Making Visible the Invisible

[Disclaimer: All images were grabbed by doing an image search on Google.]

As I’ve been teaching introductory chemistry to two different groups of students (science majors and non-science majors), I’ve been pondering how chemists use different representations to explain tiny things that we cannot see. A chemistry demo in class gives the viewer a macroscopic observation of a chemical reaction – the louder and brighter, the better! But the whizz-bang of the demo is merely a prelude, at least in the mind of a chemistry teacher, to the microscopic (or perhaps more accurately nanoscopic) description that “explains” the observation.

The modern expensive chemistry textbook is fully illustrated with colored balls and sticks connected to each other in a sometimes intricate arrangement. “Atoms First” is the current fad in chemistry textbooks. What this means is that the atomistic or molecular view takes center stage in the early chapters. Older textbooks had fewer pictures and started with macroscopic observations of chemical reactions but then used strange symbols and equations to represent them.

As a quantum mechanic who spends time thinking about the nature of the chemical bond, I personally like having atoms and molecules be front and center. However, picking a suitable model of the atom to describe the invisible (to us) particles can be challenging. It is clear that the heavily mathematical quantum model that I teach in an upper division physical chemistry course is unsuitable at the introductory level. In the non-majors class, we use the Bohr/shell model, not just for the hydrogen atom (where it works marvelously) but for every other atom in the periodic table where the simplistic model is actually wrong. It is however very, very useful. Students can get a feel for general trends in the periodic table and an atomistic level description of chemistry just using the shell model.

In science majors chemistry, we wade into atomic orbitals. This allows a finer grain description of atomic properties across the periodic table and a more detailed description of chemical bonds. The students are introduced to the “four quantum numbers” without much idea where they come from or why they are used. (An alternative approach that I have used ignores the numbers and makes use of photoelectron spectroscopy data.) We draw pictures of circles, dumbbells and cloverleafs alongside energy diagrams – and it’s a wonder that the students aren’t more confused as we throw a dizzying area of symbols and representations at them – all in an attempt to make visible the invisible.

Here’s an example. All my students recognize the symbolic formula for the water molecule, H₂O. (This is thanks to commercial product advertising, much more than chemistry classes!) Even without my telling them, I can project the following “space-filling” picture and they can all automatically tell me that it is a molecule of H₂O.

They have no problem recognizing the ball-and-stick model either. Do either of these pictures represent what a water molecule “truly” looks like? Why do we choose one representation over the other? (These are good questions to toss at students who often haven’t stopped to think about it.)

Here’s a shell model showing just the valence electrons.

Which can be “reduced” to the Lewis structure of the water molecule.

And after talking about Valence Shell Electron Pair Repulsion (VSEPR) Theory to predict molecular shape, we talk about “hybridization”. I’m pretty sure the students are rather clueless as to why we teach them this. (Some instructors may be clueless too.)

And if you were a Molecular Orbital aficionado you might show the students the following diagram from an Inorganic Chemistry textbook.

My students in both classes learn how to draw Lewis structures. In the non-majors class we talk about the principle of keeping electron clouds away from each other (explaining the difference between Pauli repulsion and electrostatic repulsion is not helpful to them so we don’t delve into it). I don’t use the term VSEPR theory since I want students to understand the concept and not try to memorize a fancy term.

In the majors introductory class, they do need to know the fancy term and we do discuss the qualitative difference between the aforementioned types of repulsion (although it’s unclear to me that all but the strongest students actually get the idea). Then I dutifully cover hybridization because we have many General Chemistry sections, and students are expected to have seen this before they get to Organic Chemistry. While I think I’ve managed to persuade most of my colleagues that d-orbitals hardly contribute to “hypervalent” molecules, it wasn’t until the textbooks (30 years late) started mentioning this in passing that I’ve seen instructors move away from using it. I do very little molecular orbital theory in my General Chemistry class even though it is “covered” in the textbook, although I do cover it in great detail when I teach upper division physical chemistry and/or inorganic chemistry.

We’ve got all these different representations to discuss the different properties of a single water molecule. But that’s not how any of us experiences water. We experience it in dollops of gazillions of molecules. Now clearly no one is going to draw a mole (6.022 x 10²³) of water molecules, the amount of water you might experience cupped in your hands.

Instead, we have pictures like the one below to tell us about the wonders of intermolecular forces! All represented by just five molecules.

Where am I going with all this? I don’t really know. But writing about it has made me more acute to the myriad ways that chemistry is represented. As an experienced practitioner, I see different symbols and my trained brain knows what information to extract from them and to cut straight to the salient points being illustrated. Students newly exposed to chemistry, on the other hand, do not have that advantage. I guess I’m trying to remind myself to be more judicious about the models that I use, to take wise advantage of the power of illustration, but to point out to my students why certain representations are being used and not to assume that the “picture tells a thousand words”.

Finally, I’m amazed by the ability of the human brain that conceptualizes all this abstract model with the aid of such pictures and illustrations. This is how we see that which is unseen. Through Art!