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#### Inspiration

In the early spring of 2019, I was listening to an AACT webinar by Paul Price entitled, “The Mole of Reaction. Why It Is Important and Useful.” Price defined a mole of reaction as, “how many times a given reaction event has occurred as described by the balanced chemical equation.” Although his talk focused on the importance of this thermodynamics concept for AP students, he mentioned an additional use as well: limiting reactant problems.

I was intrigued by this comment for two reasons. First, I was not completely satisfied with my approach to teaching limiting reactants in my first-year advanced chemistry course, and second, I was interested in how introducing the mole of reaction concept in my first-year course could aid learning, since those students would have a familiarity with it when they saw it again in AP Chemistry.

#### Introduction in first-year advanced chemistry

I teach limiting reactants at the end of my stoichiometry unit. After my students have developed an understanding of balanced equations and the basics of stoichiometry, we delve into limiting reactants. First, students are exposed to this concept conceptually at the particle level, with a series of activities using the PhET “Reactants, Products & Leftovers” simulation as well as a variant of the classic “s’mores” activity. Through these activities, students develop an understanding of what a limiting reactant is, and then we move on to applying it to moles (including calculations).

There are many ways to teach students how to identify limiting reactants via calculations. One popular method is the “Before, Change and After” (BCA) chart. In a BCA, the starting moles, change in moles (determined using the proportions indicated by the balanced equation coefficients), and final moles are recorded in a table. This approach is embraced by both the American Modeling Teachers Association (AMTA) and Process Guided Inquiry Approach (POGIL).

A second method involves calculating the moles of each reactant, then dividing each by the balanced equation coefficient. The one that generates a smaller value is the limiting reactant (for more about this method, see this lesson produced by the CK-12 Foundation). A third method identifies the limiting reactant by calculating the moles of each reactant present, then comparing those values to the required ratio of reactants as indicated by the balanced equation coefficients (for an example, see Zumdahl and Zumdahl, 2014, pp. 117-191).

Previously, I had used an approach where students used factor labelling to determine the moles of product generated from each reactant. The one producing the smaller moles of product was the limiting reactant. An example of such a calculation is shown in Figure 1. I preferred this method to the others described above, since I felt it reinforced the concept of what a limiting reactant does (limit the amount of product generated), as students used the smaller amount of product produced as a means to identify the limiting reactant (see Zumdahl and Zumdahl, pp. 119-211). More recently, before going into the calculations, I’ve introduced the mole of reaction as a unit, using the definition provided by Price. Once students had grasped the basics of what this unit represented, I showed them how to use the concept to determine which reactant “limited” the amount of product generated by reacting all of it; doing so resulted in a smaller number of moles of reaction, or causing the reaction to occur to a lesser extent. An example of such a calculation is shown in Figure 2.

 Figure 1. An example of the factor-labelling method used to determine the limiting reactant. Figure 2. An example using the mole of reaction as a unit to determine the limiting reactant.

After students demonstrated a basic understanding of the approach, I showed them that the moles of reaction (as determined by the limiting reactant) could then be used to both predict the moles of product generated as well as the moles of leftover reagent. An example of each type of calculation is shown in Figures 3a and 3b.

 Figure 3a. An example using the mole of reaction to determine the moles of product. Figure 3b. An example using the mole of reaction to determine the moles of excess reactant required.

After allowing students to grapple with this approach through some practice activities (see examples in the associated classroom resource), I then extended the concept to include grams. I chose to demonstrate this in two steps (finding limiting reactant-predicted moles of reaction, and then using that value to calculate grams of product) so as to emphasize moles of reaction. An example of this is shown in Figures 4a and 4b. Students were then given the opportunity to practice with this type of calculation.

 Figure 4a. An example using the mole of reaction to determine the limiting reactant from grams of reactant. Figure 4b. An example using the mole of reaction to determine the mass of product generated.

#### Impact on student learning in advanced chemistry

Although the sample size is limited, using a mole of reaction approach has had a positive impact on my students’ ability to master both the concept of limiting reagents and how to conduct these types of calculations. As a group, their level of mastery on formal assessments (quizzes, tests, etc.) as well as informal assessments (formative activities, discussions in class, and one-on-one help sessions) was as good or better than I had experienced in years past. I had less examples of students doing seemingly “random” factor label calculations.

Furthermore, the students seemed to better be able to articulate what they were calculating when doing limiting reactant calculations, as well as describe the “why” behind those calculations. In addition, the students themselves had a positive response to this approach. In a survey reflecting on their level of mastery in different topics we grappled with during the year, more students self-identified limiting reactants as an area of strength than in previous years.

While my overall impression of the approach is positive, it was not without some drawbacks. First of all, this approach is not as efficient as others (such as calculating the grams of product via one-step factor label setups). Some of the stronger students were resistant to the approach, as they could intuit other, quicker ways to get to the answer. While I encouraged them to use the mole of reaction approach I had outlined, I did not require them to do so, as long as they could show work to support their process. In addition, some weaker students struggled with the mole of reaction as a unit. They had difficulty grasping what it meant and this hampered their ability to use it effectively in their calculations. For some in this category, additional meetings with me to clarify their understanding and additional practice led to proficiency, but others continued to struggle despite these efforts.

#### Impact on AP chemistry

This past year was the first time I’ve taught AP chemistry students who had already been exposed to mole of reaction as a concept. I was interested to see the impact this would have, if any, on their ability to use mole of reaction concepts during our thermodynamics unit. My hope was that having a background familiarity with the idea of mole of reaction would enable them to better utilize this idea in AP chemistry. This seemed especially important, since the mole of reaction has become a recent point of emphasis.

Overall, I did find that students more quickly adapted to the use of mole of reaction as a unit component when calculating changes in enthalpy, entropy, and Gibbs free energy. In years past, I needed to spend a lot more time getting students to feel comfortable with using a J or kJ/mole reaction as a unit when calculating these quantities. This year, after a quick reminder as to what mole of reaction represents, they readily adopted it. While my AP students generally are those who were stronger first-year chemistry students, there was a noticeable increase in the inclusion of mole of reaction in their unit for these types of calculations. In addition, they were also more successful in executing the thermodynamic calculations correctly when explicitly including moles of reaction.

#### Final thoughts

Overall, I am pleased with the early results of introducing mole of reaction in limiting reagent calculations during first-year advanced chemistry. First-year students seem to better understand what they are calculating in these types of problems, and can also execute them more successfully. In addition, those AP students who were originally introduced to moles of reaction in first-year chemistry have seemed more comfortable using this unit in thermodynamic calculations. While the approach still needs some tweaks, I am definitely going to continue to include mole of reaction as a means to teach limiting reagents to my first-year chemistry students.

#### References

1. Zumdahl, Steven S., and Zumdahl, Susan A. Chemistry, 9th Ed. Cengage Learning, 2014.

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