’s more order to the system, so there’s less entropy. So like the final minus the initial states would be... negative.” Thinking of entropy as disorder led students like Gavin to draw the correct conclusion about the signs of the change in entropy in phases 2, 4, and 5. However, these students were unable to go beyond the metaphor of disorder that they discussed in the prior knowledge phase of the interview to sufficiently explain how they reasoned from their observations to their conclusions about entropy changes. Six students (n = 2 GC, n = 4 PC/BPC) connected their observations of dissolving and precipitation to their ideas from the prior knowledge portion of the interview about entropy as indicative of the freedom of movement of the particles. These students articulated a meaningful connection between the knowledge they brought to the interview and the observation tasks that were presented to them during the interview. Five students (n = 3 GC, n = 2 PC/BPC) connected their observations of dissolving and precipitation to the number of particles present in order to determine the entropy change. Luna (PC) explained her thought process about the change in entropy after observing the dissolution of magnesium chloride: “Entropy is increasing because you go from less particles to more particles. So, well you start off with like, so this [MgCl2] is just one thing and then you end up with three things [Mg2+ and 2 Cl].” Students like Luna counted the number of moles of ions and determined that the greater the number of moles present, the higher the entropy of the system. This seems to be a heuristic used by these students that more moles means more entropy.28 Two PC/BPC students connected their observations of dissolving and precipitation to the concept of microstates in order to describe the entropy change that occurred during these processes. Consider Hank’s (BPC) explanation: “...you had a solid crystal lattice which is a highly ordered structure. Umm and dissolved in the water so you have each individual ion that was in the crystalline form, and the salt can take so many different microstates in the solution versus if it’s in a crystal.” While both of these PC/BPC students used their prior knowledge about microstates to explain their observations, the four other students who mentioned microstates in the first phase of the interview did not use the concept in any other parts of the interview. No student mentioned energy when explaining the entropy changes in terms of microstates. Two students (n = 1 GC, n = 1 PC/BPC) did not use any visual observations of dissolving or precipitation to reason about changes in entropy, but rather they reasoned from their tactile observations that there was a change in temperature; i.e., the vial grew either hot or cold to the touch. These students determined the change in entropy by reasoning with the Gibbs free energy equation, ΔG = ΔH − TΔS. For example, Stephanie (GC) observed the dissolution of silver nitrate and identified the process as spontaneous because the solid dissolved in water.

Six students (n = 1 GC, n = 5 PC/BPC) invoked the concept of microstates to describe entropy. Five of these students described microstates as the number of ways the particles in the system could be arranged, including Jake (GC): “Umm so entropy’s a little complicated. Umm essentially in the most basic definition is like umm... like increased freedom or increased motion of particles. Umm like the more technical is that like the products, increasing entropy increases like the microstates... it’s increasing the freedom of motion...” Although Jake explains that entropy causes microstates to increase in number, he knows that there is a connection between the number of microstates and the value of entropy. Hank (BPC) was the only student to explicitly connect microstates to energy: “But the, the microstates are, I mean, like orientation and movement of each individual particle in the solution. So it’s colloquially described as disorder. So like more movement and kinetic energy and I guess spinning and rotating like that would increase the number of possible microstates that the system could be in which is higher entropy.” While Hank’s explanation was incomplete in that he does not explain why an increase in kinetic energy would increase the entropy, he was able to describe a connection between an increase in kinetic energy and an increase in available microstates. One student (n = 1 GC) conflated Ksp with entropy, stating that the value of entropy determined how much of a given compound will dissociate. When asked about entropy, Ami (GC) responded: “Umm how much of the compound would dissociate... like for entropy, if it has a higher entropy it would dissociate more, whereas if it had a low one it wouldn’t.” Dissolving and Precipitation Observations. There were 22 students (n = 12 GC, n = 10 PC/BPC) who reasoned correctly and consistently that there was an increase in entropy in both phase 2 and phase 4 (dissolving of ionic solids) and a decrease in entropy in phase 5 (precipitation reaction). Most students (n = 7 GC, n = 12 PC/BPC) reasoned about the entropy change on the basis of their observation that a phase change had occurred (Table 2). Students drew inferences about the phase change using four different patterns of reasoning that were identified through analysis of the data (disorder, freedom of motion, moles of reactants and products, and microstates) in order to draw a conclusion about the change in entropy. Table 2. How Students Reasoned about Entropy During Dissolution and Precipitation Category Reasoning based on observation that solid dissolved/solid precipitated Disorder Freedom of motion Moles of reactants and products Microstates Reasoning based on observation that temperature of vial increased/decreased Reasoning with Gibbs free energy equation Improper use of equation

GC (n = 19)

PC/BPC (n = 13)

Total (N = 32)

7

12

19

3 2 3 0 2

7 4 2 2 4

10 6 5 2 6

1

1

2

1

3

4 D



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Stephanie explained that if a process was spontaneous, ΔG would need to be negative. She also stated that the change in enthalpy would be positive because she decided that the process was endothermic. Therefore, Stephanie drew the conclusion that “...the [change in] entropy was positive ’cause then the ΔG would still be negative. I think.” The interviewer then asked her if she could explain why the change in entropy was positive, but she could not. This showed that Stephanie could correctly determine the sign for the change in entropy for the processes that she observed by reasoning with an equation, even though she did not have a conceptual understanding of entropy. Three PC/BPC students used their tactile observations of a change in temperature and then invoked eq 1 to reason incorrectly that that there was a decrease in entropy in phase 2 (exothermic dissolving process) and correctly that there was an increase in entropy in phase 4 (endothermic dissolving process), despite the fact that both phases 2 and 4 of the interview involved observing the dissolution of an ionic solid. On the basis of their tactile observations, they reasoned that the change in energy of the system was negative for the exothermic processes and, therefore, concluded that there was a negative change in entropy of the system. They then applied the opposite reasoning to explain their observations about the endothermic process. ΔS =

change in entropy of the system. Each of these 11 students, all of whom had described entropy as disorder in the prior knowledge phase of the interview, invoked similar reasoning in this phase (Emily, PC): “Umm well I guess our entropy change we saw for this didn’t, I mean nothing, nothing became more disordered. Umm that this ΔS value is essentially zero... nothing really happened...” Three students (n = 1 GC, n = 2 PC/BPC) described the solid as sparingly soluble and concluded that therefore there was in fact a slight increase in the entropy of the system after the solid was added to the water (Sam, GC): “I mean umm it’s [entropy] probably a little bit higher than what we started with because originally when they, because a solid and liquid separate would be umm lower entropy then when they’re put together and a little bit dissolves. So I guess it’s [entropy] a little bit higher.” Four students (n = 2 GC, n = 2 PC/BPC) commented that there would have been an increase in entropy if the solid had in fact dissolved. Each of these students reasoned that an input of energy, or an increase in temperature, would cause the solid to dissolve, and, in doing so, increase the entropy of the system. Spontaneity

Prior Knowledge. When students were asked to explain what they knew about the meaning of the term spontaneous in a chemical context, most students (n = 14 GC, n = 10 PC/BPC) answered that a spontaneous reaction did not require an input of energy to proceed (Table 4). They described a spontaneous

Δqrev (1)

T

However, none of the processes that they observed were thermodynamically reversible; therefore, eq 1 was not appropriate to use to determine the change in entropy of the system. While this equation is not appropriate to use for any of the processes the students observed, it actually led students to correctly determine the changes in entropy for the endothermic dissolving process and the precipitation reaction. One GC student, Ryan, did not use eq 1 but invoked similar reasoning involving the transfer of energy from the system to the surroundings: “Umm it was being released as heat. So the enthalpy umm was negative. Umm and then I think the entropy inside the solution decreased but umm when it released all the heat to the surroundings the entropy increased in the universe.” Insoluble Compound. In phase 3 of the interview there were no visual or tactile changes for students to notice when they added solid silver chloride to a beaker of water. In this phase of the interview, students drew three different conclusions (Table 3): (1) there was no change in entropy of the system, (2) there was a slight increase in entropy of the system, and (3) the entropy would increase if the solid had in fact dissolved. Because there were no observable changes (visual or tactile), 8 GC students and 3 PC/BPC students concluded that there was no

Table 4. Students’ Prior Knowledge Ideas about Spontaneity Category No outside interference No connections to enthalpy, entropy, or temperature Connections to enthalpy, entropy, and temperature Focused on entropy only Focused on enthalpy only Rate

GC (n = 18)

PC/BPC (n = 10)

Total (N = 28)a

No change in entropy Slight change in entropy Entropy would change

8 1 2

3 2 2

11 3 4

PC/BPC (n = 13)

Total (N = 32)

14 12

10 5

24 17

4

8

12

4 2 3

8 2 0

12 4 3

reaction as one that “happens on its own” or ‘without outside interference.’ Of these students, however, 17 (n = 12 GC, n = 5 PC/BPC) struggled to describe connections among enthalpy, entropy, and temperature when explaning what factors affect the spontaneity of a reaction. For instance, Hannah (PC) described spontaneous as “...the reaction will happen at room temperature. Uhh like it will not involve any external factors. Like it will just happen.” but makes no mention of thermodynamic factors such as enthalpy or entropy. She specified that the process will occur “at room temperature”, implying that this is the only temperature at which chemical processes can be spontaneous. There were 12 students (n = 4 GC, n = 8 PC/BPC) who discussed the connection between spontaneity and enthalpy, entropy, and temperature, as in the case of Jake (GC): “Umm and so ΔH and ΔS alone don’t depict if the reaction’s gonna happen or not. So you might think, oh it’s exothermic, it’s definitely gonna happen, but that’s not true depending on what the entropy is.”

Table 3. Students’ Ideas about Entropy Change after Observing an Insoluble Salt Category

GC (n = 19)

a

Note: Four students did not participate in this task because they had to end the interview after one hour in order to attend class. E



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“preferred state”. The compounds were not originally in their “preferred state”, so they were able to spontaneously go to a more “preferred state”. For example, phases 2 and 4 both started with a solid that dissolved into ions, while phase 5 began with dissolved ions that formed a solid, as described by Emily (BPC): “Umm a solid would form based on the interaction between umm some of the ions that ultimately like in their standard state would prefer to be a solid than would prefer to be a liquid [aqueous].” These students talked about spontaneous changes by anthropomorphizing the ions that were present as if they chose to undergo the processes or reaction.29 They did not mention any underlying thermodynamic variables when explaining why what they observed was spontaneous. Rather, their conclusions were based merely on their visual observations of a phase change that required no outside interference. Six students (n = 1 GC, n = 5 PC/BPC) explained that the processes they observed were spontaneous because there was a decrease in free energy. These students did not focus on the fact that they had observed a change and therefore the process was spontaneous. Rather, they understood that the change in the free energy of the system is what determines whether a chemical process is or is not spontaneous. Consider Jake’s (GC) explanation of why the dissolution of magnesium chloride was spontaneous: “Umm it happened. I didn’t have to add anything. Umm and then if I look at the [Gibbs free energy] equation, I know that... ΔS is positive... you’re going from solid to aqueous. I felt that it was a negative ΔH. With this reaction ΔH minus umm, at any temperature this [TΔS] is going to be a positive number... and so you get negative [ΔH] minus a positive [TΔS]. No matter what the temperature is, ΔG is always gonna be negative.” Jake used both his tactile and visual observations to help him reason about the changes in enthalpy and entropy. He connected the temperature change he felt to the sign for ΔH. He also used the phase change he observed from solid to aqueous to help him determine the sign of the change in entropy. He then combined these two factors to determine that the free energy change of the system would be negative at all temperatures, meaning that this process would be spontaneous at all temperatures. Jake and the other students that related spontaneity to a decrease in free energy of the system understood that changes in enthalpy and entropy lead to the changes in free energy. There were 12 students (n = 10 GC, n = 2 PC/BPC) who concluded that phase 4 (the endothermic dissolving of silver nitrate) was nonspontaneous, with 4 students (n = 3 GC, n = 1 PC/BPC) claiming that the dissolving could not be spontaneous because the system required a constant input of energy in order to proceed (Christine, GC): “It’s breaking apart, it’s cold. I would say no, it’s not [spontaneous]. Cause it requires energy to come into the system. Yea we’ll go with no.” Although these students used their tactile observations, they used them to incorrectly determine the spontaneity of the system. These students thought that the change in enthalpy determined the spontaneity of a system, just as they had in the prior knowledge phase of the interview. Four students (n = 3 GC, n = 1 PC/BPC) reasoned that an input of energy was required for the process to proceed, but they concluded that this process was nonspontaneous because they shook the vial in order to help the solid dissolve. These students

Jake made clear that there were three thermodynamic factors that impacted spontaneity and that all of them need to be considered and their magnitudes weighed against one another. Some students offered explanations of spontaneity that focused on only a single factor. Four students (n = 2 GC, n = 2 PC/BPC) said that a reaction must be exothermic in order to be spontaneous, neglecting considerations of both entropy change and temperature. There were 12 students (n = 4 GC, n = 8 PC/BPC) who offered explanations that focused only on the change in entropy, stating that there must be a positive change in entropy for a reaction to be spontaneous. A few students (n = 3 GC) conflated thermodynamics with kinetics and explained that the rate of the reaction determined whether a reaction was spontaneous or not (Jenny, GC): “Umm... I think the, the longer the reaction takes you can tell like it’s not spontaneous. The quicker the reaction the more spontaneous it is.” Dissolving and Precipitation Observations. During phases 2−5 of the interview, students were asked to decide whether each process they observed was spontaneous or nonspontaneous and to explain their choice. There were 20 (n = 9 GC, n = 11 PC/BPC) of the 32 students who were able to correctly determine that both dissolving processes and the precipitation reaction were spontaneous (Table 5). Table 5. Students’ Ideas about Spontaneity after Observing Dissolution and Precipitation Category Spontaneous Strength of attractions Preferred state Decrease in free energy Nonspontaneous Endothermic process Shaking the vial Rate

GC (n = 19) PC/BPC (n = 13) 9 10 3 1 10 3 3 4

11 9 3 5 2 1 1 0

Total (N = 32) 20 19 6 6 12 4 4 4

There were 19 (n = 10 GC, n = 9 PC/BPC) students who described the relative strengths of attractions within the solvent, attractions within the solute, and attractions between the solvent and solute in order to explain why the processes they observed had occurred. Consider Ryan’s (GC) explanation of why the solid magnesium chloride dissolved: Interviewer: “...why did this happen?” Ryan: “Umm the, there’s ionic bonds between the Mg and the Cls and umm chloride is, I think it’s more electronegative than Mg. So umm the chlorine atoms are umm, are a slightly more negative than the Mg is. Umm and then the H plus end is slightly more positive, those are slightly more positive than umm O minus which is negative. So umm those, those attractions resulted in the breaking apart of MgCl.” While students like Ryan spoke of competing attractions at play in both dissolving and precipitation, none of these 19 students connected these attractions to enthalpy changes, nor even to their tactile observations or the overall free energy change of the system. These 19 students also never mentioned entropy as a driving force; these students focused only on the visual observation of a phase change as evidence that a reaction or process had spontaneously occurred. Six students (n = 3 GC, n = 3 PC/BPC) said that the processes they observed were spontaneous because the species went to a F



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Henry: “Yea. In order to make this [ΔG] my observed result. It would dissolve if I raised the temperature enough and this [TΔS] became more negative than this [ΔH] was positive.” There were 11 students (n = 7 GC, n = 4 PC/BPC) who concluded that there was no change in entropy because these students did not observe any changes for the solid. Therefore, when trying to reason with the Gibbs free energy equation, they said that the value for ΔS must be zero as shown in the quote by Emily above. These students did not understand that the values used to calculate the change in Gibbs free energy are based on what the change in the entropy of the system is when the process occurs. Therefore, the ΔS value for the dissolution of silver chloride would not be zero. Interestingly, these same students included a nonzero value for the change in enthalpy, even though no temperature change was noted by the students. Consider Sara’s (GC) explanation: “Umm... so this [ΔG] one is I guess positive. Umm yea I guess if like entropy isn’t a factor maybe the, these [ΔG and ΔH] just equal each other. So then this [ΔG] would be positive which would make it nonspontaneous.” These students eliminated the temperature and entropy term from the Gibbs free energy equation (Figure 3) and argued that the free energy change was only determined by the change in enthalpy for this process.

viewed this mechanical disturbance of the system as a continuous input of external energy into the system. Ally (GC) explained: “’Cause I had to shake it. I feel like it’s not spontaneous if you have to shake it. I could be incredibly wrong. I probably am. But I feel like if you’re doing this you’re applying energy in some way ’cause you’re doing things. I feel like it’s not spontaneous.” These students’ observations that all of the solid did not dissolve before they shook the vial led them to conclude that shaking the vial was required for the process to occur. They did not consider the thermodynamic variables and therefore viewed shaking the vial as a constant input of external energy. A third group of students (n = 4 GC) focused their explanations upon the rate at which the solid dissolved. They interpreted the slow dissolving of the solid to mean that the process was nonspontaneous. This focus on the speed at which the solid dissolved is additional evidence of students not being able to differentiate between kinetics and thermodynamics. Insoluble Compound. All 28 students (n = 18 GC, n = 10 PC/BPC) decided that their observation of silver chloride as insoluble in water meant this was a nonspontaneous process (Table 6). When discussing the roles of enthalpy and entropy, 9 Table 6. Students’ Reasoning about Spontaneity of an Insoluble Salt Category Raising temperature Unsure how to handle entropy

GC (n = 18)

PC/BPC (n = 10)

Total (N = 28)

4 7

5 4

9 11

Figure 2. Equation used by Henry to reason about the spontaneity of dissolving silver chloride in water.

students (n = 4 GC, n = 5 PC/BPC) said that raising the temperature of the water or adding energy to the system would cause the solid to dissolve. Note that these students were not asked what might cause the solid to spontaneously dissolve, but rather they brought up this idea on their own. Consider this exchange as Henry (BPC) reasoned using the Gibbs free energy equation (Figure 2): Interviewer: “So what was the role of enthalpy and entropy in this?” Henry: “Yea, so I mean your, your entropy is still gonna be positive because you’re just gonna have more freedom of movement in a liquid versus a solid or aqueous versus solid... so if this [ΔS] is positive because you’re going from a solid to aqueous phase then that would mean this [ΔH] would have to be positive to a greater extent than this [TΔS] at this temperature.” Interviewer: “So just based on the fact that you know that it’s not spontaneous the enthalpy has to be positive?”

Figure 3. Sara equating the change in Gibbs free energy to the change in enthalpy.

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CONCLUSIONS These findings describe students’ thinking about entropy and spontaneity in the contexts of their observations of visual and tactile changes during dissolving and precipitation. Students were able to make the observations that were expected, i.e., changes in both phase and temperature, but they drew different conclusions from their observations when reasoning about entropy and spontaneity. Students tended to rely on their visual observations to reason about changes in entropy. Consistent with the findings of several previous studies, the most common description for entropy was disorder,1−6 although students defined disorder in several different ways. However, only some of the students were able to use their prior knowledge to explain what they observed in the later phases of the interview, and some students reasoned with new ideas that they had not mentioned G



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students found it challenging to apply the Gibbs free energy equation. Students tended to eliminate entropy from the Gibbs free energy equation by setting it equal to zero because they did not observe a change, not realizing that the equation uses values that are based on what the change is when the process occurs.

previously (e.g., the number of moles of reactants and products). Only six students mentioned the term microstates in the prior knowledge phase of the interview, and only two of those students used the concept of microstates to correctly explain their observations during the interviews, indicating the absence of meaningful connections between the students’ prior knowledge and their observations and reasoning about the phenomena observed during the interviews. Students correctly determined the change in entropy for the endothermic dissolving and precipitation reaction. The few students who were not able to correctly determine the change in entropy struggled with the exothermic dissolution of magnesium chloride because they made inappropriate connections between enthalpy and entropy; in opposition to Carson and Watson’s findings,1 these students concluded that a negative change in enthalpy resulted in a negative change in entropy. Similar to those in other studies, these students did not understand that the mathematical model they used was not intended to represent the systems they observed.19 In the third phase of the interview (sparingly soluble silver chloride), many students relied on their (lack of) observation to determine the entropy change. Some students were able to reason beyond their observations and apply their knowledge of solubility to conclude that there was a small increase in entropy due to the dissolution of some of the solid. Others were able to speculate that an increase in temperature might cause more of the solid to dissolve and result in an increase in entropy. Students’ reasoning about the absence of any observable change has not been previously reported, so it is interesting to see that some students, albeit just a few, did not limit themselves to ony their observations but were able to apply knowledge not directly related to what they observed. Students correctly determined that exothermic dissolving and precipitation were spontaneous processes. They relied on the idea that spontaneous processes occur without any outside influence rather than considering the underlying thermodynamic factors, as has been previously reported.1,9 However, the literature is silent regarding what students consider to be “outside influence”. Several students thought that any energy being absorbed by the system from the surroundings, even if the system was not being continuously heated, qualified as outside influence and led these students to conclude that all endothermic processes are nonspontaneous. Other students identified mechanical disturbances such as shaking or stirring as outside influences. Many students demonstrated that they did not have a clear understanding of what is meant by “outside influence” because they lacked any meaningful understanding between the concepts of Gibbs free energy and spontaneity. Only 6 students stated that there must be a decrease in free energy of the system for a process to be spontaneous. Unlike Bain et al. the findings from this study suggest that anthropomorphic reasoning about spontaneity is as prominent in GC students as it is among upper-division students.3 Our findings also suggest that while the lack of connections among enthalpy, entropy, temperature, and spontaneity was more prevalent with lower-division students, almost one-quarter of the upper-division students still lacked these meaningful connections. Although Becker and Towns investigated students’ application of calculus to thermodynamics, our study includes a similar finding in that students struggled to observe a chemical phenomenon and translate their observations to a mathematical model.14 When explaining why a process was nonspontaneous,

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IMPLICATIONS FOR RESEARCH AND TEACHING The findings of this research suggest that additional investigations are warranted regarding students’ reasoning about why certain processes are nonspontaneous. To the authors’ knowledge this is the only study reported to date that presented students with a nonspontaneous process and asked them to explain. The use of demonstrations and laboratory experiments to help students form connections between macroscopic observations (be they tactile or visual) and the underlying particulate models of matter necessitate some observable change such as a color change, precipitation, gas evolution, or change in temperature. The findings reported herein that faculty should consider expanding beyond teaching students to reason about what they see to also reason about what they do not see. It is important to investigate students’ reasoning between their macroscopic observations (visual and tactile) and their knowledge of entropy changes and spontaneity to prompt explanations beyond the algorithms typically used to calculate the signs of ΔS and ΔG. Some laboratory experiments have been developed that show that students are able to use nonvisual observations to collect data and to draw conclusions from.30−32 However, there has been very little research into how and what connections students are able to make between their visual and nonvisual observations and chemical phenomena. This study and a few others have shown the viability of using chemical phenomena and students’ observations to gather data in an interview setting.3,26,33 The laboratory is often thought of the place within the curriculum where students learn to make observations and draw conclusions, but these experiments tend to be more focused on quantitative conclusions. Students need to be provided with opportunities in the classroom to make macroscopic observations and draw connections from the conceptual knowledge they learn about in the classroom setting where feedback and guidance can be given from peers and instructors. The chemical phenomena observed by the students in the interviews can easily be done in the classroom, including the use of an insoluble salt. All observations can be made when using sealable plastic bags and a small amount of salt and water. Further research needs to be on how to best implement such an activity and what guiding material would best be suited for this activity based on the results from this study. Limitations

This analysis, along with the previously published analysis from the same study,26 has shown the value in asking the same questions of both lower- and upper-division students. Longitudinal studies can be logistically challenging and expensive to conduct, but cross-sectional studies, like this one, can help to illuminate the gaps and misconceptions that persist in students’ thoughts from their first year in college through degree completion. One limitation to this type of study design lies in using the same interview guide and questions for both general chemistry students and physical/biophysical chemistry students which limited the mathematical reasoning that we could investigate with the upper-division students as our H



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(7) Lambert, F. L. Disorder - A Cracked Crutch for Supporting Entropy Discussions. J. Chem. Educ. 2002, 79 (2), 187. (8) Bain, K.; Moon, A.; Mack, M. R.; Towns, M. H. A Review of Research on the Teaching and Learning of Thermodynamics at the University Level. Chem. Educ. Res. Pract. 2014, 15 (3), 320−335. (9) Gabriela, M.; Ribeiro, T. C.; Costa Pereira, D. J. V.; Maskill, R. Reaction and Spontaneity: The Influence of Meaning from Everyday Language on Fourth Year Undergraduates’ Interpretations of Some Simple Chemical Phenomena. Int. J. Sci. Educ. 1990, 12 (4), 391−401. (10) Sö zbilir, M. Turkish Chemistry Undergraduate Students’ Misunderstandings of Gibbs Free Energy. Univ. Chem. Educ. 2002, 6 (6), 39−89. (11) Sözbilir, M.; Pinarbasi, T.; Canpolat, N. Prospective Chemistry Teachers’ Conceptions of Chemical Thermodynamics and Kinetics. EURASIA J. Math. Sci. Technol. Educ. 2010, 6 (2), 111−120. (12) Christensen, W. M.; Meltzer, D. E.; Ogilvie, C. A. Student Ideas Regarding Entropy and the Second Law of Thermodynamics in an Introductory Physics Course. Am. J. Phys. 2009, 77 (10), 907−917. (13) Teichert, M. A.; Stacy, A. M. Promoting Understanding of Chemical Bonding and Spontaneity through Student Explanation and Integration of Ideas. J. Res. Sci. Teach. 2002, 39 (6), 464−496. (14) Becker, N.; Towns, M. H. Students’ Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin’s Symbolic Forms. Chem. Educ. Res. Pract. 2012, 13 (13), 209−220. (15) Pollock, E. B.; Thompson, J. R.; Mountcastle, D. B. Student Understanding of the Physics and Mathematics of Process Variables in P-V Diagrams. AIP Conf. Proc. 2007, 951, 168−171. (16) Loverude, M. E.; Kautz, C. H.; Heron, P. R. L. Student Understanding of the First Law of Thermodynamics: Relating Work to the Adiabatic Compression of an Ideal Gas. Am. J. Phys. 2002, 70 (2), 137−148. (17) Thompson, J. R.; Bucy, B. R.; Mountcastle, D. B. Assessing Student Understanding of Partial Derivatives in Thermodynamics. AIP Conf. Proc. 2005, 818 (July), 77−80. (18) Hadfield, L. C.; Wieman, C. E. Student Interpretations of Equations Related to the First Law of Thermodynamics. J. Chem. Educ. 2010, 87 (7), 750−755. (19) Becker, N. M.; Rupp, C. A.; Brandriet, A. Engaging Students in Analyzing and Interpreting Data to Construct Mathematical Models: An Analysis of Students’ Reasoning in a Method of Initial Rates Task. Chem. Educ. Res. Pract. 2017, 18 (4), 798−810. (20) Novak, J. D. Learning, Creating, and Using Knowledge: Concept Maps as Facilitative Tools in Schools and Corporations; Taylor & Francis Group: New York, 2010. (21) Bretz, S. L. Novak’s Theory of Education: Human Constructivism and Meaningful Learning. J. Chem. Educ. 2001, 78, 1107. (22) Bodner, G. M. Constructivism: A Theory of Knowledge. J. Chem. Educ. 1986, 63 (10), 873−878. (23) Silberberg, M.; Amateis, P. Chemistry: The Molecular Nature of Matter and Change, 7 th ed.; McGraw-Hill Education: New York, 2014. (24) Linenberger, K. J.; Bretz, S. L. A Novel Technology to Investigate Students’ Understandings. J. Coll. Sci. Teach. 2012, 42 (1), 45−49. (25) Johnstone, A. H. Why Is Science Difficult to Learn? Things Are Seldom What They Seem. J. Comput. Assist. Learn. 1991, 7 (2), 75−83. (26) Abell, T. N.; Bretz, S. L. Dissolving Salts in Water: Students’ Particulate Explanations of Temperature Changes. J. Chem. Educ. 2018, 95 (4), 504−511. (27) NVivo Qualitative Data Analysis Software, Version 11; QSR International Pty Ltd., 2015. (28) McClary, L.; Talanquer, V. Heuristic Reasoning in Chemistry: Making Decisions about Acid Strength. Int. J. Sci. Educ. 2011, 33 (10), 1433−1454. (29) Talanquer, V. When Atoms Want. J. Chem. Educ. 2013, 90 (11), 1419−1424. (30) Bromfield-Lee, D. C.; Oliver-Hoyo, M. T. A Qualitative Organic Analysis That Exploits the Senses of Smell, Touch, and Sound. J. Chem. Educ. 2007, 84 (12), 1976−1978.

protocol needed to be equally accessible and appropriate for both samples. This study only investigated students’ qualitative understandings and explanations of dissolving and precipitation reactions. The study could be expanded by offering students a thermometer to provide quantitative information regarding the changes in temperature; this would afford students additional information with which to reason. This study was limited to aqueous solutions and to ionic solutes. Further research could be done with nonpolar solvents and/or molecular solutes to investigate how students reason about solvent effects. Other limitations of this study that could be investigated in future studies include intentionally investigating student reasoning about Ksp and equilibrium with regard to sparingly soluble compounds. Each of the suggested future studies should be conducted to incorporate scientific practices by providing opportunities for students to observe the chemical phenomena and generate explanations based on their observations.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.8b01007.

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Interview guide that includes the primary questions asked to students (not including all follow-up questions asked as a part of the semistructured interviews) (PDF, DOCX)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Stacey Lowery Bretz: 0000-0001-5503-8987 Notes

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based in part upon work supported by the National Science Foundation under Award 1432466. We thank the students who volunteered to participate in this study.

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REFERENCES

(1) Carson, E. M.; Watson, J. R. Undergraduate Students’ Understandings of Entropy and Gibbs Free Energy. Univ. Chem. Educ. 2002, 6, 4−12. (2) Sözbilir, M.; Bennett, J. M. A Study of Turkish Chemistry Undergraduates’ Understanding of Entropy. J. Chem. Educ. 2007, 84 (7), 1204. (3) Bain, K.; Towns, M. H. Investigation of Undergraduate and Graduate Chemistry Students’ Understanding of Thermodynamic Driving Forces in Chemical Reactions and Dissolution. J. Chem. Educ. 2018, 95 (4), 512−520. (4) Haglund, J.; Andersson, S.; Elmgren, M. Chemical Engineering Students’ Ideas of Entropy. Chem. Educ. Res. Pract. 2015, 16, 537−551. (5) Haglund, J.; Andersson, S.; Elmgren, M. Language Aspects of Engineering Students’ View of Entropy. Chem. Educ. Res. Pract. 2016, 17 (3), 489−508. (6) Johnstone, A. H.; Macdonald, J. J.; Webb, G. Misconceptions in School Thermodynamics. Phys. Educ. 1977, 12 (4), 248. I



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(31) Bromfield-Lee, D. C.; Oliver-Hoyo, M. T. An Esterification Kinetics Experiment That Relies on the Sense of Smell. J. Chem. Educ. 2009, 86 (1), 82−84. (32) Neppel, K.; Oliver-Hoyo, M. T.; Queen, C.; Reed, N. A Closer Look at Acid−Base Olfactory Titrations. J. Chem. Educ. 2005, 82 (4), 607−610. (33) Carson, E. M.; Watson, J. R. Undergraduate Students’ Understanding of Enthalpy Change. Univ. Chem. Educ. 1999, 3 (2), 46−51.

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Macroscopic Observations of Dissolving, Insolubility, and Precipitation

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