I got annoyed at myself while teaching my General Chemistry classes this past week. I had a meta-moment or an epiphany while I was going through the motions of explaining some observed chemistry-related factoids. I’m good at explaining this stuff because I’ve spent a lot of time thinking about it, not just at the superficial level but a little more deeply. But even as I was talking in class, a part of my mind was questioning why I was doing so. Is this factoid or its explanation even important? At the General Chemistry level? At some point, I transitioned into saying that the rest of the explanation was beyond the purposes of the class, but I would be happy to discuss the subject at length in office hours. I don’t think the students noticed my frustration with myself; but then again no one has come by my office to query me about the finer points yet.
Today’s rant is about exceptions-to-the-rule that showed up this past week in my General Chemistry classes. With some examples, I will briefly state the general rule, why the general rule is important, the exceptions, and then rhetorically pose the question “Who Cares?” Finally, I will muse about some situations where one might care about the answer.
To write the ground state electronic configuration of an atom, one can mechanically use two rules: place electrons in the lowest energy orbitals first, and each orbital can only accommodate two electrons. (They’re called the “aufbau” and “Pauli” principles respectively.) Why is this important? Chemistry is all about what electrons are doing in an atom. Knowing something about their arrangement allows us to describe chemical structure and reactivity. Why the ground state? Under standard conditions, electrons arrange themselves to be in the most stable state which has the lowest energy – what we call the ground state. But there are exceptions. For example, chromium’s valence electron configuration is 4s13d5 in its ground state rather than the expected 4s23d4 if you followed the two rules. There are less-than-satisfactory “explanations” for these provided in the typical G-Chem textbook, but I say: Who Cares?
There’s a third rule mentioned when it comes to writing ground state electron configurations known as Hund’s Rule: When you place more than one electron in orbitals of the same energy, put the electrons in separate orbitals and keep them spin-aligned where possible. Why is this important? Having electrons in separate orbitals is useful when we discuss covalent chemical bonds as the overlap of singly-occupied orbitals from when two atoms approach each other. Thus, knowing this helps us understand chemical structure and reactivity. There’s also an explanation why the electrons should be spin-aligned But: Who cares?
After students learn to write ground state electron configurations of neutral atoms, we move on to ions. Once again, learning this is useful to subsequently describe chemical structure and reactivity of ions. Generally, ions follow the same rules as neutral atoms except when you get to the transition metals. An example exception to the rule: For d-block atoms, when removing electrons, remove the valence s electrons before the seemingly “higher energy” d electrons. Once again, there is an explanation. And once again: Who cares?
Once we can write electron configurations for atoms and ions, we can discuss several useful trends across the periodic table. For example, the first ionization energy of an atom decreases down a column and increases across a row. Why is this useful? Knowing the trends tells you that the bottom left corner of the periodic table (Francium) has the lowest ionization energy, and the top right corner (Helium) has the highest ionization energy. This allows you to classify elements into two broad categories: metals and non-metals. Those two categories can then broadly be used to classify three types of chemical bonds (metallic, ionic, covalent) and relate these to the macroscopic properties of compounds. It’s one of the most useful classifications in chemistry. But there are exceptions to the ionization energy trend. Going across a row, there are two kinks. I wrote a previous post examining this (which I assign as optional reading for the curious student). With regard to this exception: Who Cares?
What made me annoyed about these exceptions is that their inclusion in the textbook and on typical standardized exams results primarily in a mechanism to identify students who know the exceptions and can (somewhat vaguely) articulate them. The explanations in G-Chem textbooks for these cases are incomplete at best and downright misleading at worse. If that’s all we use them for – as a way to separate the A from the B students – then I for one would prefer to jettison them. Who Cares?
Who might actually care? The inorganic chemist might. When you’re delving into the details of transition metals, detailed knowledge of electron configurations and spin states are important. The curious student might. What makes chemistry interesting is that while the general rules are a powerful way of organizing knowledge, there are all sorts of intriguing exceptions that give chemistry its unique unruly flavor. The messy details become very interesting if you’re really into chemistry! In my classes, I regularly include little tidbits outside of the standard syllabus in the hope I will intrigue students into wanting to explore the subject more. I want students to be surprised by chemistry!
The Pauli Exclusion Principle is one such under-utilized concept. It’s not just an esoteric rule about quantum numbers – it gets at the heart of what keeps fundamental particles distinct, and yet indistinguishable when they “switch” places and you can’t tell the difference. It’s why humans can’t walk through brick walls even though atoms are mostly empty space – a demonstration I do every year after which I throw in a tidbit about quantum tunneling. It explains the shape of molecules through VSEPR theory. It’s both strange and surprising. I try to tell students this every year. Not sure if they believe me.
I haven’t decided what to do about the exceptions I’ve mentioned when I teach first-semester G-Chem again (next Fall semester). I’ve made my peace with including orbitals in G-Chem, since they are quite interesting and useful in discussing some of the nuances of electronic structure. But I’m no longer as interested in, for example, students memorizing exactly how to draw the five d-orbitals transformed in Cartesian space. I wonder what else I will get annoyed by as we progress through the semester. Last Fall, I was just trying to not screw up and do the best I can for my students while teaching remotely. But now I have more bandwidth to think a little more carefully about what’s important and why we should care about some particular concept as a foundation for learning chemistry.
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