November 2017 | Resource Feature
A Particulate Representation of Molarity
By Mary E. Sande
In many chemistry classrooms, it is typical for students to conduct experiments or observe demonstrations about a certain concept. Students are asked to describe what they see and what happened to the reactants during the experiment or demonstration, and we often expect them to write chemical equations based on what they observed.
For example, students may observe placing a piece of magnesium ribbon in the flame of a Bunsen burner. Students observe that a bright white light is produced during the burning process and a white ashy substance is left after the burning has concluded. We then ask students to write the chemical equation 2Mg + O2 → 2MgO to describe what was observed — expecting students to completely understand that what they observed is the same as the chemical equation.
I believe, however, that this is a more advanced skill, and most students struggle with using symbols to describe an event observed with the naked eye. In addition, I posit that we are leaving out a crucial step for student understanding: the particulate representation that connects the observable macroscopic world with that of the symbolic. In order to properly prepare students for a complete understanding of chemistry, we need to spend time in the chemistry classroom explicitly teaching students about the particulate representation.
There are multiple representations with which students can understand what is happening in a chemistry class. These representations stem from Johnstone’s triangle1. When he originally published his article on this topic in 1991, Johnstone suggested three representations for understanding chemistry: Macro, Symbolics, and Sub-micro (see Figure 1). An updated version of Johnstone’s concept applies more directly to my approach in the chemistry classroom (Figure 2).
In Figure 2 above, the first representation remains the “Macroscopic” representation, i.e., what is seen with the naked eye. Examples could include two colorless liquids turning yellow when mixed, a piece of metal bursting into flame, or water boiling in a vacuum pump. Students can make direct observations of such phenomena and tell you what occurred.
The second representation is the “Particulate” representation (a re-naming of what was labeled “Sub-micro” in Johnstone’s original work). This representation focuses on the particles or molecules of the chemicals, atoms and ions, and their behavior. For example, one type of this representation could be a computer animation that shows solid spheres moving and colliding in a closed container at a specific temperature and pressure.
The third representation is the “Symbolic,” where chemical symbols, graphs, and equations are developed to describe a phenomenon. An example of this representation is the molarity equation:
Molarity = moles of solute/liters of solvent
It is essential that students become facile in switching between the three representations in order to have a complete understanding of chemical processes. It is incumbent upon chemistry teachers to teach students the three different representations and how to use them to understand chemistry.
The Next Generation Science Standards (NGSS) ask us to utilize the particulate representation through Science and Engineering Practices (SEP) and Crosscutting Concepts. In the SEP section of the High School Physical Science Standards, “Developing and Using Models” is the first standard. As NGSS explains, “Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed world(s). Use a model to predict the relationships between systems or between components of a system.”2 In the Crosscutting Concepts section, “Patterns” is the first standard, about which NGSS elaborates in this way: “Different patterns may be observed at each of the scales at which a system is studied and can provide evidence for causality in explanations of phenomena.”3
Case in point: Teaching molarity
To understand how these teaching strategies can be implemented in the classroom, consider the topic of molarity. As the opening activity for my solutions unit, I have my students make concentrated and dilute Kool-Aid solutions. I give them a packet of Kool-Aid powder, water, and two cups. Without any additional instruction, I tell my students to make a cup of highly concentrated Kool-Aid and a cup of Kool-Aid that is weak in concentration. They easily do so. Students can tell me that the dark-colored Kool-Aid is strong and the light-colored Kool-Aid is weak. This is the macroscopic representation. I then ask the students to draw the particles of Kool-Aid and water in the two cups. Figure 3 is a typical student response.
Figure 3: Student drawings of strong and weak Kool-Aid solutions.
Then I prompt students to imagine Kool-Aid particles as circles. Students then typically add to their original drawing and produce one like that shown in Figure 4.
Figure 4: Student drawings of strong and weak Kool-Aid solutions, including particles.
Students intuitively know that more Kool-Aid particles make a strong solution, and less particles make a weak solution. What students are drawing in Figure 4 is essentially a particulate representation of molarity — they just do not know it yet. At the same time, students are developing models to predict and show relationships between variables in accordance with SEP of the NGSS. At this point, I can capitalize on my students’ prior knowledge and begin teaching the chemistry concept of molarity.
Instead of giving the equation for molarity and having students calculate concentrations, I have students work with their particulate representations of molarity. I encourage them to look for patterns on their own, so that they can construct their own knowledge about determining concentrations of solutions. I create sets of cards with 18 pictures of various concentrations of solutions, and also cards that indicate values for moles of solute, liters of solution, and molarity (Figure 5).
Figure 5: Molarity cards.
Each dot in the picture of the solution (the orange card shown in Figure 5) represents one mole of solute. Students are given a specific concentration value for a solution, and then they find the matching picture card, the correct mole value card, and associated liters of solvent card that collectively define the given concentration. (Refer to the classroom resource for these handouts and more specific information about this activity.)
By finding the moles and liters cards that correspond to the picture cards, students are working with the symbolic representation too. Students are engaging in using models they created and the activity cards, and also analyzing data looking for patterns, all emphasized in the NGSS SEP and Crosscutting Concepts – Patterns. Once students are proficient at identifying concentrations with the picture, moles, and liters cards, I ask them to divide the fraction of moles/liters. This is represented on the yellow card indicating molarity.
Many students already make the connection of the fraction of moles/liters and begin to use the molarity cards—without even knowing what the “M” stands for on the molarity card. There are a variety of combinations of cards that could be used to describe most concentrations. (Please check out the free download of the Molarity card set.) After this activity, students are then asked to calculate concentrations via a traditional worksheet.
Throughout the unit on solutions, the Kool-Aid drawings and cards serve as anchor (or reference) charts for my students. Anchor charts contain important information and critical notes, written on large chart paper or a whiteboard, and are displayed in the classroom for students to refer to during a unit of study. For example, the anchor chart for molarity that I display in my classroom while students study solutions is included as Figure 6. In this chart, you will see the Kool-Aid example found in Figure 3, the definitions of concentrated and dilute solutions, and the equation for calculating molarity. This is the important information that my students will constantly refer to as we progress through the unit on solutions.
Figure 6: Molarity anchor chart.
I constantly refer to the Kool-Aid activity when discussing concentrated and dilute solutions, as well as calculating molarity using the anchor chart. For example, when students are trying to determine if a solution is concentrated or dilute, I point to the anchor chart and ask them if the solution has a dark or light color. I might also ask students if there are more or less particles, or moles, in the solution in question, and how they would calculate the molarity of the solution (while pointing to the anchor chart with the equation for molarity).
By focusing on the particulate representation using
diagrams, students are able to connect the macroscopic representation of making
Kool-Aid to the symbolic representation of calculating molarity. Using all
three representations provides a more complete understanding of the nature of
chemistry and what is happening with the particles of solute.
My chemistry colleagues and I collected data to determine if the particulate representation and this activity had an effect on students’ understanding of molarity. Based on our quiz and test scores, we saw a 21% increase in students who were proficient on concentration questions on our weekly quizzes and unit test as compared to the same data from the year before. Since we had such an increase in student proficiency, we also used the same activity except when calculating molality. (Molality cards are included in the available classroom resource). You could also create cards for other concentration calculations for solutions, such as part per million and part per billion. Let us know how you have used the cards and your experiences on the AACT discussion board. My chemistry colleagues and I would be very interested in hearing your stories.