Chemical Education-Becker.pdf

JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 51, NO. 6, PP. 789–808 (2014)
ResearchArticle
College ChemistryStudents’ Understanding of PotentialEnergy in the
Context of Atomic–MolecularInteractions
Nicole M. Becker and Melanie M. Cooper
Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48823
Received 24 January 2014; Accepted 8 June 2014
Abstract: Understanding the energy changes that occur as atoms and molecules interact forms the
foundation for understanding the macroscopic energy changes that accompany chemical processes. In order
to identify ways to scaffold students’ understanding of the connections between atomic–molecular and
macroscopic energy perspectives, we conducted a qualitative study of students’ conceptualization of
potential energy at the atomic–molecular level. We used semi-structured interviews and open-ended surveys
to explore how students understand potential energy and use the idea of potential energy to explain atomic–
molecular interactions in simple systems. Findings suggest that undergraduate chemistry students may rely
on intuitive interpretations of potential energy, incorrect interpretations of curricular definitions (including
theideathatpotentialenergyrepresentsstoredenergy)andheuristicsratherthanfoundationalunderstandings
of the relationships between atomic–molecular structure, electrostatic forces and energy. Thus, we suggest
that more explicit attention to the nature and role of potential energy in the undergraduate chemistry
curriculummaybeneeded. # 2014 Wiley Periodicals, Inc. J Res Sci Teach 51: 789–808, 2014
Keywords: chemistry; misconceptions; conceptual change
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
Contractgrant sponsor: NSFDUEAwards;Contractgrantnumbers:0816692;1122472.
Correspondenceto:N.M.Becker;E-mail:beckern3@msu.edu,nicole-becker@uiowa.edu
DOI10.1002/tea.21159
Publishedonline7July2014inWileyOnlineLibrary(wileyonlinelibrary.com).
# 2014 Wiley Periodicals, Inc.

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).Evenafterinstruction,around50%
ofundergraduatestudentsstillholdthisbelief(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 acrossboth atomic–molecular and macroscopic contexts. Asthe Frameworknotes,
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 energyin 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
macroscopicscales.
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
Journal of Research in Science Teaching
790 BECKER AND COOPER

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, Fak ¼ q1q2
r2 , 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
asheat energyreleased byan exothermicchemicalreaction,originate inenergy 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
bondingto 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
betweenspecies.Forinstance,tounderstandenergychangesthataccompanyinteractionsbetween
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)
theoryand understanding of additional concepts such aselectronegativity maybe 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 (Nahumet 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.
COLLEGE CHEMISTRY STUDENTS OF POTENTIAL ENERGY 791

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 definedsystem. As such,
undergraduate chemistry students must not only be able to relate atomic–molecular perspective
on energy change to macroscopic phenomena, theymust also develop the capacity to compare and
contrast multiple models ofthe energy changes inchemical 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
newcontexts such as atomic–molecularinteractions. 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
Figure 1. Potentialenergycurveforhydrogenatominteractions.

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 differencesmay be difficulttoappreciate.
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
aimstoaddress this gap intheliterature by describing students’ understandings ofpotential 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
tomacroscopicperspectiveson energy.
Methods
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 inthe 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–molecularlevel. 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
exampletoillustrateyour thinking.
Students enrolled in three chemistry courses completed the survey online as part of the
homeworkrequirements fortheircourses(Table 1).Allcoursesweretaughtusingapredominantly
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).
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 tothe surveyused to gather the data forthis study.
Semi-Structured Interviews
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
refinedforclarity prior to thefull 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,inorganicchemistry, etc.).
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 theinterviewsverbatim.
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
Total 333

Data Analysis
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 thesurvey and interviewswere combined for thefinaliteration ofanalysis and both
datasets were analyzed using thesame set ofcodes.
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
ofagreement between thetwo raters (Cohen’sKappa 0.84with p 0.001).
Findings
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 undergochange. 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 oreffect 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–molecularscale.
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
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

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 someway, 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 asatoms approach towardsa distance at whichtheywould “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
hisreasoning asfollows.
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 sothatkinda affects the potentialenergy.
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 witha greater likelihood offorming 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 ofinteracting
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.
Potentialenergywouldminimizedatthebondlengthbecauseofthefactthatattractiveinteractions
and repulsiveforces between thespecies are balanced at thebond lengthdistance.

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 orkinetic energywould occur asthe helium atoms interact.
Paul: They’re extremely unlikely to make any sort of attempt at making a bond so they’re
notgoingto need tochange energyfrom potentialto 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 ofinteraction. 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
itsrelationship toelectrostatic 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
accompanyintermolecular 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 scalewas 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% inGC2, 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
abelief that energy could be stored by bondsand released when bonds were broken.
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
toconnect accounts of potential energy change across different atomic–molecularcontexts.
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
theatoms could interact viaLondon dispersion interactions and that interactionsbetween particles
could be either attractive or repulsive depending on the distance between the atoms. When asked
todescribehisunderstandingofhowtheenergyofthesystem might change astheatoms approach,
Kenneth drew on hisunderstanding of theelectromagneticinteractionbetween theparticles.
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 molecule-
s. . .the electrical energy between them, is probably not very strong, there’s not a strong
electricfield,youknow, potentialbetweenthe two ifthey’refar apart.
Interviewer:Ok. Sowhat iftheystart 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
thinkit’s veryeasyto form covalentbondsbetweenthem.
When asked what would happen if the helium atoms were to continue moving closer together,
henotedthat 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
highrepulsive force.
Figure 2. Percent of student responses that indicated that potential energy could be stored in nuclei or stored in bonds.
GC1N ¼ 142,GC2N ¼ 188,GCN ¼ 102.

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
thesystemdecreased, kineticenergywouldincrease,resultinginincreased motionoftheparticles.
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 incovalent 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
conditionsto dowork onthe environmentaroundthem. There’s energy storedin thatbond.
When prompted by theinterviewer toelaborate on his understanding of energy in this context,
Kenneth tried to explain how energy might be stored in a bond by appealing towhat 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,soit’s potentialin 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 energyonly 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 covalentbonds“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 arrange-
ments 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
thanthe system shown inFigure 3a. He explained hisreasoning asfollows:
Calvin:Thisone [arrangement in Figure 3a]wants to separate because positivesare 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 inhydrogen bonding interaction that causes the system tobe 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 energychange 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 likea molecularly[sic] kineticenergyto get totheir stablesystem.
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 theforces present in thesystem.
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 tohave moreenergy for thetwo ofthem thanthe onemolecule [sic] had alone.
When asked toelaborate hisunderstanding of theterm 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
productivefor me.
Figure 3. Calvin’sdepictionof watermolecules arrangedtobelessstable(a)andlessstable(b).

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
beconsidered morestable.
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).
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 avariety ofcontexts.
Discussion and Conclusions
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 energychanges, 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 behelped tounderstandthat energy is stored ininteractions between two particles
because of electrostatic forces and that a system of objects interacting in a bond ‘stores’ less
energy than separatedatoms.
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 ¼ 142,
GC2N ¼ 188,GCN ¼ 102.

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 offorces 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 makeconnections between force and energyideas.
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
frameworkthat students can use across thedisciplines.
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
authorsand donotnecessarily reflect theviews ofthe NationalScience Foundation.

Notes
1
A description of the beSocratic assessment system can be found at http://besocratic.
chemistry.msu.edu/
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