Energy Map Exercise

My second semester G-Chem class largely deals with energy; we discuss this topic broadly on the first day of class. Students write a definition on an index card before we begin. The most common answers refer to the “ability or capacity to do work”. A few folks will quote the energy conservation principle. This year one student wrote E=mc². Another cleverly said that energy is “what makes things work”. Three years ago, I had a perceptive student who said that no one really knows what energy is! I agree with her. It’s a shapeshifter that takes different forms, but one thing scientists and engineers know how to do is quantify energy.

There are so many kinds of energies encountered in first-year general chemistry that it’s hard to keep track of them all. To help my students do this, we try to sketch an energy map. On the first day of class, students work in groups to sketch an initial map and present it to their peers. Five weeks into the semester, after covering a large chunk of thermodynamics, I gave a written assignment: Submit an updated energy map with some accompanying text explaining choices made and difficulties encountered in generating the map.

The typical student map I was expecting looks something like what I’ve generated above, a composite of what students turned in. Most of them chose to work in groups but some submitted their assignments individually. The more extensive maps had some sort of color-coding and different types of lines/arrows connecting the categories. Almost all groups chose Kinetic and Potential energies as the two first branching points, although they realized that some things defy easy classification into one of the two. If asked to do this exercise, I would likely have produced something similar.

But sometimes I get a pleasant surprise! Below is a creative and clever map generated by one of the students or student groups (hereafter referred to as “the student”).

The main organization follows the First Law of Thermodynamics, exemplified by DeltaE = q + w. The student took seriously the two models used to measure heat and work, the insulated water bath and the piston-and-shaft respectively. I was very pleased to see this since most students don’t recognize the importance (and limitations) of models. The most important equations we have covered in class the first five weeks all appear in the picture. The categories Potential and Kinetic energy appear outside and make connections to both sides. Chemical energy is placed in the center with a connection to both Potential and Kinetic. As a chemist I’m pleased to see this!

The other exemplary thing in this picture was the emphasis on chemical Bonds in the Enthalpy half since they are by far the largest contributor to enthalpy change. The student also subdivided these into intra versus intermolecular bonds, and further subdivided these categories in a way that overall makes good sense. This is the heart of chemistry: making and breaking chemical bonds. Thus, I was very pleased to see these details emphasized. On the piston side, the main subdivision was molecular motion and thus its connection to the entropy of the system. Again the molecular emphasis!

I have some minor quibbles with the diagram. Some things I would change: I would have clearly designated where the “chemical system” resides on both sides. Thus the entropy equation would reside in the system while the PV work equation refers to the piston movement. I’d have moved Gravitational outside the piston-and-shaft. In the middle top I would have put the two First Law statements together and moved the Free Energy equation to the bottom of the diagram where I would have connected heat flow with changing the entropy of the thermal surroundings and then connecting the two pieces to illustrate the Second Law of thermodynamics. But these are very minor quibbles. After all, I’ve spent years thinking about energy and thermodynamics and the student has barely had a five-week introduction.

That being said, I was blown away by the student’s overall vision. By choosing a different starting point, energy relationships were illuminated in different and important ways. The student also had a good eye for layout and balance – and I was tickled by the simple yet effective illustration of the two halves. I was reminded why it can be a good thing to have the occasional open-ended assignment. Most of my homework assignments are more tightly prescribed, having only a little open-endedness in speculative application questions. So I’m glad I kept this assignment open-ended. While I mostly got convention, I also received this gem! Students can bring refreshment and creativity to my sometimes stale approach, and I should welcome those opportunities more often.