Energy represents a core idea across scientific disciplines and is central to understanding the behavior of chemical systems. From interactions between atoms and molecules to the networked reactions of biological systems, understanding the role of energy is key to understanding these systems. As such, the recent Framework for Science Education highlights the role of energy as both a core idea and a crosscutting concept that extends throughout numerous STEM disciplines (National Research Council, 2012). The Framework suggests that by emphasizing relationships between accounts of energy transfer and transformation across different scales and disciplinary contexts instructors may be able to help students develop more coherent frameworks for reasoning about energy-related phenomena.
However, there is considerable evidence that few students develop such a coherent understanding as the result of participation in undergraduate-level chemistry courses (Bain, Moon, Mack, & Towns, 2014; Goedhart & Kaper, 2003; Sreenivasulu & Subramaniam, 2012; Taber, 2003). For instance, students' understanding of the energy changes that accompany bonding and interactions between chemical species are, at best, inconsistent (Barker & Millar, 2000; Boo, 1998; Ebenezer & Fraser, 2001; Galley, 2004; Nahum, Mamloka Naaman, Hofstein, & Krajcik, 2007; Teichert & Stacy, 2002). Teichert and Stacy (2002) reported that undergraduate students may believe energy is released both on bond formation and on bond breaking, suggesting that they hold discordant and inconsistent views about how energy changes as bonds are formed. Especially problematic is the observation that students may believe that bond breaking releases energy, despite the fact that bond breaking is an endothermic process (Barker & Millar, 2000; Boo, 1998; Galley, 2004; Storey, 1992; Teichert & Stacy, 2002). Even after instruction, around 50% of undergraduate students still hold this belief (Barker & Millar, 2000; Boo, 1998).
Similarly, energy topics ranging from ionization energy to enthalpy have also been shown to be challenging for students. When reasoning about ionization energy, students may struggle to apply basic principles of electrostatics and may explain ionization energy trends using, for example, the octet rule or ideas about stability rather than a foundational understanding of the relationship between energy and atomic–molecular structure (Taber, 2003). Similarly, in thermodynamics contexts, Nilsson and Niedderer (2014) observed that students may attribute work to atomic–molecular phenomena such as the conversion of potential to kinetic energy rather than macroscopic changes in pressure and volume, suggesting a disconnect between macroscopic ideas such as heat and work to their understandings of molecular-level processes. Lacking a coherent framework for reasoning about energy in chemical systems, even advanced students who are otherwise successful in using mathematical resources may struggle to understand what those representations mean in terms of fundamental energy concepts and the atomic–molecular scale (Hadfield & Wieman, 2010). Given that understanding energy changes at the atomic–molecular level forms the foundation for understanding the macroscopic energy changes that accompany chemical processes, these observations are troubling (Cooper, Klymkowsky, & Becker, 2014).
A Re-Evaluation of the Role of Energy at the Atomic–Molecular Level
One recommendation for improving students' understanding of energy concepts has been made by the recent Framework for Science Education (National Research Council, 2012), which advises simplifying energy instruction to focus on a smaller number of core energy concepts that can be applied across both atomic–molecular and macroscopic contexts. As the Framework notes,
The idea that there are different forms of energy, such as thermal energy, mechanical energy, and chemical energy, is misleading, as it implies that the nature of the energy in each of these manifestations is distinct when in fact they all are ultimately, at the atomic scale, some mixture of kinetic energy, stored energy, and radiation (National Research Council, 2012, p. 122).
At the heart of the Framework's approach to energy instruction is an electrostatic model of atomic–molecular interaction in which energy changes are modeled both as motion of particles (kinetic energy) and “stored energy,” representing energy stored in the electrical, magnetic, or gravitational fields that mediate interactions between particles (National Research Council, p. 121). The Next Generation Science Standards (Achieve, 2013), which uses the Framework as a guide for establishing what students should learn and the sequence in which they should learn it at the K-12 level, reflect this emphasis on the ideas of “stored” energy (also called potential energy) and kinetic energy as tools to predict and explain energy phenomena across atomic–molecular and macroscopic scales.
A crosscutting concept closely tied to the idea of potential energy in chemical systems is the cause and effect relationship between forces and change in energy. The Framework suggests that by grade 12 students should recognize that electrostatic forces between atoms and molecules arise from the subatomic structure of atoms. Students should also identify that these electrostatic forces are the mechanism by which atoms and molecules interact and by which energy is stored or transferred between particles. Mathematical expressions may be used to quantify how the electrical force or stored energy of a system depends on the charges of particles and their relative positions. For instance, electrostatic interactions between particles are commonly modeled by Coulomb's law, , where q1 and q2 represent the charges of the interacting particles and r represents the distance between them (or in the case of London dispersion forces may be proportional to 1/r6).
A second crosscutting concept closely linked to the idea of potential energy in chemical systems is the idea that systems evolve towards more stable states that minimize the amount of energy stored in magnetic or electrical fields. In atomic–molecular contexts, stability and the minimization of potential energy determine equilibrium distances for interactions between atoms and molecules.
The aim of this approach is to have students recognize that macroscopic energy changes, such as heat energy released by an exothermic chemical reaction, originate in energy changes that occur as atoms and molecules interact. Ideally this approach provides students with a coherent approach to energy ideas that cuts across disciplines and allows students to make connections between treatments of energy that have historically been quite disparate.
The Role of Potential Energy in Undergraduate General Chemistry
Although the Framework is designed to address learning at the K-12 level, it is our contention that the approach to energy instruction outlined by Framework may provide an opportunity to present more a connected account of energy in undergraduate introductory chemistry courses as well. We find that electrostatic models of atomic–molecular interaction and corresponding models of energy as potential and kinetic energy are among several models that are commonly introduced in undergraduate chemistry contexts (e.g., see Bruice, 2010; Tro, 2012). The electrostatic model of interaction plays a prominent role in the curricula as it may be used to explain a wide array of concepts, ranging from the energy changes that accompany covalent bonding to emergent properties of macroscopic systems such as melting and boiling points.
In order to reason about energy changes in more complex atomic–molecular systems typically encountered at the undergraduate level, students must refine their understanding of atomic–molecular structure and connect it to their understanding of electrical interactions between species. For instance, to understand energy changes that accompany interactions between neutral atoms (such as helium), students must identify that random fluctuations in electron density give rise to temporary dipoles, which in turn contribute to induced dipole interactions between adjacent species. To understand the energy changes that accompany interactions between species such as water or ethanol, an understanding of valence shell electron pair repulsion (VSEPR) theory and understanding of additional concepts such as electronegativity may be necessary.
At the undergraduate level, graphical models that more closely approximate the contribution of attractive and repulsive interactions to the potential energy of the system may also be introduced. For example, the Morse potential (Figure 1) may be used to model potential energy as a function of inter-nuclear distance for a system of two interacting hydrogen atoms. To interpret models such as this, students must that recognize that the potential “well” (or minimum) in Figure 1 corresponds to a state at which the system is said to be “stable.” They must also identify that stable interactions are formed when there is a balance between these attractive and repulsive forces (Nahum et al., 2007).
While bonding phenomena are most often approached from an electrostatics perspective at the K-12 level, undergraduate chemistry students will also be exposed to alternate models of the energy changes associated with bonding such as valence bond theory or molecular orbital theory, both of which draw from quantum-mechanical models of atomic structure and interaction. Additionally, energy phenomena may be approached from a thermodynamics perspective in which mathematical models are used to track energy flux into and out of a defined system. As such, undergraduate chemistry students must not only be able to relate atomic–molecular perspective on energy change to macroscopic phenomena, they must also develop the capacity to compare and contrast multiple models of the energy changes in chemical systems.
There is certainly evidence from related disciplines, including biology and physics contexts, which suggests that developing an understanding of potential energy or “stored” energy may be challenging for students. In physics contexts, it has been demonstrated that students may consider gravitational potential energy to be a property of a single object rather than a system of interacting objects (Jewett, 2008; Lindsey, Heron, & Shaffer, 2012). Students may also interpret the potential energy quite literally as the “potential” or capability for an object to move or cause change (Loverude, 2005), an idea that may hinder their ability to extend the idea of potential energy to new contexts such as atomic–molecular interactions. In biology contexts, it has been noted that the way bond energies are treated in biological systems tends to reinforce the idea that bonds store energy and release energy when those bonds are broken, rather than when new bonds are formed (Cooper & Klymkowsky, 2013; Storey, 1992).
Even if students entered general chemistry courses with a solid foundation for understanding potential energy in macroscopic contexts, for instance in gravitational systems, translating those understandings to the atomic–molecular level may be challenging. While students may reasonably be expected to infer that potential energy at the atomic–molecular level pertains to systems of interacting objects based on their positions in the same way that gravitational potential energy does, there are several key differences between potential energy in gravitational and electrical contexts that may escape students' notice. First, the nature of the relevant force in each context is distinct: the gravitational at the macroscopic scale, versus predominantly electrostatic at the atomic–molecular. While gravitational potential is always attractive, meaning that the potential energy stored in the system will decrease as the objects move closer together, electrostatic interactions may involve interactions between positive or negatively charged objects and thus the electrostatic potential energy may increase or decrease as the objects move closer together. When left to their own devices to compare their understanding of potential energy in macroscopic systems (gravitational potential energy) with potential energy in atomic–molecular systems (electrical potential energy), these differences may be difficult to appreciate.
While a robust understanding of energetics at the atomic–molecular scale may well support the development of a coherent framework for discussing energy in chemical systems little research from chemistry contexts exists to support this idea. The qualitative study presented here aims to address this gap in the literature by describing students' understandings of potential energy in atomic–molecular systems. This work will serve as a foundation for further exploration of how undergraduate students connect their understanding of atomic–molecular energy transformations to macroscopic perspectives on energy.
- Top of page
- Discussion and Conclusions
- Supporting Information
The goal of this study was to investigate how students understand the concept of potential energy in the context of interactions between atoms and molecules. If chemistry instructors are to help students connect their understanding of potential energy in atomic–molecular systems to macroscopic energy, we must better understand how students reason about potential energy in the first place and what prior knowledge they bring to chemistry contexts (Novak, 2002; Vygotsky, 1978). To this end, we conducted a qualitative study in order to explore the following research questions:
- How do students understand the concept of potential energy in general, and at the atomic–molecular level?
- How do students conceptualize potential energy in the context of atomic–molecular interactions?
Participants for this research study were recruited from undergraduate chemistry courses at a medium-sized Southeastern research university. Participants ranged from first-year science students enrolled in general chemistry to upper-division chemistry majors. All students pursued majors in science or health science fields and were enrolled in chemistry as part of the requirements for their degree programs. Students were notified of their rights as research participants and provided informed consent prior to participation in the study.
Online Open-Ended Survey
In order to explore our first research question, we developed an open-ended survey that asked students to describe their understanding of kinetic and potential energy in general and at the atomic–molecular level. Questions related to potential energy included:
- What do you think potential energy is? Please provide an example to illustrate your thinking.
- At the atomic–molecular level, what do you think potential energy is? Please give an example to illustrate your thinking.
Students enrolled in three chemistry courses completed the survey online as part of the homework requirements for their courses (Table 1). All courses were taught using a predominantly lecture format, with periodic “clicker” questions and small group activities during class time. The second author was the instructor for the organic chemistry course. Of the 142 participants enrolled in Fall 2012 cohort of the general chemistry 1 (GC1) class, 61 of these students were also enrolled in the Spring 2013 semester of general chemistry 2 (GC2) (taught by same instructor as the GC1 course).
Table 1. Participants for online written questionnaire
|Course||Number of Participants|
|General chemistry I, GC1 (Fall 2012)||142|
|General chemistry II, GC2 (Spring 2013)||188|
|Organic chemistry I, OC (Fall 2012)||102|
In each of these three courses, the beSocratic online platform1 was used for homework tasks (Bryfczynski, 2012; Byrfczynski et al., 2012). Homework tasks were graded for completion. In the majority of homework tasks, students received feedback on the appropriateness of their responses through the pre-established conditions in the beSocratic program that were set by the instructor. Students were allowed to revise their responses based on the feedback. Homework tasks in each of the three courses were used as contexts for in-class discussion as the instructors routinely selected samples of student work for in-class review. However, students received no feedback on their responses to the survey used to gather the data for this study.
To examine students' understanding of potential energy in atomic–molecular systems with greater depth, we developed a semi-structured interview protocol in order to elicit students' understandings of the energy changes that accompany atomic–molecular interactions in simple systems. As contexts for the discussion, students were asked to consider interactions and energy changes that might occur in simple atomic–molecular systems, for instance as two helium atoms or two water molecules interact (full interview protocol in the Supporting Information). The interview protocol was piloted with five advanced undergraduate and graduate students and was refined for clarity prior to the full study.
Participants for the full study were recruited on a voluntary basis from the GC1 course during the last month of the Fall 2012 semester. Interviews were conducted by a post-doctoral researcher (first author) who was not involved in the instruction of any of the courses and a graduate student who was a teaching assistant for the GC1 course. Participants were not identified to the course instructor and no incentives were offered to interview participants. The graduate student researcher was not present when interviewing students enrolled in her teaching sections.
Our initial analysis of the survey data from GC1 and OC suggested that many students struggled to use the idea of potential energy productively in atomic–molecular contexts. Thus we opted to expand our participant pool to include students from advanced chemistry courses in order to better represent the ways in which students' ideas about atomic–molecular level energetics might evolve as they develop expertise. Table 2 summarizes the number of participants and the courses in which they were enrolled. Participants designated as “upper division” (UD) were enrolled in advanced undergraduate chemistry courses other than organic chemistry (for example, physical chemistry, inorganic chemistry, etc.).
Table 2. Interview participants
|Course||Number of Participants|
|General chemistry I (GC1)||8|
|General chemistry II (GC2)||1|
|Organic chemistry I (OC)||9|
|Upper division (UD)||4|
|Total interview participants||22|
Interviews lasted between 15 and 45 minutes in length. Audio and written works generated during the interviews were recorded using a Livescribe pen (http://www.livescribe.com/en-us/) and copies of student written work were collected at the completion of each interview. The research team transcribed the interviews verbatim.
Data were analyzed using an inductive approach informed by the constant comparative method (Corbin & Strauss, 2008). We began our analysis by open coding student responses to the online survey with the aim of identifying trends in student reasoning. A preliminary set of codes was developed using the online survey dataset and was refined upon analysis of the interview data. Data from both the survey and interviews were combined for the final iteration of analysis and both datasets were analyzed using the same set of codes.
In order to determine coding reliability for our analysis, two researchers independently coded a portion of the online survey responses (∼20% of responses for two different questions). Inter-rater reliability was evaluated using the Cohen's kappa statistic, which indicated a high level of agreement between the two raters (Cohen's Kappa ≥ 0.84 with p < 0.001).
- Top of page
- Discussion and Conclusions
- Supporting Information
Across all groups of participants, we observed that many students struggled to appropriately connect their understanding of potential energy at the atomic–molecular scale to their understanding of atomic–molecular structure and electrostatic forces between atoms and molecules. We observed three trends in students' conceptualization of potential energy that we believe contributed to student difficulties in reasoning about potential energy changes in atomic–molecular systems. First, we observed that students frequently conceptualized potential energy as the capability of atomic–molecular species to interact, react, or undergo change. While in a certain sense, potential energy can be considered related to a capacity for motion or change, the idea that potential energy represents an ability to form a bond was of little use in explaining energy changes that accompany interactions that did not obviously involve covalent bonding. Second, we observed that some students considered potential energy to energy “stored” in interactions between atoms and molecules, though few could explain under what circumstances energy would be stored by a system. Third, we observed that students commonly associated potential energy with the stability of a system, though most often without a clear sense of whether stability was a cause or effect of a change in energy.
While in some contexts interpretations of potential energy as capability, stored energy, and stability are not necessarily incorrect, without a concomitant understanding of the role of electrostatic force and relative position of particles in determining the potential energy of a system these ideas often seemed to inhibit more productive attempts at reasoning about the energy changes at the atomic–molecular scale.
Potential Energy as Capability
The most prevalent conceptualization of potential energy in chemical systems was the idea that potential energy represents a literal “potential” or capability for motion or change. At the atomic–molecular level, participants used the idea of potential energy as capability with a range of interpretations, from the idea that potential energy represents an ability of an atom or molecule to move, interact, or react. Most common was the idea that potential energy represents the ability of an atom or molecule to move or change configuration. For instance, one general chemistry student commented that he understood potential energy as the “ability of the atom or sub-atomic particle to be moved/borrowed between atoms” (GC1, survey). Similarly, an organic chemistry student commented that she viewed potential energy as “the potential to undergo a change in structure or configuration.” (OC, survey).
Other participants interpreted potential energy as related to a system's ability to react or interact. For instance, a participant in the second semester general chemistry course described potential energy as “the potential for molecules to interact” and illustrated her thinking with the following example: “If two molecules are across the room from each other, they will have a low potential energy. However, as they move towards each other the potential energy increases for them to react” (GC2, survey). According to her interpretation of potential energy as related to the likelihood of reacting, this student predicted that potential energy would increase as the two molecules approach. While she indicated the atoms would react in some way, she did not elaborate on how she believed the atoms would interact. Thus it is unclear as to whether or not she understood potential energy to be related to electrical interactions between particles. Assuming that the particles might interact in a favorable way, her prediction that potential energy would increase as atoms approach towards a distance at which they would “react” would be incorrect.
Example of Student Reasoning About Potential Energy as Capability From Interviews
Similarly, in the semi-structured interviews we observed that the idea of potential energy as the ability to react or bond was seldom a useful tool for predicting and explaining energy changes as atoms and molecules interact. To illustrate this trend consider Paul, an organic chemistry student who expressed a belief that potential energy represents an atom's ability to form a covalent bond. When prompted to discuss his understanding of how two hydrogen atoms might interact, Paul commented that he believed the two hydrogen atoms would approach and form a covalent bond, which he described as the formation of a molecule by the sharing of electrons. When asked to describe how that interaction might affect the energy of the system, Paul concluded (correctly) that forming a bond would result in a decrease in the potential energy of the system. He explained his reasoning as follows.
Paul: Well, they have greater potential energy when they're further apart than when they're closer together because they have greater potential to make an atom when they're closer together, um a molecule. The farther apart they get the less likely they're going to form a molecule so that kinda affects the potential energy.
Paul's prediction that potential energy would decrease as the atoms approach seemed based on his understanding of the probability of forming a bond at different distances; he viewed atoms that were closer to one another as more likely to form a bond than those that were further apart. He also seemed to associate lower potential energy with a greater likelihood of forming a bond.
A more complete account of bonding and its influence on the potential energy of the system would also address the role of electrical forces between hydrogen atoms. The system of interacting hydrogen atoms can be considered to store potential energy based on the relative positions of the atoms and the uneven charge distributions imparted by their fluctuating electron densities. Potential energy would minimized at the bond length because of the fact that attractive interactions and repulsive forces between the species are balanced at the bond length distance.
While Paul correctly predicted that potential energy would be lowered by the formation of a covalent bond between two hydrogen atoms, his framing of potential energy as an ability to form a bond became problematic as he considered other systems of atoms and molecules. For instance, as he reasoned about how two helium atoms would interact, he recalled that in contrast with a system of hydrogen atoms, helium atoms would be unlikely to form a covalent bond. Based on his framing of potential energy as the ability to form a covalent bond, he concluded that no change in either potential or kinetic energy would occur as the helium atoms interact.
Paul: They're extremely unlikely to make any sort of attempt at making a bond so they're not going to need to change energy from potential to kinetic.
In fact, helium atoms may interact via London dispersion interactions, electrical interactions caused by momentary fluctuations in electron distribution around a neutral atom. Though weaker than covalent bonds (in part because of the distance over which they act) these interactions result in a similar change in the potential energy of the system: potential energy is minimized at the distances at which the interaction is most stable. Later in his interview, Paul listed London dispersion forces as a type of interaction that could be formed by helium atoms, suggesting familiarity with this type of interaction. However, when asked to elaborate on his understanding of London dispersion forces, he was unable to provide a description in terms of atomic structure and its relationship to electrostatic interactions.
Paul's incorrect conclusion that interactions between helium atoms would not change the potential energy of the system may in part stem from his framing of potential energy as exclusively related to covalent bonding. The tendency of students to view covalent and ionic bonding as distinct from intermolecular interactions, despite the fact that all arise from similar types of electrostatic interactions, has been noted as a persistent difficulty and one that may be encouraged by traditional approaches to instruction (Kronik, Levy Nahum, Mamlok-Naaman, & Hofstein, 2008; Nahum et al., 2007; Taber, 2003). Our own experience suggests that while traditional general chemistry texts may discuss potential energy changes in conjunction with formation of covalent bonds, explicit discussions of atomic structure and their relationship to forces and potential energy in the context of intermolecular interaction are far less common. Prior to his interview, Paul may have never been explicitly asked to think about how potential energy would change as two helium atoms interact. Thus it is not surprising that he struggled to reconcile his understanding of energy changes that accompany covalent bonding with energy changes that accompany intermolecular interactions.
Potential Energy as Stored Energy
The second most prevalent conceptualization of potential energy in chemical systems was the idea that potential energy represents “stored” energy. According to an electrostatic model of particle interaction, potential energy is “stored” by the system based on the relative positions of interacting particles. To an expert, an interpretation of potential energy as stored energy is meaningful only with a concurrent understanding of the factors that influence energy storage in a particular context, namely the forces that determine the interaction between species and their relative positions. Our participants' interpretations of stored energy varied considerably, ranging from relatively robust discussions which referenced the ways in which the potential energy of a system depends on the charge distributions and the relative positions of interacting particles to less sophisticated interpretations in which potential energy was viewed as stored within an atom or bond but without a concurrent discussion of charge and position of particles.
As an example of a more sophisticated interpretation of potential energy at the atomic–molecular level, one organic chemistry student highlighted the role of position of interacting objects, describing potential energy as “the stored energy a molecule has due to the position of its substituents, bond lengths, bond angles etc.” (OC, survey). Another student emphasized the role of forces between particles, noting that potential energy relates to “energy stored from repulsions between atoms” (OC, survey). For the majority of students, the exact nature of forces acting at the atomic–molecular scale was largely implicit. Rather than discussing electrostatic forces mediated by electric fields, students discussed attractive or repulsive interactions. This is not surprising given that this is nearly always how students are taught to reason about interactions at the atomic–molecular level.
Relatively sophisticated interpretations of potential energy such as these were in the minority and students held a range of alternative interpretations. For instance, some participants described potential energy as related to the extent to which a particle is in motion. A general chemistry student, for instance, commented that she believed that “an atom has stored energy before it is moving” (GC1, survey). Another explained that he believed atoms had potential energy “when atoms are sitting still, like the atoms of a solid” (GC1, survey). This idea may stem in part from macroscopic observations related to kinetic and potential energy. For instance, a stationary object such as a ball may be said to have potential energy based on its position relative to the earth. If released from a position above the ground, the potential energy of the ball may be transformed to kinetic energy, which is readily observed as motion. However, at the atomic–molecular level, the idea that potential energy represents the energy of a stationary particle is troublesome as atoms and molecules are in constant motion. This idea was most prevalent among general chemistry students and considerably less prevalent in the organic chemistry responses (12.7% in GC1, 10.1% in GC2, 3% in OC).
Some students considered stored energy to be a property of an individual object such as an atom or subatomic particle. For instance, a first-semester general chemistry student described potential energy as “the amount of energy the atom can have, such as how much energy the protons, electrons, and neutrons hold,” (GC1, survey). Students in second-semester general chemistry more often attributed potential energy to bonds or interactions between molecules (Figure 2). This observation may indicate a potentially positive shift towards localizing relevant energy interactions between atoms and molecules (rather than at the nuclear level). However, students who indicated that energy could be stored by bonds often did so with the assumption that energy was stored could be released if the bond were broken. As one student described their understanding, “Potential energy at the molecular level would be the energy that is in bonds. This energy is stored and can be released” (GC2, survey). In fact, the opposite is true and breaking both covalent bonds and intermolecular interactions requires an input of energy (Boo, 1998; Teichert & Stacy, 2002). This idea was also fairly prevalent in the semi-structured interviews. Of the 22 interview participants, 6 participants from organic chemistry and upper division courses indicated a belief that energy could be stored by bonds and released when bonds were broken.
Figure 2. Percent of student responses that indicated that potential energy could be stored in nuclei or stored in bonds. GC1 N = 142, GC2 N = 188, GC N = 102.
Download figure to PowerPoint
While there is truth to the idea that energy is “stored” by interactions of atoms and molecules, it is important to qualify that a system of atoms in a bond “store” less energy in their interaction than the two un-bonded atoms and thus energy would be required to separate the atoms in a bond. The colloquial use of the term “stored” seemed to impede some students from making this interpretation.
Example of Student Reasoning About “Stored” Energy From Interviews
To illustrate the way in which students' conceptualization of potential energy as “stored energy” contributed to students' reasoning about energy changes in atomic–molecular systems, consider Kenneth, an upper-division student enrolled in a physical chemistry course. While Kenneth was able to correctly predict changes in potential and kinetic energy in simple atomic–molecular systems, his interpretation of potential energy as stored energy made it difficult for him to connect accounts of potential energy change across different atomic–molecular contexts.
In all three atomic–molecular systems (interaction of helium atoms, hydrogen atoms, and water molecules) Kenneth demonstrated an ability to appropriately coordinate his understanding of atomic–molecular structure, electrical forces and energy changes. For example, when asked to describe his understanding of how two helium atoms would interact he described each helium atom as having fluctuating electron density around a positively charged nucleus. He identified that the atoms could interact via London dispersion interactions and that interactions between particles could be either attractive or repulsive depending on the distance between the atoms. When asked to describe his understanding of how the energy of the system might change as the atoms approach, Kenneth drew on his understanding of the electromagnetic interaction between the particles.
Kenneth: Well, these [helium atoms] as they're pretty far apart then, the potential energy between them is pretty low because they're very weakly interacting inert gas molecules…the electrical energy between them, is probably not very strong, there's not a strong electric field, you know, potential between the two if they're far apart.
Interviewer: Ok. So what if they start moving closer together?
Kenneth: If they start moving closer together then, their electron clouds are going to start interacting and repelling each other. If they get close enough then they are, the protons will be attracted to the, um, electrons, but only, uh fleetingly attracted to each other since I don't think it's very easy to form covalent bonds between them.
When asked what would happen if the helium atoms were to continue moving closer together, he noted that the interaction would become repulsive.
Kenneth: I think you would more have a repulsive electron interaction if they got really close to each other. Potential energy would increase as they got closer together if there was a high repulsive force.
In this context, Kenneth associated repulsive interactions with increasing the potential energy of the system. Though he did not specifically discuss energy minimization in the context of helium atoms, he later predicted (correctly) that forming a hydrogen bond between two water molecules would minimize the potential energy of the system. He also discussed how as potential energy of the system decreased, kinetic energy would increase, resulting in increased motion of the particles. Thus, he correctly identified bond formation in the context of hydrogen bonding between water molecules as exothermic. However, when Kenneth discussed his understanding of potential energy at the atomic–molecular level more generally, he expressed a belief that energy can be stored in covalent bonds.
Kenneth: Potential energy at that level [the atomic–molecular level] would be the energy of a covalent bond for instance. The energy of that bond can be released under certain conditions to do work on the environment around them. There's energy stored in that bond.
When prompted by the interviewer to elaborate on his understanding of energy in this context, Kenneth tried to explain how energy might be stored in a bond by appealing to what he knew about how covalent bonds behave. He described a model in which two covalently bonded atoms vibrate relative to one another. Referring to potential energy as “positional energy,” he described how the potential energy of the system would increase as the atoms moved away from their neutral bond length.
Kenneth: If it is stretched from its neutral bond length, it has potential energy because it's being stored and it can be released. It can heat the environment or be used to cause other chemical changes, so it's potential in that way.
While Kenneth's description of energy change in this system accounted for small fluctuations of energy that occur as atoms within a bond vibrate relative to one another, it did not address the question at hand, which was how energy would change if a covalent bond were broken. Kenneth did not seem to recognize that his model failed to account for the process of bond breaking or that his interpretation of potential energy as energy stored by a covalent bond (and thus able to be released when the bond was broken) seemed to contradict his earlier conclusion that overcoming intermolecular interactions would require, rather than release, energy. Kenneth did not bring up the idea of “stored energy” in the context of helium atoms or water molecules and perhaps associated stored energy only with covalent bonds.
As Teichert and Stacy have noted (2002), the idea that bond breaking releases energy is a persistent difficulty. We believe this idea may stem in part, from students' misinterpretation of potential energy as “stored” energy, which as we have noted is a common curricular definition of potential energy. For the idea of potential energy to be meaningful, it is critical that students develop an understanding of the relationship between potential energy and electrostatic interactions between particles. Prior to his interview, Kenneth had probably never been explicitly asked to think about what it means to say that energy is “stored” by a bond or how potential energy changes that occur as atoms and molecules interact relate to energy changes upon bond formation. Thus it is not surprising that Kenneth was unable to reconcile his understanding of how and why bonding interactions form with his intuitive idea that covalent bonds “store” energy.
Potential Energy as Related to Stability
The third theme that emerged from our analysis was that students commonly attributed an increase or decrease in potential energy to the stability of the system. Students who identified the trend that lower potential corresponds to a more stable state (and conversely, higher potential energy corresponds to an unstable state) most often did so with little elaboration of their understanding of the factors which contributed to the stability of the system, such as electrical forces. For example, one organic chemistry student described her understanding of potential energy as follows: “potential energy at the atomic/molecular level is related to stability. In the Newman conformations, the lower the potential energy the more stable the molecule is.” (OC, survey). Similarly, another student described potential energy at the atomic–molecular level as “the energy of a system when it is unstable. When two atoms are close together, they have high potential energy and thus will force apart” (GC2, survey). Though the second student seemed to conflate the ideas of energy and stability, both responses suggest an association between lower potential energy and higher stability of a system.
In the semi-structured interviews a number of participants used the idea of stability in attempts to explain energy changes in atomic–molecular systems, though often without explicit discussion of the mechanisms by which systems become stable. That is, students rarely identified that systems are said to be “stable” when forces acting within the system become equilibrated such that a small change in the system would result in a force that returns the system to the stable state in which the forces are balanced and potential energy is minimized. We view this observation as potentially problematic since most students used the idea of stability to reason about energy changes in ways that while seeming superficially correct were not necessarily well anchored to their understanding of atomic–molecular structure and forces at the molecular scale.
To illustrate this trend, consider Calvin and Frank, both organic chemistry students who used the idea of stability to reason about interactions between atoms or molecules. When asked to describe how he thought two water molecules might interact, Calvin commented on the electronegativity differences between hydrogen and oxygen atoms and how the electronegativity difference contributed to the polarity of the molecules. He drew two arrangements of water molecules (Figure 3) to illustrate some ways that he believed water molecules might interact.
When asked to describe how he thought potential energy of the two systems in Figure 3 might compare, Calvin asserted that the system shown in Figure 3b would have lower potential energy than the system shown in Figure 3a. He explained his reasoning as follows:
Calvin: This one [arrangement in Figure 3a] wants to separate because positives are lined up with positives, negatives lined up with negatives, and charges don't like that way. And this one [arrangement in Figure 3b] is more stable because positives are lined up with negatives and create a chain, and that opposite attraction creates more stability than the same attraction.
Calvin reasoned that the arrangement of molecules in Figure 3b would be more stable than the arrangement in Figure 3a based on the fact that the interaction between the molecules would be attractive (rather than repulsive as in the arrangement in 3a). While the particular arrangement for hydrogen bonding in Figure 3b would be extremely unlikely, Calvin was correct in his assumption that attractive interactions would lower the system's potential energy. However, a more complete response might also include the idea that it is the balance between attractive and repulsive forces that occur in hydrogen bonding interaction that causes the system to be stable.
When asked to further elaborate his understanding of the idea of stability, Calvin commented that “more stable means lower potential energy” and explained his understanding of the relationship between stability and potential energy change as follows.
Calvin: When you have unstable systems, there's potential energy because they want to go to a stable system. And so they're going to do whatever they can to turn the potential energy into like a molecularly [sic] kinetic energy to get to their stable system.
While earlier in his interview Calvin seemed to associate attractive and repulsive forces with the idea of stability, he did not revisit the idea of forces in his second attempt at explaining why potential energy would change. Instead, he appealed to a teleological explanation of energy transformation in which he attributed change in potential energy of the system to the water molecule's desire to reach a certain state (Talanquer, 2007). While an expert would consider the minimization of the potential energy of the system to be a consequence of the change in the system, Calvin seems to suggest that stability would be the cause of the change rather than an effect. Thus, Calvin's explanation missing is the causal relationship between change in potential energy and the forces present in the system.
Frank, another organic chemistry student, used the idea of stability in order to explain the energy changes that would accompany interactions between hydrogen atoms. He described breaking a covalent bond between hydrogen atoms as a process that would require an input of energy and related that energy input to the relatives stabilities of species before and after interaction.
Frank: We'll say a, hydrogen molecule, H2, to pull those two molecules [sic] apart, it's gonna require energy because they're less stable apart than they are together. And they're going to have more energy for the two of them than the one molecule [sic] had alone.
When asked to elaborate his understanding of the term stability in this context, Frank noted,
Frank: When I think of stable, I think of low potential energy. I think of something not waiting to do anything, something without the means, the conditions to do anything productive for me.
Like Calvin, Frank seemed to associate stable systems with low potential energy (and conversely unstable systems with higher potential energy). In explaining why a system would be stable he returned to an interpretation of potential energy as the ability to cause change or motion in a system, which he had discussed earlier in his interview. Perhaps because the presence of charged particles was not as readily apparent as in the context of interacting hydrogen atoms as compared to interacting water molecules, Frank did not relate the idea of stability to attractive or repulsive interactions.
While Frank's explanation sounds quite appropriate, it is questionable whether his attribution of potential energy changes is associated with a deeper conceptual understanding of the relationship between force, energy, and stability. Instead, the trend “more stable, less potential energy” seemed to function as a heuristic for Frank. While heuristics such as these may be useful in that they provide a way simplifying an otherwise more complex reasoning tasks (Maeyer & Talanquer, 2013) it is well established that students may fail to attend to the conditions under which a given heuristic may be appropriate and thus may be more likely to apply heuristics in contexts in which they are not valid (Cooper, Corley, & Sonia, 2013; Maeyer & Talanquer, 2013; Taber, 2009). While the idea of potential energy change as determined by a system's “desire” to become stable can be useful in easily recognized contexts (such as the familiar case of hydrogen atoms forming a diatomic molecule), in novel contexts it may be less obvious which species might be considered more stable.
Prevalence of Themes Across Student Groups
As shown in Figure 4, all groups of students frequently conceptualized potential energy as stored energy or capability. While the idea of potential energy as related to stability was less prevalent in the survey data (<10% for all groups), stability was used by 12 out of 22 interview participants when reasoning about interactions of atoms. Across both survey and interview data, we observed that a greater proportion of students in organic chemistry courses used the idea of stability compared to general chemistry students, almost certainly because the idea of stability is frequently used in organic chemistry courses. Figure 4 also highlights that very few students identified relationships between potential energy, electrical forces, and position of interacting particles in their reasoning about potential energy (<2% of students in all groups).
Figure 4. Percentage of student responses using ideas of potential energy as stored energy, capability, and stability in response to online survey prompt: “At the atomicmolecular level, what do you think potential energy is?”, GC1 N = 142, GC2 N = 188, GC N = 102.
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As we have discussed, each of the three conceptions of potential energy described here (storage, capability and stability) has some merit. However, without the associated ideas of forces and position of interacting objects it becomes very difficult for students to form a coherent and useful model of potential energy that can help them make sense of atomic and molecular interactions across a variety of contexts.
Discussion and Conclusions
- Top of page
- Discussion and Conclusions
- Supporting Information
As highlighted by the recent Framework for Science Education (National Research Council, 2012), energy has the potential to serve as a crosscutting concept that can be used to predict and explain a wide range of phenomena. By understanding relationships between energy ideas, students may be better able to use energy ideas as a tool for solving problems and explaining phenomena (Fortus & Krajcik, 2012). In undergraduate chemistry contexts, the ultimate goal would be to have students use the ideas of electrical interactions and potential energy changes at the atomic scale to explain macroscopic observations such as a temperature increase as a reaction occurs or properties such as melting point or boiling point for different substances.
However, our findings illustrate that there may be significant challenges associated with students' reasoning about the atomic–molecular level that may make it difficult for students to make these connections on their own. Instead of relying on an understanding of forces and their connection to energy changes, we found that students more often relied on intuitive interpretations of potential energy such as the idea that potential energy represents an ability to form a bond, to interact, or to move. Such intuitive interpretations were rarely productive tools for reasoning about energy changes across different atomic–molecular systems. Students also reasoned about potential energy as “stored energy” in atomic–molecular systems but often without the qualification that potential energy is stored by a system of interacting particles based on their relative position and charges. Especially problematic was the idea that potential energy can be “stored” within a bond and thus released when the bond is broken. We also observed that while many students related potential energy to the stability of the system, most did so without a recognition that stability of a system is an effect that arises from forces and interactions between atoms and molecules.
A more explicit discussion of potential and kinetic energy as models of energy at the atomic–molecular scale may help students better connect energy ideas across scales and disciplinary contexts. Framing potential energy as “stored” in interactions between atoms and molecules may be especially productive since this idea can be applied to systems at both atomic–molecular and macroscopic scales (National Research Council, 2012). However, as we have demonstrated, the idea of “stored” energy can be problematic. If students are to productively extend the idea of potential energy across contexts, discussions of potential energy as “stored” energy must be accompanied by explicit instruction about how and under what conditions energy is stored. That is, students must be helped to understand that energy is stored in interactions between two particles because of electrostatic forces and that a system of objects interacting in a bond ‘stores’ less energy than separated atoms.
Given the great explanatory power of electrostatic interactions in chemistry (from periodic trends, to bonding and intermolecular forces, to the energy changes that accompany chemical processes), it is quite surprising that there is seldom an explicit discussion of the nature of forces at the atomic–molecular scale in undergraduate chemistry courses. We believe that it may too often be assumed that students already have appropriate prior understandings about the relationships between forces and potential energy and thus these relationships may not be explicitly discussed, leaving students without a coherent framework with which to make sense of these ideas. Given that students' prior knowledge related to potential energy may be fragmented or incomplete (diSessa, Gillespie, & Esterly, 2004), it is critical that chemistry instructors both attend to students prior knowledge about energy ideas and provide appropriate support for helping students make connections between force and energy ideas. For instance, activities that engage students in constructing models and explanations for energy changes in atomic–molecular systems may be particularly appropriate for both eliciting prior knowledge and providing opportunities for students to make connections between force and energy ideas.
One promising route towards helping students develop a more coherent understanding of energy ideas within chemistry contexts may be the use of a learning progression approach to aligning curriculum, assessment, and prior research on students' understanding of energy ideas. Learning progressions represent empirically validated descriptions of pathways along which students understanding may progress (Duschl, Maeng, & Sezen, 2011). While there is currently no empirically validated learning progression for teaching various aspects of the energy concepts at the undergraduate level, a considerable amount of foundational work towards the development learning progressions for energy at the K-12 level has been accomplished (Jin & Anderson, 2012; Lacy, Tobin, Wiser, & Crissman, 2014; Neumann, Viering, Boone, & Fischer, 2013; Nordine, Krajcik, & Fortus, 2011). Furthermore, there is evidence from K-12 contexts that a learning progression approach to teaching energy ideas may improve students understanding of energy-related phenomena (Nordine et al., 2011).
Our ongoing work in this direction focuses on the development and assessment of an evidence-based learning progression for energy in the context of an undergraduate general chemistry course called Chemistry, Life, the Universe, and Everything (Cooper & Klymkowsky, 2012). By beginning with a discussion of energy at the atomic–molecular level and by making explicit connections to students' prior understanding of energy ideas, the aim is to provide a more robust foundation for understanding discussions of macroscopic energy ideas in chemistry contexts (Cooper et al., 2014). In order to refine learning progression approaches such as this, more work is needed that explores how students coordinate across electrostatic, macroscopic, and quantum mechanical perspectives on energy in chemistry contexts.
Given the ongoing nature of reforms at the K-12 level, we consider a learning progression approach to have the potential to not only help improve students' understanding of energy topics in chemistry contexts, but also to provide learning experiences at the undergraduate level which will be more aligned with ongoing K-12 reforms (National Research Council, 2012). In addition, if this approach is transferred to other college level disciplines, specifically physics and biological sciences, it may help students make connections that are otherwise absent. Our goal is not only to improve students' understanding of energy in chemical systems, but also to provide a continuing framework that students can use across the disciplines.
This work was supported in part by NSF DUE awards 0816692 and 1122472. 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.