May 2016

# Equilibrium concept through interactive analogies

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Sharon Geyer, Pomfret School, Pomfret CT

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Equilibrium is a challenging topic for high school chemistry students to understand. This year I decided to tackle the conceptual understanding of equilibrium first with three different analogies and a Process Oriented Guided Inquiry Learning (POGIL) activity before even mentioning the words "equilibrium expression". The outcome was very positive from my perspective. With a firm grasp on the concept of equilibrium, the application of the mathematical description of a system was easier for my students to master.

To kick off the unit I showed the students the "Red Pill or Blue Pill" clip from the Matrix. I likened understanding chemical equilibrium with taking the red pill because you have to open your eyes to the real world of chemistry. We can no longer pretend that every reaction goes all the way to completion! Maybe this scared the students more than amused them, but it set the stage with a little humor and a bit of anticipation of what was to come.

Photo 1: Water transfer equilibrium analogy: notice the transfer beakers are different in size.

Without any introduction, I launched into the first equilibrium analogy: the famous water transfer reaction with two different sized transfer cups. The transfers were made between two large bowls, labeled as "reactants" and "products". The reactant bowl was filled half way with blue water and the product bowl was empty at the beginning of the reaction. One student volunteered to transfer water from reactants to products and another from products to reactants, each scooping water using a different sized beaker — a 50 mL and a 250 mL beaker (Photo 1). Students are not allowed to tip the bowl when they scooped out water with the beakers. This simple demonstration was an excellent way for my students to visualize the changes in a system as it approaches equilibrium. When the reaction began, the product to reactant transfer was very small, but steadily gained in volume with each additional transfer. Meanwhile, the reactant to product transfer started with a large volume and gradually shrank in size.

Photo 2: Two different sizes of straws to transfer water.

Periodically we tested to see if we had reached equilibrium by measuring the volume of water transferred in each direction. When equilibrium is reached in the simulation, the different-sized beakers both scoop up the same volume due to the water level in each bowl. The goal of this demonstration was to help my students understand that equilibrium is reached when the forward and reverse rates are equal, not when the amount of reactant and product are equal.

With this conceptual understanding in their grasp, the students were ready to put some numbers to another water transfer equilibrium analogy. Next they conducted the classic experiment with two same-sized graduated cylinders and two different sized straws. Using their index fingers, students pipetted colored water using drinking straws from one graduated cylinder to the other (Photo 2). After each transfer between reactants and products, the volume of water was measured in each cylinder (Photo 3). (McDonalds has really large straws that are perfect for this activity.) Students were instructed to put the straws to the very bottom of each cylinder to get accurate results. The result was a beautiful graph of the concentration of the "reactants" and "products" as they approach equilibrium (Fig. 1). It took about 12 transfers for the system to reach equilibrium, which was just about all the patience my students had for the water transfer using drinking straws. At equilibrium the volumes are different in each cylinder — one approximately 12.1 mL and the other 12.6 mL — and do not change after each transfer.

Once again, the conceptual understanding of equilibrium was reinforced with this experiment, with the addition of a graphical treatment of the data.

Fig. 1. Equilibrium demonstration: Straw transfer: Reaction simulation reaching equilibrium using different-sized straws transferring volume from one cylinder to another.

At this point, my students were ready to incorporate the concepts of “reaction quotient” (Q) and “equilibrium constant expression” (K) in their description of the system. Using the graph of their data, students calculated the ratio of reactants to products after each transfer. By comparing the value of this ratio, the students begin to see how the ratio changed until equilibrium is established.

The third activity on the opening day of equilibrium involved another transfer reaction but this time with pennies. The students labeled one dish "reactants" and another dish "products". Starting with 42 pennies, they transferred pennies at a fixed rate in both directions. In this activity, the students kept the transfer rates constant (1/3 rate for the forward reaction and 1/4 for the reverse reaction). The critical part of this activity to round down to the nearest whole number. Once again, the reaction started with just reactants — no products — and it gradually reached equilibrium in approximately six transfers. The graph of the data obtained from this activity is shown in Fig. 2. Students repeated the activity several times, experimenting with a variety of the initial conditions.

Photo 3: Checking the volumes after each transfer. Equilibrium has not been reached.

The next table shows the first three rounds in the pennies activity. The forward “reaction rate” was at a constant rate of 1/3 reactants and the reverse “reaction rate” was at a constant rate of 1/4 of the product. The initial conditions of the system are shown in the first entry.

| Reactant Transferred | New reactant amount | Product transferred | New product amount
Start | - | 42 | - | 0
Round 1 | 42/3 = 14 | 42 - 14 + 0 = 28 | 0/4 = 0 | 0 + 14 = 14
Round 2 | 28/3 ≈ 9 | 28 - 9 + 3 = 22 | 14/4 ≈ 3 | 14 + 9 - 3 = 20
Round 3 | 22/3 ≈ 7 | 22 - 7 + 5 = 20 | 20/4 = 5 | 20 + 7 - 5 = 22

They tried using more reactants, all products and no reactants, as well as an even split between products and reactants. They also added reactants to a system at equilibrium to see how that would change the equilibrium "concentrations". Through these variations of the penny transfer analogy, the students could see with their own eyes (and data), how a reversible reaction will reach equilibrium from many different starting conditions.

On Day Two of our equilibrium unit, in groups of three and four, students worked on a POGIL worksheet. The POGIL activity inched them a little closer toward the equilibrium expression because the examples given were based on a chemical reaction (A ⇌ B). This activity was also data driven, similar to the penny and the straw water transfer, but using moles of A and B. Each student was given a different set of starting conditions for one of two equilibrium systems. By sharing their results, the class derived the results necessary to calculate the ratio of products to reactants. The POGIL worksheet was the perfect transition from the reversible reaction concept to an equilibrium expression calculation using molarity and determining the increase and decrease of the species in the system.

Fig. 2. Pennies in reaction: Initially only reactant no product. Graph shows that the amount of reactants and the products (pennies) are not equal at equilibrium — it is the rate of pennies going back and forth that is equal.

On Day Three students learned how to write an equilibrium expression and use it for calculations. I was pleased at how quickly this new concept was mastered. I believe that the previous hands-on activities and equilibrium analogies gave them the perfect conceptual groundwork for understanding the equilibrium expression.

The fourth and final equilibrium analogy was the "tank equilibrium". I used a large fish tank as the “reaction vessel”. The chemical reaction was the assembly of a film canister and top into a complete unit. The forward reaction volunteer assembled a film canister from a canister and a lid (synthesis), while the reverse reaction volunteer took the completed canister apart (decomposition). All of this was happening in the fish tank (Photo 4). This fun game was the perfect introduction to Le Châtelier's Principle. The reaction started with only reactants and no products. The forward reaction was much slower than the reverse reaction. Eventually, the rates evened out ― we did not actually wait to establish equilibrium in the system. At some point in the "reaction", I dumped a bag full of product into the mixture. The reverse reaction picked up steam and generated reactants more quickly. Later, I put a blindfold on the reverse reaction volunteer to see how this would change the equilibrium conditions. Now the forward reaction was faster.

Photo 4: The synthesis reaction (putting film canisters together) is the forward reaction. The decomposition reaction (taking canisters apart) is the reverse. In this case, a blindfold reduces the reverse rate.

With each change in the system, I prompted the students to consider how the rates of the forward or reverse reaction were affected. This demo was a lot of fun and sparked a productive conversation about stress on a system.

Even with all of these fun activities the equilibrium unit was still one of the most challenging topics in my AP Chemistry class this year. However, with the conceptual understanding that they gained from doing these fun activities, I feel my students had more confidence working through the mathematical treatment of an equilibrium system. In addition, I used these analogies to put a reaction scenario into a familiar context for my students when they got stuck on a problem. With a common language and concrete examples to refer back to throughout the unit, equilibrium was not as daunting as Neo choosing the Red Pill and opening his eyes to the “real world”.

## References

1. Equilibrium Demonstrations — The Good, the Bad, and the Ugly, Models and Simulations, Flinn Scientific, Inc. Publication No. 91735 (from the eLearning series)
2. Equilibrium POGIL Activities for High School Chemistry, Copyright © 2012 Flinn Scientific, Inc., page 235
3. Penny Equilibrium “Penny-Ante Equilibrium” ChemTopics Labs: Equilibrium, Volume 15, Copyright 2003, page 57

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