Undergraduate chemistry students’ misconceptions about reaction coordinate diagrams

Abstract

Misconceptions are the “the old, the bad, and the ugly” prior knowledge, ideas or conceptions that the learners have that hinder their further learning in science. Several types of misconceptions that undergraduate students hold about reaction coordinate diagrams (from here on we use the term “reaction coordinate diagrams” and “energy diagrams” interchangeably) are described herein. The rationale of 223 students were coded based on their responses to a multiple-choice question on the topic, and interviews (n = 10) were used to delve deeper into the students’ knowledge structures. The results of the open coding of the rationale and the interviews were used in developing an instrument which was administered to 57 students. In this paper, we present the assessment instrument and the alternate conceptions that students have regarding energy diagrams that have not been reported in the literature yet. Implications for instructional approaches particular to the energy diagram topic are discussed.

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Introduction

A misconception can be considered “the old, the bad, and the ugly” of prior knowledge, ideas or conceptions that learners have. When learners justify their correct or incorrect answers with reasoning based on information that is different from the scientifically-accepted explanations of a concept, this is as an example of a misconception (Nilson, 2010; Bruning et al., 2011). According to Taber and Coll (2002), lack of information, incorrect strategies being applied during instruction and memorization are some of the causes of misconceptions. It is safe to say that misconceptions are held by all students (Schneps and Sadler, 1988), thus it is critical for educators to understand their nature and source to be more effective in addressing them. Since many educators think misconceptions are simply common errors or a particular concept that students did not master (Duis, 2011), most classes do not address misconceptions during the normal learning process. Despite being pervasive, most educators are not taught how to identify or remediate misconceptions (Duit and Treagust, 2003; Nilson, 2010).

According to Cognitive Learning Theory, the human mind depends upon organization. It acquires and stores new knowledge or concepts only if it finds a logical place within the mental structure of prior knowledge (Anderson, 1984; Bransford et al., 1999). If existing knowledge includes misconceptions, then the students build or store new knowledge that incorporates these misconceptions, often leading to continual faulty learning. Remedying misconceptions is not an easy task, and traditional teaching methods and strategies have been shown ineffective in bringing about conceptual change (Champagne et al., 1982; Duit and Treagust, 2003). Conceptual change is a process by which “people's central, organizing concepts change from one set of concepts to another set incompatible with first.” (Posner et al., 1982, p. 211). The goal of conceptual change is thus to shift students’ misconceptions into correct conceptions held by the scientific community. Nussbaum and Novick (1982) have proposed a three step strategy for bringing about conceptual change: (1) revealing and understanding student misconceptions, (2) creating conceptual conflict with those misconceptions, and (3) encouraging the development of revised or new schemata about the topic/phenomena in question. Thus the first and the most critical step before researchers and educators can remediate misconceptions is to identify those that the students hold.

In this paper we identify undergraduate students’ misconceptions about energy diagrams (from here on we use the term “energy diagram” as a description for “reaction coordinate diagrams”). First, we address the significance of energy diagrams in learning chemistry, including students’ misconceptions of energy diagrams or related topics as explored by other scholars. Next, we present our current research, elaborating on how our results have implications for teaching chemistry at the undergraduate level.

Relevant literature on energy diagrams

Energy diagrams are taught in undergraduate General Chemistry courses and utilized in further coursework such as Organic Chemistry, in order to introduce students to the concepts of thermodynamics and the kinetics of reactions. According to studies by American Chemical Society (ACS) Exams Institute, “energy” and “time scale” are anchoring concepts in the undergraduate chemistry curriculum (Murphy et al., 2012; Holme et al., 2015). Concepts such as activation energy, transition state, exothermic and endothermic reactions, stability of reactants versus products and reaction mechanisms are taught with the help of energy diagrams. Catalysis and Hammond's postulate are taught implicitly by embedding the concepts in energy diagrams (Carey and Sundberg, 2007; Carey and Giuliano, 2014).

Yet, there is a dearth of educational research on the topic of energy diagrams and students’ conceptions about them, especially at the tertiary level (Bain and Towns, 2016). Warner et al. (2013) looked at how computational exercises in an undergraduate organic chemistry laboratory helped students reinforce the significance of the traditional topics taught in a lecture. The participants in the study generated the reaction coordinate diagrams for substitution and elimination reactions between 2-bromobutane and various alkoxide bases and they examined the energetics of the starting materials, possible products, and theoretical transition states. The study did not go into depth about student understanding of the various components or nuances of the energy diagram but focused more on the favorability of the products formed in substitution and elimination reactions.

Sozbilir (2002) used open-ended diagnostic questions and semi-structured interviews to delve into Turkish undergraduate chemistry students’ understandings of Gibbs free energy. Sozbilir found some students’ misconceptions when the students were asked to compose drawings that depicted Gibbs free energy change (ΔG) in terms of the extent of the reaction A going to B (A → B). Sozbilir determined there were misconceptions regarding the ΔG and how that affected the rate at which reactions proceeded. Some misunderstandings identified by the author regarding ΔG include: (i) the slower the reaction the smaller change in ΔG, (ii) the bigger ΔG means the faster the reaction occurs, (iii) the reaction with bigger ΔG goes towards full completion.

Research involving secondary and tertiary Turkish students has shown that students have difficulties in defining “rate” (Cakmakci and Leach, 2005; Cakmakci et al., 2006; Cakmakci, 2010). Some alternate conceptions pointed out by these studies include students defining reaction rate as simply reaction time or that rate depends on both the concentrations of reactants and products. Bain and Towns (2016) in their literature review on chemical kinetics talk about research that revealed students’ (both secondary and tertiary) alternate conceptions about rate laws; activation energy; effect of catalyst in the rate of the reaction; and endothermic and exothermic reactions. Turányi and Tóth (2013) revealed Hungarian university students theorizing concentrations of reactants in a rate equation having exponents equal to the stoichiometric coefficients of the reactants in the balanced equation for the reaction. On the other hand, Kolomuç and Tekin (2011) uncovered misconceptions that reaction rate is equal to the product of concentrations and reactants in secondary in-service chemistry teachers in Turkey.

With regards to how catalysts affect a reaction, Yalçınkaya et al. (2012) revealed misconceptions in high school students as to how a catalyst increases reaction rate by decreasing the kinetic energy of the molecules. In contrast, Taştan-Kırık and Boz (2010) found that high school students conceptualize catalysts increasing the average speed of the molecules (or increasing the number of collisions). Taştan-Kırık and Boz (2012), and Yalçınkaya et al. (2012) explored students’ thought processes about endothermic and exothermic reactions too and found students conceptualized exothermic reactions as having lower activation energy than endothermic reactions. With regards to activation energy, there were various other misconceptions that students held too. Yalçınkaya et al. (2012) found high school students equating an increase in temperature with increasing activation energy whereas in Taştan-Kırık and Boz (2012) study, students conceptualized an increase in temperature as responsible for decreasing activation energy. Taştan-Kırık and Boz (2010), Yalçınkaya et al. (2012), and Taştan-Kırık and Boz (2012) along with revealing the misconceptions in their studies explored how strategies such as case-based learning and cooperative learning can be used to bring about conceptual change in high school students with regards to concepts of chemical kinetics and all three studies showed these instructional methods enabled better understanding of the concepts of chemical kinetics. Cakmakci (2010) found that upper secondary school students (ages 15–16), first year and third-year university students held the belief that activation energy is the kinetic energy of the reactants molecules.

Research aims and significance of the study

These kinetics and thermodynamic concepts such as rate laws, activation energy, use of catalyst, etc. are usually taught with the aid of energy diagrams and thus make clear the importance of understanding energy diagrams (Murphy et al., 2012; Holme et al., 2015). Yet, there is a dearth of research studies that have explored university students’ conceptions about energy diagrams, especially their features. Bearing these points in mind, this study addresses the following research question:

What are undergraduate students’ conceptions about energy diagrams and their features?

In this paper, the term “alternate conceptions” or “misconceptions” is used to describe ideas students develop about a topic that do not align with scientifically correct conceptions (Duit and Treagust, 2003). To answer the research question, we have situated the paper in this way: we first describe the creation of an assessment instrument that can be used to reveal students’ thinking about concepts such as rate, bond-breaking and -making, etc. with the aid of an energy diagram. Next, we delve into some conceptions and misconceptions not addressed by extant literature that undergraduate students carry into introductory organic chemistry from their general chemistry courses regarding the topic of energy diagrams.

Methods

Participants and setting

This research study was conducted at a large, research-intensive, public university in the Midwestern United States. Student participation in all parts of the study was voluntary and informed consent was obtained. The Institutional Review Board of the University approved the study. Each student received a $10 gift card for participating in the interview. To protect identity of students who participated in the study, their names have been replaced by pseudonyms in this paper. All students were enrolled in a three-credit, first-semester organic chemistry course after obtaining a C- or better in the mandatory general chemistry course. The learning objectives related to potential energy diagrams that have potential energy in the y-axis and reaction coordinate on the x-axis in the general chemistry course at our institution are listed below:

(i) Identify the location of reactants, products, and transition state.

(ii) Draw a molecular representation of a possible transition state for the reaction.

(iii) Determine the activation energy for the forward and reverse reaction.

(iv) Determine if reaction is endo or exothermic. Is energy released or absorbed?

(v) Relate the magnitude of the activation energy to the rate constant with the aid of Arrhenius equation.

(vi) Relate the rate constants for the forward and reverse reactions (determined by activation energies) to the equilibrium constant.

(vii) Draw a new potential energy diagram after addition of a catalyst.

(viii) For a multi-step reaction, identify reaction intermediates.

To attain learning objectives (i) through (viii), the instruction focuses mostly on the y-axis of energy diagrams. For example, during instruction when identifying reactants, products, and transition state (learning objective (i)) or when determining endothermic or exothermic reaction and if energy is absorbed or released (learning objective (iv)), the focus is on the amount of energy which is the y-axis. Instructors even label the y-axis with numbers (example, from 0 to 200 kJ mol⁻¹). The x-axis is defined and labeled as reaction progress or reaction coordinate during instruction. Numbers are not put on the x-axis similar to y-axis because of its qualitative nature.

We break this study into three phases for clarity. In Phase 1, the students responded to a multiple-choice question (MCQ) and also provided their reasoning for their selections with regards to energy diagrams (refer to Fig. 1). From here on, when we speak of ‘responses’, we are referring to their choices on the MCQ as shown in Fig. 1 and not the rationale or reasoning they provided.

Fig. 1 Multiple choice question on energy diagram.

The question that the students were assessed on was taken directly from the general chemistry teaching materials used in the class, and thus the content validity is inherent (Weiner and Graham, 2003), while also acknowledging that “it is incorrect to speak of validity as ever being established in the once-and-for-all sense of the word” (Lederman et al., 2002). A total of 223 students (43.5% male, 56.5% female) participated in Phase 1 of the research study.

After finding the common themes in students’ rationales provided for MCQ in Phase 1, two pilot interviews were conducted by the first author to evaluate the effectiveness of the interview questions. Based on these interviews, slight adjustments were made to the prompts to allow for probing of students’ rationales in Phase 2.

Participants for the interviews for Phase 2 were recruited via email in the 10th week of a 16 week semester. All the interviews were conducted by the first author and took place during weeks 11 and 12. Of the 10 students who participated in the interview, 7 of them were female and 3 were male. We attempted to recruit students who responded with something other than ‘A’ (which is the correct response) as their response to the MCQ but only got one volunteer for the interview. The other nine students responded with the correct choice including two students who completed the pilot interviews. Each student was interviewed individually in a private room by the first author. The interviews lasted between 8 to 10 minutes. The interviewer did not tell the students if they had correctly answered the question or not. Each student was given their MCQ response and asked to explain in depth about their ‘responses’ and rationale they had provided with respect to energy diagrams during the interview. After they explained the rationale for their choice, they were asked questions in the order outlined below with other probing questions when deemed necessary:

(i) What does activation energy mean or what does it mean to you when you use the phrase sufficient energy?

(ii) Is there any difference between diagrams A and C (refer to Fig. 1)? Could you elaborate more?

(iii) What do you think the x- and the y-axis signify?

(iv) Where do you think the reaction starts in the energy diagram?

(v) Have you heard of Arrhenius equation? Do you remember what the expression is or what it can be used for?

Based on the results of Phases 1 and 2, the third phase consisted of developing an instrument to further assess these misconceptions. Phase 3 was carried out in the summer of 2017 with 57 students (36.8% male, 63.2% female) participating in the study out of possible 70 students enrolled in an organic chemistry lecture. These students were not a part of the original 223 students from Phase 1 and they came from the first session of a summer organic chemistry lecture at the same university. We report on all the misconceptions uncovered during the various phases of analysis.

Data analysis

Phases 1 & 2.
Coding of rationales. The rationales of 223 students were evaluated through an emergent thematic coding approach to find common themes, upon which the interview questions were prepared (Creswell, 2012). Codes were refined using the constant comparison method. According to Glaser and Strauss (1967), the constant comparison method involves breaking down the data into discrete ‘incidents’ or ‘units’ and coding them to categories. Categories undergo content and definition changes along with deletion as “units” and “incidents” are compared and categorised, and are developed and refined over the course of the analytical process. The students’ rationales regarding the slowest reaction depicting energy diagrams were categorized under four subcategories (see Table 1).

Table 1 Coded themes, percentages, and example student responses for energy diagram

Factors that determined the slowest reaction	Percentage (n = 223)	Example from students’ rationale from multiple choice questions
(1) Activation energy highest	53.3%	“Diagram A requires more activation energy and thus the slowest.”
		“Most amount of energy (activation energy) needed for reaction to happen.”
(2) Energy in general	13.5%	“Diagram A because the greatest amount of energy must be gained for the reaction to proceed forward.”
		“Diagram A needs the most energy to start.”
		“Diagram A has to surmount the most energy.”
(3) Slope and length	19.7%	“Reactants take longer to be used up in diagram A.”
		“Diagram A takes the longest to get to the reaction peak.”
		“Largest first step in A.”
		“Diagram C slowest because it completes the reaction in quickest time.”
(4) Energy of activation/general energy with the inclusion of the energy of the reactants or products	13.5%	“Products greater energy than reactants, and activation energy large.” (choice of A)
		“Large threshold energy, and a higher ground state energy in product.” (choice of A)
		“Requires high energy and eventually becomes less stable.” (choice of diagram C)
		“Largest change in energy from highest point, but C requires a higher activation energy.”

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Interviews. The student interviews were recorded and then transcribed verbatim. The interview transcripts were analyzed for emergent themes using an open coding strategy, and the key issues regarding the misconceptions on energy diagrams were identified in the process (Corbin and Strauss, 2008). For example, “use of analogy” was one of the themes that we identified. Three out of ten students during the interview used analogies to explain their rationale for the activation energy (E_a) being high and its relation to the speed of the reaction. We identified the themes and recorded key issues regarding the misconceptions on energy diagrams in those analogies.

Phase 3.
Coding of rationales. The rationales of 57 students were evaluated through an emergent thematic coding approach to find common themes (Creswell, 2012). Codes were refined using the constant comparison method (Glaser and Strauss, 1967). The first author initially coded the rationale. The codes and the explanation (scheme) for the codes developed by the first author was used by the second author to code the rationales of the 57 students. The interrater reliability, which was calculated by looking at the percent agreement between the first and the second author, was above 95% for the codes in both Tables 2 and 3. The codes were discussed and refined by coding together with the second author when there was any disagreement. Disagreements in the coding were revisited and any issues resolved after discussion between the coders. The students’ coding of rationales regarding the different concepts related to energy diagrams have been listed in Tables 2 and 3.

Table 2 Coded themes, percentages, and example student meaning for “start of a reaction”

“Start of a reaction” (n = 18)	Example from students
(1) Reactant starting to change with no mention of energy (n = 9, 50%)	“Whenever the chemicals start to change from their original state”.
	“The time a reaction start to occur. The structures start to change”.
(2) Reactant and their energy mentioned (n = 5, 27%)	“The start of the reaction is the relative potential energy state of the reactants. The reaction proceeds off this starting point”.
	“When the molecules are brought together + energy put into the system”
(3) Rephrasing “start of the reaction” (n = 3, 17%)	“…beginning of the rxn”
	“…reactant starting point”
(4) Attempted to use an application (n = 1, 6%)	“When an acid or base is protonated/deprotonated to further react to form the products”

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Table 3 Coded themes, percentages, and example student meaning for “start of a reaction”

“Start of a reaction” (n = 35)	Example from students
(1) Reactant starting to change and/or bond breaking and forming (n = 10, 28%)	“When molecules collide & begin electron exchange”.
	“The start of the reaction contains the starting materials, such as the reactants and solvents or sources of energy”.
	“Where bonds begin to break and new ones form”
	“When the reactants start to rearrange themselves”
(2) Reactants reached enough energy (n = 14, 40%)	“The start of the reaction is when the reactants have reached the activation energy needed for the reaction to occur”
	“One there is enough energy to pass the energy barrier”
	“When the Ea has been achieved and the reactants are reacting”
(3) Rephrasing “start of the reaction” (n = 3, 9%)	“When things start to happen”
	“…is when the reaction begins”
(4) Transition state is the start of the reaction (n = 8, 23%)	“When transition state emerges from two reactants”
	“…is the highest point on the graph that indicates the transition state”
	“The transition state is the start of the reaction”
	“It means where the substituents begin to interact forming TS”.

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Results and discussion

Coding of responses (Phase 1)

Seventy-nine percent of 223 students correctly chose A as their “response” for the MCQ. The rationales from 223 students were examined in this study to understand their thinking about how energy diagrams describe the rate of the reaction. The results are shown in Table 1. The rationales were coded into four categories by the first and the second author along with the percentage of students that fall under each category. Each category is presented with some examples to clarify the code. While our first review produced seven codes, these were reduced to four after discussion and revision. For example, code four (Table 1) was formed from two previous codes: rationalizing the rate of the reaction with ‘the stability of products’ and another reasoning with ‘endothermic and exothermic reaction’. In a typical undergraduate organic chemistry textbook, exothermic and endothermic reactions are mentioned in terms of thermodynamic stability of products and reactants (Carey and Giuliano, 2014), which is why we decided to merge the two codes to form one. After the revision of the codes, the interrater reliability was calculated by looking at the percent agreement between the first and the second author in coding the student rationales which was 94%. The disagreement in the coding of the 6% students were revisited and the issues resolved after discussion between the coders. They agreed that the code “slope and length” should not include any reference to energy or activation energy. Additionally, they discussed that the first code “activation energy highest” should only include students who explicitly use the terms ‘activation energy.’

Among the 223 rationales coded, the majority attributed activation energy as being related to the rate of the reaction. One fifth of participants (19.7%) manipulated the graph and used rationale with terms of “slope and length” without any hint about the activation energy or energy required to get to the transition state. Two other groups of responses were coded, approximately 14% of responses each. One group did not use the term activation energy explicitly but had rationale that mentioned energy in some form to support their response. The other group included the energy of the products or reactants as being important in determining the rate of the reaction along with the threshold, activation energy, or energy in general. To delve deeper into students’ rationale about energy diagrams, we next discuss the interview results.

Interviews (Phase 2)

For the energy diagram MCQ, of the 10 students interviewed, 9 picked Diagram A as their response and 1 student picked Diagram C (Fig. 1). Since the interview study was voluntary, we did not have any control over which students volunteered to participate. From the coding of the 10 interviews, results indicated that the students had a good grasp on concepts such as energy of the reactants and the products (which has the higher energy), activation energy, and significance of the y-axis in the energy coordinate diagram. Interestingly, the student who chose the incorrect representation (Diagram C) did so despite her rationale matching the other nine students who said that “the activation energy is the highest for Diagram A, and thus the energy diagram describes the slowest reaction.”

Additionally, some students came up with interesting and clever analogies to explain their rationale for the activation energy (E_a) being high and its relation to the speed of the reaction. Having defined the students’ analogies as clever, we do acknowledge that analogies can be “two-edged swords” because sometimes the knowledge they generate is accompanied by alternate conceptions (Harrison and Treagust, 2006). For example, Brianna's and Lindsay's explanation does not necessarily show their understanding of an energy diagram which has the same activation energy but different slopes. This is explored further in Phase 3. The analogies presented below provide some examples:

Analogy 1 (Varun): “Activation energy is more or less, once a certain energy is contained in the system it can use that energy for physical work or in this case chemical work. It can use that amount of energy to alter a bond or do some other conformational change or bond within an atom. It's like if you are opening a very heavy door, you can continue tugging it and tugging it, and once you get that energy to open the door then you can proceed and go through.”

Analogy 2 (Brianna): “If you are running up a large hill, it will take much more energy than going up or running up a speed bump or a short hill. So that's the first thing.”

Analogy 3 (Lindsay): “Yeah. I thought of Hilly Lane that is north of here and that is a very steep hill and it takes you forever to walk up it. So I thought of the reaction happening, and the highest one is going to be a very slow climb without the catalyst. So that's why I picked that.”

One of the other things we examined was the students’ familiarity with the Arrhenius equation, and their ability to use it to support their answer choice for the energy diagram question. Based on the interviews, all 10 students studied the Arrhenius equation in their introductory chemistry course as mentioned earlier under learning objectives (“Methods” section) but when they were asked “Do you remember what the expression is and what it can be used for?”, none of them could answer the first part of the question or recall how to use the mathematical expression and tie it to their choice of energy diagram. The interviewer then wrote the Arrhenius equation for the students to explore if they were able to relate activation energy (E_a) and the rate of the reaction using the equation. Only one student seemed comfortable in using and explaining the mathematical relationship. A couple of dialog segments (1 & 2) showcase students’ difficulties in understanding, interpreting or using the Arrhenius equation:

Dialogue 1 with KELLY

Interviewer: So this small k = A e^−E_a/RT. Do you know what does small k and E_a refer to?

Kelly: ‘k’ is the rate of the reaction, I believe. E_a is the activation energy.

Interviewer: How are they related then?

Kelly: They are equal. So basically, I mean altogether all of this equal to k. I would take that to mean the speed of the reaction equals the E_a or getting it started. That's what I would take that to mean.

Dialogue 2 with MATT

Interviewer: So this small k = A e^−E_a/RT. Can you tell me what's E_a and k here if you remember?

Matt: I think ‘k’ is some kind of a constant, reaction constant and E_a is the activation energy.

Interviewer: Do you think we can use this equation to explain what's happening in our question?

Matt: Umm. Isn’t ‘T’ for temperature?

Interviewer: Uh. Huh.

Matt: If we do not have the temperature, how can we use that?

As seen in examples 1 and 2, Kelly and Matt did not seem comfortable when asked to apply the equation to see if rate constant ‘k’ and activation energy ‘E_a’ are related. In example 1, Kelly responds that the “speed of the reaction equals the E_a”, which argues against her choice of the correct answer (Diagram A) in Fig. 1. Her argument would describe the energy diagram with highest activation energy (E_a) as the fastest reaction. This incorrect use of Arrhenius equation to talk about the rate of the reaction and activation energy was something we observed as a common theme in the majority of students’ explanation of their reasoning in Phase 3 as well.

Along with the mathematical concept derivation from the Arrhenius equation, the students’ weak understanding of the rate constant ‘k’ was apparent. It was not surprising to us that students’ understanding of rate constant ‘k’ was not strong since studies show that students have difficulties when defining reaction rate (Cakmakci and Leach, 2005; Cakmakci et al., 2006; Cakmakci, 2010). As seen in Dialogue 1, Kelly clearly has a weak understanding of the difference between rate of the reaction and the rate constant ‘k’. These results add to the existing knowledge regarding students’ difficulties in understanding and using simple mathematical relationships and equations applied to chemical applications (Potgeiter et al., 2007). The ability to use the Arrhenius equation when all the terms were made known to the students was something we explored in Phase 3.

Results from Phase 1 indicated that 38% (n = 82) of the students along with the activation energy mentioned about “taking a lot of time to start the reaction”, “reaction to happen”, and “reactants taking longer to be used up” (see Table 1). Based on this, Phase 2 interviews investigated where the students thought the reaction started in the energy diagram along with what the x- and the y-axes signified. Students were asked “to pinpoint in the energy diagram where the reaction started”, and from the 10 student interviews, we obtained 3 different answers that are categorized in Fig. 2. Among ten students, four students reasoned through Fig. 2A for where the reaction started in an energy diagram. The other two students chose to draw Fig. 2B and the remaining four students pinpointed with Fig. 2C.

Fig. 2 Different categories of students’ responses (A–C) as to where the reaction started. [Note: the red arrow points to where the students circled their answers on the energy diagram.]

The following is an interview except from one of the students whose response was B in Fig. 2. In this response she explains where the reaction started.

Brianna: Umm. Where the reaction starts? Probably not the very beginning, it has to be right after that (points at x). The very beginning is just the reactant.

Interviewer: So can you point out with a circle what you mean by that?

Brianna: Like, where it starts to go up.

Interviewer: So where the incline starts?

Brianna: Yes.

It was surprising to see such variation in answers to the question about the “start of the reaction”. We explored these variations to understand what students meant by the “start of the reaction” in Phase 3. Regarding the coordinate planes in the energy diagram, all the students correctly identified the y-axis as free energy (or change in energy). But nearly all students (9 out of 10) labeled the x-axis as ‘time’ when they were asked to explain the “reaction coordinate” or the “progress of the reaction.” We are reminded that energy diagrams are describing the surface upon which the molecules are traveling as a function of their structure (Anslyn and Dougherty, 2006). These results suggest that we may not be teaching the use and context of potential energy diagrams as best as we could. Based on this, we explored the significance of x-axis further in Phase 3.

Misconceptions inventory questions (Phase 3)

To explore students’ ideas further, we devised a series of questions to assess students’ misconceptions about energy diagrams and related concepts in Phase 3. There were 57 students who participated in the study in Phase 3.

The assessment started out with the same MCQ used in Phase 1 (Fig. 1). Eighty-two percent of the students correctly chose A as their response, which closely aligned with 78% of 223 students choosing the correct response in Phase 1. The MCQ was followed by an open-ended question based on Arrhenius equation and its relation to the rate of the reaction (Fig. 3). In Phase 2, we revealed many students (9 out of 10) being uncomfortable in using the equation and these new data in Phase 3 confirmed this.

Fig. 3 Arrhenius equation and rate of the reaction.

Out of 57 students who took part in Phase 3 of the research study, 12% of the students responded with a ‘NO’ to the question in Fig. 3. These students reasoned that since the information was not given to them, they could not manipulate the equation to explain the rate of the reaction. Here are examples of students’ responses:

Sai: No, because there is not enough information to determine.

Lauren: None of the values are given.

The remaining 50 students indicated that the Arrhenius equation is related to the rate of the reaction. Of these students, nearly half (46%) provided vague responses as to how the rate of the reaction was related to the activation energy in the Arrhenius equation and did not connect to their choice of answer in MCQ in Box 1. Example student rationales:

Caroline: Yes, the rate constant is strongly dependent on the value of E_a.

Tabatha: It gives a rate for reaction.

Tim: Yes, because the activation energy is a major component of the equation and also in the rate determining step of the reaction.

Only 14 of the 50 students (28%) were able to reason with the help of Arrhenius equation for their choice of slowest reaction in the given energy diagrams. As can be seen in the examples below, Mitch and Maria understand how exponents work in a mathematical relationship.

Example student rationales:

Mitch: Yes, it does support my rationale since its activation energy would be a larger quantity, and since it is −E_a/RT, the higher the E_a, the slower the reaction (rate constant).

Maria: The larger the E_a, the smaller the rate constant because it is a negative exponent, so as it grows larger, the rate constant gets smaller.

Thirteen students (26%) manipulated the Arrhenius equation where they reasoned that a higher activation energy would lead to a higher rate constant. This is in complete contrast to their choice of A (correct answer) for the question in Fig. 1. Example student rationales from this group:

Krishna: Yes, the equation can be used. The E_a activation energy is in the numerator of the exponent. Therefore the larger the activation energy, the greater the rate constant.

Andre: Yes, if everything else is constant, a higher E_a gives one a higher exponential, thus a larger k.

Brita: The larger the value of E_a, the greater the value of the rate constant, which indicates a slower reaction.

Huidi: k decrease when E_a decrease. Since A has the highest E_a, the rate constant is lowest.

Students seemed to have a very tenuous understanding of exponentials. According to research, equations containing logarithmic relationships between variables such as Nernst equation in electrochemistry and Henderson–Hasselbach equation for buffer systems in weak acids generally pose problems in undergraduate chemistry students (Potgeiter et al., 2007). Thus this result was not surprising since the Arrhenius equation can be written in the form of natural log as ln k = ln A − E_a/RT. Additionally, the rate constant concept seems to confuse students and how that is related to the rate of the reaction i.e. how fast or slow a reaction proceeds (e.g., Brita, Huidi). Huidi contradicts her first statement with the second even though she got the “response” correct for the MCQ in Fig. 1. Students’ difficulty with the ‘rate of the reaction’ has been documented in the literature (Cakmakci and Leach, 2005; Cakmakci, 2010; Bektasli and Cakmakci, 2011) but we reveal students’ discomfort in relating rate constant and rate of the reaction too. To explore the students’ understanding of the x-axis and if that affected the rate of the reaction we used the question in Fig. 4.

Fig. 4 y-axis vs. x-axis in an energy diagram.

Thirty-one of the students (54%) chose B as their response for the question in Fig. 4. We created this item to see if labeling of the x-axis as TIME could possibly be problematic based on our interviews in Phase 2. Of the 31 students who chose B as their response, nearly three quarters labeled the x-axis as time and provided rationale where they ignore the y-axis (the activation energy). The x-axis in the energy diagram in an undergraduate chemistry curriculum is labeled as reaction progress, and based on these results it seems like students equate “reaction progress” with time conceptually and while thinking about reaction rate in an energy diagram. The implications regarding this issue will be discussed later in the paper. There were some students (6 out of 26) who had picked both A and B being the same as their response but still labeled their x-axis as time. The remaining 20 students correctly labeled their x-axis as reaction coordinate or reaction progress.

The National Governors Association (NGA) center explains coordinate plane as two perpendicular number lines on which to plot points (NGA Center and CCSSO, 2010). The ordered pairs or the plotted points on a coordinate plane have two numbers or represents two quantities’ values. A point is named based on the intersection of two projections, one each from the horizontal axis (x-axis) and the other from the vertical axis (y-axis) (Earnest, 2015). This is the conception that the coordinate plane of the energy diagram does not necessarily adhere to, yet this is the concept that undergraduate students are likely used to based on the results obtained from the question in Fig. 4. We believe this gap is where the students generate the alternate conception when reaction rate is just talked about in terms of the y-axis while ignoring the x-axis. Besides the students’ understanding of the x-axis, we explored variations in students’ responses when asked for the “start of the reaction” in Fig. 2 (Phase 2) with the help of the question in Fig. 5 below in Phase 3.

Fig. 5 “Start of the reaction” in an energy diagram.

Students were asked: “Can you pinpoint with a circle as to where you think reaction starts in both A and B energy diagrams?’. The codes for all student responses fell into three categories we developed in Phase 2 as seen in Fig. 2 (A, “at the start of the energy diagram”, 32%), (B, “past the start” or “past the transition state point”, 7%), and (C, “at the transition state”, 61%).

“At the start of the energy diagram” (Group A, 32% (n = 18)): within this group, we found four variations as to how they defined or understood the start of the reaction (Table 2).

We coded for the student rationales for picking the spot for the start of the reaction. Among all 18 responses, students rationalized in one of the three ways for making their decision: (a) that the starting material is beginning to change, (b) the energy of the system is beginning to increase or the substrate beginning to take up energy, or (c) start of the activation energy. All three codes for the rationales align as to when a reaction starts in an energy diagram.

“At the transition state” (Group C, 61% (n = 35)): within this group, we found four variations as to how they defined or understood the start of the reaction (Table 3).

In contrast to the group of students who chose (A), sixty-one percent of students rationalized for picking the spot “at the transition state” in one of three ways: (a) there is enough energy now where the molecules involved in the reaction begin to rearrange, (b) activation energy has been overcome so this must be the beginning of the reaction, or (c) highest point or the transition state forms here.

When we examine Table 3, we see that all the meanings of the “start of the reaction” are in contrast to where the students pinpointed in the energy diagram. For example, students who we coded as “Reactant starting to change and/or bond breaking and forming” for the definition for “where the reaction” start should have responded as Fig. 2A and not Fig. 2C. These results suggest that students focused too heavily on the transition state as being the culmination of the reaction without recognizing that molecules are gaining and losing energy along a continuum. From the student comments, we deduce that many perceive the transition state as the only time when molecules are rearranging, colliding and gaining energy in order to react. This group of students may have learned but likely forgotten or likely never learned this to the level of understanding that all the reactants have some energy associated with the inherent molecules and bond energy perturbations commence as soon as reactants come into contact with each other.

We added a question to assess the undergraduate students’ comfort in defining a chemical reaction along with their understanding of the “start of the reaction” (Fig. 5). Chemical reaction is defined in terms of chemical change which occurs when atoms (or ions) in reactants are rearranged to form new substances (Kind, 2004). When defining “chemical reaction”, all the students responded in terms of “chemical change.” The students’ ideas about what a chemical reaction is aligned with how experts in chemistry define it. Students’ definitions of ‘chemical reaction’ were coded into two themes.

Theme 1: “where two or more substances (compounds, substrates, molecules, etc.) form a new substance”

Theme 2: “a progress involved rearrangement of molecular or ionic structure” or “breaking and making bonds”

Forty-five students (79%) answered along the line of Theme 1 (generally without the mention of structural changes or bonds making and breaking) whereas the rest (21%) defined chemical reaction as in Theme 2. These student responses are in line with Strong's (1970, p. 689) evaluation of defining “chemical change”:

(1) Identity of product determined by identity of initial materials,

(2) Mixing of initial materials is essential when more than one reagent is involved,

(3) Discontinuity between properties of initial materials and final product,

(4) Invariance of product properties when temperature, pressure and initial composition are varied.

In addition to the many alternative conceptions, Phase 3 revealed two overarching findings mentioned in the literature. The first finding is the discomfort that undergraduate students feel when they have to use mathematics in understanding or reasoning about a chemical concept (Potgeiter et al., 2007). The second overarching finding was students demonstrating difficulty interpreting graphical representations in the context of chemical kinetics problem-solving situations (Cakmakci et al., 2006).

Conclusions

This study sheds new light on students’ difficulties with energy coordinate diagrams. The assessment instrument could potentially serve as the basis for a (mis)conception inventory for energy diagrams. We found that some alternative conceptions mirrored those previously seen with students in introductory chemistry, indicating the prevalence of such alternative conceptions. On one hand, the results showed that students have a conceptual understanding of some of the topics related to energy diagrams. For example, students’ use of analogies to express their understanding in a correct way, their labeling of y-axis, the transition states and the activation energy. On the other hand, their inability to use the Arrhenius equation, their tenuous understanding of the “start of the reaction” and the significance of x-axis demonstrates students’ lack of understanding of this tool (energy diagram) and its features after instruction in general chemistry and the first semester organic chemistry. This speaks to the challenges that students have and oversimplifications that educators make when utilizing tools introduced and employed in previous coursework. We present this research with the intent of revealing and understanding misconceptions undergraduate students have about energy diagrams, which is the first step in the three step strategy for bringing about conceptual change according to Nussbaum and Novick (1982). We suggest that the information on students' conceptions about energy diagrams revealed in this paper can also be used to create more plausible distractors for MCQ's that would inform instructors about the prevalence of these conceptions.

Implications for instruction and research

A two-dimensional energy diagram that undergraduate students use is a simplification of the structural coordinates that occur in three-dimensional space. The two-dimensional diagram is the minimum energy pathway from the reactant to the transition state which is the weighted average of all the possible pathways (Anslyn and Dougherty, 2006). Many curricula describe the minimum energy ‘pathway’ as the reaction coordinate which is along the x-axis and that is where they stop. For undergraduates who are used to understanding a coordinate plane as representing two quantitative values, it is likely they interpret the x-axis as conveying a ratio-level quantitative measure. As we mentioned in the “Methods” section, the x-axis can not be labeled using numbers similar to y-axis in energy coordinate diagrams because of its qualitative nature. In our opinion, curriculum should support the conceptualization of x-axis better and teachers should be very explicit about what x-axis means (and does not mean) and how it is different than the traditional x-axis. By being explicit, the teachers are drawing out existing misconceptions and using these as starting points for new learning (Bransford et al., 1999).

Educators can possibly look at these existing misconceptions, and organize and develop effective instruction plans that will help confront various misconceptions associated with this topic. Effective instruction plans would benefit if they followed the last two steps of Nussbaum and Novick (1982) three-step strategy for bringing about conceptual change: (1) revealing and understanding student misconceptions, (2) creating conceptual conflict with those misconceptions, and (3) encouraging the development of revised or new schemata about the topic/phenomena in question. For example, to aid students in bringing about conceptual change regarding the “significance of the x-axis”, a simple pair of SN2 reactions (which look different but are actually the same) shown in an energy diagram can possibly be used (Fig. 6). If students respond with the first diagram when asked about which is the slower reaction in Fig. 6, pointing out that these both diagrams are for the same SN2 reaction under the same conditions could possibly cause conceptual conflict in the students.

Fig. 6 A simple SN2 reaction depicted with an energy diagram.

Additionally, being explicit that the energy diagram is a two dimensional depiction of the energy of the molecules as a function of the structure (Anslyn and Dougherty, 2006) and not time could possibly aid in conceptual conflict and encouragement of new schemata and possibly in conceptual change. To assess if students can transfer this new knowledge to solve similar problems, questions depicted in Fig. 3 can possibly be used. Substantial instructional time must be used to present students with situations such as mentioned above that expose and confront their naïve ideas. One caution when attempting for conceptual change is the need for patience in science educators as conceptual change is an evolutionary process not a revolutionary one (Savion, 2009; Zimrot and Ashkenazi, 2007).

Active learning methods such as cooperative learning and case-based learning have been explored by Taştan-Kırık and Boz (2012), and Yalçınkaya et al. (2012) respectively to bring about conceptual change in students regarding chemical kinetics. These methods could possibly be examined for further research to see if they have any effects in changing students’ alternate conceptions regarding energy diagrams revealed in this paper. Identifying and addressing misconceptions through the conceptual change approach by embedding various active learning methods could potentially help students with their overall foundational chemistry knowledge as they progress through their future coursework.

Limitations of the study

The study was carried out at a large public institution (undergraduate population ca. >35 000) with a unique general chemistry curriculum (1 : 2 : 1) and thus, the research results and conclusions may have limited generalizability to other schools with various sizes and curricula. Nine out of ten students who were interviewed in Phase 2 of the study provided the correct ‘response’ to the MCQ in Fig. 1. We realize that this is one of the limitations of the study where only 1 of the 10 participants who chose the incorrect response was in the interview sample. We realize that having a perspective of other students who chose the incorrect answer is important to chart out the range of possible students’ conceptions about energy diagram. Since the interview study was voluntary, we did not have much say in what participants took part in the interview study. This study used coding the rationale of the students in conjunction with interviews to reduce the limitations that both of the methods inherently have. We might have received different responses if we did the interviews immediately after the students took the pre-quiz. However, even with the time gap, we still revealed, through these interviews and the series of questions in Phase 3, that students hold on to these misconceptions.

Despite these limitations, this study provides insight into the nascent understanding that the undergraduate chemistry students have about the concepts related to energy diagrams, one of the topics needed in understanding and succeeding in general and organic chemistry courses. The research findings open doors for further research on possible intervention and the effectiveness of the process to address misconceptions.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors are thankful for E. Wayne Gross grant received from Indiana University Bloomington, School of Education because of which this research study was made possible.

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