Do dementors get cold feet?

Question: Do dementors get cold feet? Quick answer: Sure! Cast a patronus charm at them and away they scurry!

 

Follow-up question: Do dementors even have feet? Good question. I don’t know. When first introduced in Harry Potter and the Prisoner of Azkaban, the dementor is described as “a cloaked figure that towered to the ceiling… face completely hidden beneath its hood… a hand protruding… [was] glistening, grayish, slimy-looking, and scabbed, like something dead that decayed in water.” So we know dementors are tall and have hands. Dementors are never mentioned as walking, though. They glide. But do they have feet?

 

In Harry Potter’s first encounter with a dementor, it draws a “long, slow, rattling breath, as though it were trying to suck something more than air from its surroundings. An intense cold swept over… Harry felt his own breath catch in his chest. The cold went deeper than his skin… He was drowning in cold…” That’s the book’s description. There’s also a darkness about them and they can create a chill mist. Dark and cold. In the movie, dementors seem to be patterned after the Black Riders in Peter Jackson’s Lord of the Rings rendition. They are more skeletal than decaying. And the Harry Potter movies significantly accentuate the cold. Window panes frost up. Water freezes. The thermal energy of the surroundings goes down significantly when a dementor is present. That’s interesting, thermodynamically speaking.

 

Thermodynamic Analysis: If the environment is getting much colder, then thermal energy is being transferred (“heat”) from the environment to the dementor. Is it because the dementor is colder to begin with? If so, you’d expect spontaneous transfer (Zeroth Law of Thermodynamics) until thermal equilibrium is reached. But perhaps the coldness isn’t felt unless the dementor is actively trying to absorb energy (corresponding to human “life-force” in the books), i.e., when it draws its long breath which somehow doubles as a sensor. The dementors were supposed to be searching the Hogwarts Express for Sirius Black. So maybe it’s an active absorption of thermal energy, like when a vacuum cleaner is turned on and sucks in anything in its immediate environment.

 

Does the internal energy of a dementor increase when it takes in thermal energy from the environment? Thermodynamically the answer should be yes. Will its temperature increase? Will the dementor get hotter? Not necessarily. When ice absorbs energy at its melting point, there is no change in temperature. The absorbed energy goes to breaking some of the hydrogen bonds in water. There is no mention of anyone touching a dementor to see if it feels warmer. One might wonder whether it would feel colder to the touch, but it’s unclear why that should be. If a dementor was constantly keeping itself at a temperature much lower than the environment, it would have to actively pump out energy that would otherwise flow in because of the temperature gradient. Humph, this is all sounding contradictory!

 

What if a dementor had feet? And these feet touch the ground. If the ground gets cold in the presence of a dementor, would the dementor then get cold feet? Or are its feet well-insulated from the ground to reduce any transfer of thermal energy? If dementors glide above the ground, then a cushion of air could insulate it to some extent, but it might still get cold feet because thermodynamics doesn’t care who you are, magical or not. Could the energy that the dementor sucks in travel to its feet to keep them warm? Possibly. Dementors might be thermodynamic-heat-engines of a different sort.

 

Final answer: I don’t know, but I would guess, partly yes. And I wouldn’t have thought about this if not for the movies accentuating the coldness of the environment in the presence of a dementor. Who would’ve thought that dementors could be interesting thermodynamically?

Test Anxiety

What is the most frequently reported student emotion in the college classroom? You might have guessed it: Anxiety.

 

Why is anxiety so pervasive? Here’s what Sarah Rose Cavanagh has to say in Chapter 6 of The Spark of Learning: “…there are just so many things to be anxious about: performance anxiety when giving group presentations, anxiety about speaking in class, anxiety about not being smart enough to master the material and, of course, anxiety about tests, quizzes, and grades.” I try to allay student anxieties about speaking by giving them time to think after a question is posed, the opportunity to discuss with their classmates, and I encourage them to write something down so they don’t have to speak extemporaneously. I give plenty of low-stakes five-minute quizzes (typically dropping a third of the lowest scores).

 

But the big one is test or exam anxiety. I’ve given practice self-tests and provided past-year exams, and I’m presently experimenting with providing more practice through study guides. Still, the students are anxious and this is no surprise. In reviewing the literature, Cavanagh identifies two general causes: “cognition-based worry about assessment, and physiologically based emotional arousal”. Turns out most of the research on test anxiety is on math anxiety. It’s quite common, and I certainly see it in my chemistry courses. Essentially, “students high in math anxiety take longer to solve problems and perform less well than students low in math anxiety… [and] avoid mathematics courses and careers there math is involved”. I attribute this mostly to confidence or lack thereof. But the effects are observable: the worrying steals away cognitive resources that should otherwise have gone to problem-solving.

 

Cavanagh cites a number of studies (see her book for details and references). The one that jumped out of me looked at the correlation between cortisol levels and performance in solving “large math problems”. Interestingly, high-anxiety students with higher cortisol levels did worse, while low-anxiety students with higher cortisol did better. Apparently you have to be somewhat aroused/engaged (higher cortisol) and also have sufficient working memory cognitive resources (i.e., not stolen away by anxiety) to perform well. Lower cortisol was associated with being bored and unmotivated.

 

What to do about this? Cavanagh has four suggestions: (1) Give students more time so they don’t feel rushed especially if they are slower math-problem solvers. I’m reminded that I need to take another close look at my P-Chem exams. I sometimes forget that even though the students have supposedly had math practice from the prerequisite calculus and physics courses, that this math-anxiety can actually be even more pronounced. (2) Encourage mindfulness in students. Hmm… I haven’t done anything here. (3) Be transparent and clear both in the syllabi and in teaching. I’d like to think I do a good job here. The vast majority of my students rate highly my level of organization and clarity. (4) Expose students to your testing style. I’d like to think I do a good job here, certainly in providing both examples and opportunities in multiple contexts. But students don’t always take advantage of these or they don’t take seriously the self-annotation assignments.

 

Chapter 6 in Cavanagh’s book also brought up a term I was unfamiliar with: “psychological reactance”. This has to do with negative emotions when students “perceive an unjust infraction… [and] report feeling angry, pained, frustrated, stressed, violated, cheated, disgusted and embarrassed.” This can lead to things in the classroom going downhill very quickly. It is exacerbated when students know each other outside of class (“hyperbonding” – another new term for me) and this can lead them to “encourage each other to greater heights of rebellion”. I have had the good fortune not to have personally experienced this, but I have heard the stories and I’ve personally known colleagues who found themselves in this situation. It’s a real problem, and while sometimes the instructor carries some of the blame, that’s not always true, and the rebellion is often disproportionate to the perceived injustice. I suspect being male protects me somewhat from this. Students know I have a different national origin but it’s not one they’re familiar with and they likely have not developed stereotypes about it.

 

Cavanagh discusses how to reduce psychological reactance: (1) “…use language that is low in threat or demands, expressing empathy and interpersonal similarity…” I’m not sure what to make of this. I don’t think I make threats or demands. I think I’m clear about what students need to be doing to be successful in my class. (My advice isn’t always followed.) And I don’t sense interpersonal similarity with my students. It’s stark to me that given my different background, I’m very different from them. (2) “… paying attention to the power dynamics of the classroom…” Honestly, I hadn’t thought about that very much. Maybe I need to pay more attention. Cavanagh goes through different types of power, those that are favorably and unfavorably viewed by students. I don’t have much to say about this mostly out of my own ignorance. Cavanagh did give me something to ponder here.

 

The title of Chapter 6 is “Best Laid Plans: When Emotions or Challenge Backfire” and Cavanagh ends her book by reminding us that students have emotional lives that intersect with their learning even when those things seem disconnected to their academics at first glance. It’s a reminder that we deal with human beings, many of whom are adolescents with emotional highs and lows and who deal with varying degrees of uncertainty about their present and future life. As someone who is over-the-hill, and does not experience those huge emotional shifts, I should be cognizant that my students are dealing with so much else. I can do my best as a teacher and learning might still be sub-optimal. But I should keep trying. And so should my students.

Curiosity and Mystery

I’ve been thinking about the effect of affect in learning while reading The Spark of Learning by Sarah Rose Cavanagh. While I’ve read some of the primary literature on how emotions play a role in learning, it was nice to find many of the highlights in one place. Cavanagh does a good job weaving the studies along with anecdotal material in her book to make her point that emotions do play an important role, and we as educators should take it into consideration. She provides many examples. Today’s post is on Chapter 4 (“Burning to Master: Mobilizing Student Efforts”). I’ll highlight my takeaways; but for the specific examples, please read her book!

 

How do you trigger student interest and draw them into a topic? I’ve dealt with the issue of fostering interest because I often teach the early 8am section of general chemistry – the least preferred time for many students. I’ve also had plenty of experience teaching the nonmajors chemistry course, where a number of students wish they weren’t there but need to fulfil a science requirement. Here’s Cavanagh on the topic: “Interest arises when information is new and potentially complicated, but inherently graspable. Novelty and complexity in the absence of comprehensibility only leads to confusion, which is usually not our goal.”

 

But triggering isn’t enough. How do you maintain student interest especially when some of the material is challenging? Chemistry certainly falls into this category. As Cavanagh says, after triggering, we want students “to burn to know what comes next”. That’s when curiosity is piqued! One way to do this is by introducing puzzles. Essentially you “draw people’s attention to the gap between their current state of knowledge and what they perceive as knowable”. That’s the heart of the most engaging novels and TV series. I can imagine using case studies that require applying chemical knowledge to solve a puzzle. Students get an endorphin boost by being successful in resolving the problem. It’s a virtuous cycle, and boosts confidence and motivation to solve other puzzles.

 

Cavanagh doesn’t stop there. She suggests that, in addition to puzzles, we should introduce mysteries. “Mysteries provoke a different type of curiosity than do puzzles… characterized by deep, effortful, and sustained pursuit of understanding. One engages… not just because one wants to solve and set aside a focused question, but because the quest is its own reward, and the knowledge that the quest is ongoing is enticing.” For me, the mystery I work on as a scientist is the chemical origins of life. I chose it because it’s likely to keep me motivated to the end of my career. I introduce bits and pieces of it into my classes when I can make a relevant connection. But I could improve on how I do so.

 

The subject of getting-into-the-zone or a flow state is tackled next. It draws on the pioneering work of Mihaly Czikszentmihalyi who posited that the sweet spot is to “match the challenge level of your activity to the very limit of your skills or abilities”. If things are too easy, boredom results. If too difficult, confusion followed by frustration reigns. What jumped out at me: While the studies show that eliciting the flow state does increase both interest and motivation, it doesn’t necessarily mean you’ve learned more – at least when measured via multiple-choice assessments after the activity. Cavanagh speculates that it could be “that flow increases enjoyment but not greater learning… [yet] this can only have good effects in the long term – even if it doesn’t translate into immediate learning gains.”

 

While I’ve spent time designing how I use my class time around hitting this “zone of proximal development” (from Vygotsky’s work), I haven’t spent much time designing mystery or puzzle activities that span more than one class period. (I did design a week-long Alien Periodic Table exercise that I’m proud of, but it was so time-consuming for me that I’ve never done anything like it again.) Hitting the sweet spot is difficult. What seems like a promising exercise or activity can just as well collapse into confusion.

 

Cavanagh writes: “Curiosity and confusion can be considered dark mirrors of each other, in that both involve uncertainty, and both create an itch to know more.” Curiosity is seen in a positive light, while confusion is often viewed negatively. However both can contribute to learning. Encountering confusion should perhaps be expected since we are trying to get students to cast aside faulty misconceptions they have accumulated over time that take some work to dislodge. Perhaps the students experience, for a time, some sort of cognitive dissonance, as they wrestle with seemingly incompatible ideas before they are able to refine their conceptual knowledge. Sometimes ambiguity or uncertainty helps.

 

While I think the evidence for the general effectiveness of “productive failure” is lacking (although I think it can work well in specific instances), there might be occasions when introducing some confusion may be worthwhile. Cavanagh presents guiding principles from her colleagues when applying this in the classroom: “students should possess the ability to successfully resolve the confusion; and/or when students cannot resolve the confusion on their own, there are appropriate scaffolds or buttresses in place to aid the students in their resolution of the confusion.”

 

One last takeaway from the chapter from Cavanagh: “giving feedback to students about what they’ve done right, particularly if it is a skill that they were previously lacking”. I haven’t done this much, but I should.

Life might be a noun

On the first day of my Metals in Biochemistry class, we discussed two questions: “What is Life?” and “What is Living”? In the first question, Life looks like a noun. In the second question, Living looks like a verb. The students agreed that the second question was easier to tackle than the first, and we proceeded to come up with a range of examples. We also discussed the possible fuzzy boundary between living and non-living – the realm of cyptrobiosis.

 

But maybe, the words life and living should be adjectives. Or maybe it might be instructive to examine the possible interchange of adjectives and nouns. This is what Robert Rosen does in his essay “Genericity as Information”, compiled in his Essays of Life Itself.

 

Rosen is trying to argue that context-independence, a way of slicing up the world into objective chunks, is too impoverished to describe complex systems such as life. By stripping out the subjective, science then “assert that only particular things are real, and that we can learn about them through enumeration of their adjectives.” A corollary to this is that “a set of such particulars is not itself a particular, and accordingly is allowed no such objective reality”. In chemistry, a classification method such as the periodic table is a “subjective intrusion superimposed on the particulars it assorts and classifies”. This is what it means to be a strict empiricist. Rosen is not of this clan.

 

Here’s the example Rosen provides. We can think of particular nouns such as water, oil, and air. The chemist in me is already envisioning particular (pun-intended) pictures of H₂O, hydrocarbon chains, and a box consisting of mainly N₂ and O₂ molecules. Rosen adds that we might classify these three substances as “fluids” for convenience, but the empiricist will emphasize that this is merely for convenience and that “fluid” is not a thing in itself. Rosen then says that the empiricist “has no trouble with phrases such as turbulent water, turbulent oil, and turbulent air. Here, the adjective turbulent correctly modifies a particular noun to which our empiricist will grant an objective status, or reality. But suppose we turn these phrases around, to yield water turbulence, oil turbulence, and air turbulence. We are now treating the turbulence as if it were an objective thing, and the water, oil, and air, as instantiations or adjectives of it.”

 

This interchange of noun and adjective is anathema to the strict empiricist. How can you empirically analyze turbulence in itself? When the famous physicist Erwin Schrodinger asked the question “What is Life?” he implied that it was a particular challenging question that the physics of his era was incapable of answering and that “new” physics was needed. (No, quantum mechanics was not the new physics capable of answering his question.) Perhaps that’s why it’s a little easier to compare a living cat, dead cat, and hibernating cat; and less easy to tackle what it means for a cat to be alive versus a dog to be alive. We sometimes think we can make distinctions: What it means for a bacterium to be alive might be different from what it means for a human to be alive. But it’s hard to grasp what is so distinct about life, not that there aren’t models that have been proposed.

 

The trouble with words is that attaching meaning to them seems inherently subjective. Is there a yawning abyss between syntax and semantics? Is that why describing mechanics in terms of present physics and chemistry doesn’t quite get us to biology? While systems-thinking attempts to bridge some of this gap, is it enough? And if it isn’t enough, then is it true that life cannot truly be simulated in an enclosed system computer or otherwise? Perhaps my efforts as a computational chemist studying the origin of life are doomed from the start.

Heat is not a noun

In thermodynamics, heat is not a noun. It’s a verb. This is confusing. Why? Because colloquially we think thermal energy and heat are the same thing, but in thermodynamics they are not. One is a noun and the other is a verb. Before diving into the weeds, let’s first acknowledge that nouns and verbs are labels. Keeping things simple: a noun labels a ‘thing’; a verb labels an ‘action’. Now we’re ready to define the two.

 

Thermal energy, from the chemical perspective, is the energy of molecular motion. The amount of thermal energy in a chemical system can be quantified by measuring its temperature. Thermal energy is a noun. This is confusing because its definition contains the word ‘motion’ that sounds verb-ish. Considering the two broad categories of kinetic energy and potential energy, thermal energy is more closely associated with kinetic energy, the energy due to motion.

 

Heat is the transfer of thermal energy. Heat is a verb because it involves the ‘action’ of transferring. This transfer of energy takes place spontaneously across a temperature gradient if a suitable pathway for the flow of energy is available. Heat is the flow, not the thing that flows. The thing that flows is thermal energy. The zeroth law of thermodynamics is about this flow: When a hot object is placed next to a cold object, thermal energy is transferred from the hot object to the cold one. The cold object is heated by the hot one. Simultaneously the hot object is cooled by the cold one. Heat is more closely associated with potential energy, as are other gradient-related energies such as gravitational (potential) energy.

 

But it’s hard to exclusively use heat as a verb. We easily slip into saying that ‘heat’ is transferred when something becomes hotter or colder. To repeat, heat is the transfer, not what is being transferred (which is thermal energy). In our minds, because of how we colloquially use the word ‘heat’, we associate it with temperature change – and thus conflate it with thermal energy. I tell my students to link thermal energy with thermometer (its measure). Thus, a change in thermal energy of an object leads to a change in its temperature. Many examples of heat-flow do lead to a change in temperature, but not always. Let’s look at three examples.

 

In the zeroth law example shown above, two objects at different temperatures are brought together. Spontaneously, the direction of heat-flow down the gradient is indicated by the red arrow. Both objects change temperature during the process. Finally, thermal equilibrium is reached. Both objects now measure the same temperature. The temperature gradient has been degraded – it no longer exists. We say that the two-object system has reached thermal equilibrium.

 

Chemists want to know about energy changes in a chemical reaction. In thermodynamics, we define the ‘system’ as the chemical substances. They have some energy content before the reaction, and after a chemical reaction (where chemical bonds have been made and broken) they often have a different energy content. We cannot easily measure the system’s change in energy directly, so we couple the system to what we call ‘thermal surroundings’ – typically modeled as an insulated water bath. If a chemical reaction releases energy (and most favorable reactions do), that energy is transferred to the water and when its temperature rises, we can calculate the rise in thermal energy of the thermal surroundings. A calorimeter is our device to measure this energy change. (An insulated water bath works well as a calorimeter, hence the model used!) This is illustrated below.

 

Students can quantify the heat by the formula q_therm = mCΔT where m is the mass of water, C is the specific heat capacity of water, and ΔT is the change in temperature of the water. All this is for the thermal surroundings. If the temperature goes up, ΔT is positive and therefore q_therm is also positive. But what about the system? Since the thermodynamic universe containing both the system and the surroundings is ‘isolated’, the energy gained by the thermal surroundings must have come solely from the chemical system. Thus, students learn that q_sys = –q_therm and energy is conserved. But heat is a verb. The noun that is used to represent the energy of the system is ‘enthalpy’. Textbooks and chemistry instructors often refer to it as ‘heat energy’ which is historically true (and noun-ish) but semantically confusing. This is why students have trouble with understanding the concept of state functions: enthalpy, the noun, is a state function; heat, the verb, is not.

 

A brief aside: I have skipped using the term ‘internal energy’ for the chemical system and ignored PV-work in the model of the thermodynamic universe, although I did draw the piston and shaft (in black) to represent it. Leaving PV-work out of the discussion, as I argue in a previous blog post, keeps this analysis cleaner and simpler for students.

 

In the model shown above, we only measured temperature changes in the thermal surroundings. The temperature of the system may or may not change. If we consider reactions solely carried out under ‘standard conditions’ so that we can tabulate standard enthalpies of formation, then we consider that the chemical reactants and their subsequent products to be at the same temperature. The system temperature didn’t change! But the temperature of the thermal surroundings might have. Thus heat-flow in this case only involves a temperature change in one milieu, not both. It makes sense to refer to q_therm as ‘heat’ because the thermal surroundings did change temperature, but for historical reasons, we still call q_sys ‘heat’ even though the system many not have changed in temperature. Why is there still an enthalpy change? The chemical bonds made and broken in the reaction have different enthalpies. In a typical ‘exothermic’ reaction, one that ‘releases heat to the surroundings’, weaker bonds are broken and stronger bonds are formed in the chemical system. Thus the system becomes more stable or lower in energy and ΔH, the change in enthalpy of the system, is negative.

 

Second aside: In some physical systems, students may be analyzing the opposite situation where the system is changing temperature, and exchanges energy with a thermal bath (which remains constant in temperature). For example, you could use a water bath to ‘heat’ a system as shown below. For that matter, you can consider a heating element in a reaction to act as such a reservoir of thermal energy.

 

In my final example, energy can change between the system and the surroundings without any change in temperature in either milieu. Consider the picture above where energy is being supplied by the thermal bath/reservoir to melt ice, the system, at zero Celcius. The ice receives energy and turns into liquid water at zero Celcius. Was thermal energy transferred? Hmm… no temperature change was involved. Historically we’ve come to call this ‘latent heat’. We don’t measure any temperature change although the word ‘heat’ is still invoked. In class, I avoid saying latent heat and simply refer to this as “delta-H of fusion” or ΔH_fus.

 

All this seems very clumsy. In class, I try to avoid using the phrase ‘heat of formation’ and use the more cumbersome ‘standard enthalpy of formation’. I get better every year but old habits die hard. I warn the students that they will often hear many of these enthalpies referred to as the “heat of [something]” even if there are no temperature changes. From a chemist’s point of view, I emphasize to students that when they think of ΔH, they should be thinking about changes in the strengths of chemical bonds (or interactions that fall under the rubric of “intermolecular forces”) – the old ones being broken and the new ones being made – in a chemical process. They shouldn’t think about heat per se.

 

This becomes doubly important when students begin learning about entropy. In any chemical reaction, there is an inherent entropy change. Here’s my brief one-paragraph version. If you’re utilizing a chemical reaction to do useful functional work (which may be different from PV-work), you may lose some of that energy as ‘heat’ to the thermal surroundings that isn’t due to inefficiencies in your apparatus (which may also be present). Rather, it is inherent to the chemical reaction. In the picture below, you want to minimize this ‘heat’ loss (the small double-headed arrow) and maximize the energy transfer from the system to functional work. In an equation, I would write this as ΔH = w’ + TΔS. As the enthalpy changes, the entropy changes (ΔS), and w’ (w-prime, to distinguish it from PV work) is the maximum useful work you could get out of the system, under ideal conditions. Students learn w’ as ΔG, the change in free energy of the system. When we talk about heat as the worst form of energy when it comes to utilization, we’re primarily referring to issues of entropy, not enthalpy.

 

I could go on, but this post has likely passed the TL;DR threshold. If you’re a student reading this, I hope this helped you. If you’re an instructor reading this, the take-home message is that when you use the word ‘heat’ in place of enthalpy in the context of thermodynamics, using it as a noun rather than a verb, you’re essentially using it as a label – a name – for a more abstract quantity. Your students hearing the word ‘heat’ might be associating it with temperature changes even if no such changes occur. Yes, I do want my students to use the phrases ‘endothermic’ and ‘exothermic’ correctly based on the sign of ΔH. But I want to drum into them that, conceptually, they should primarily associate ΔH in terms of the relative strengths of chemical bonds and interactions; that’s the system property chemists want to focus on! In thermodynamics, heat (unless being used as a more abstract label) is not a noun.

Context Independence

Two years after my first encounter with Robert Rosen’s work, I’m re-reading Essays on Life Itself. I’d like to think that I’m gaining more insight in my second reading, but have no way to prove it. Perhaps it’s the double-edged sword of gaining expertise. The more you know, the more your eyes are opened to what you don’t know. Questions beget more questions.

 

Today’s post surrounds a phrase Rosen uses: context independence. It shows up in chapter 2 (“Biological Challenges to Contemporary Paradigms”) in a section that questions the reduction of biology into physics. I’ll quote Rosen to set up the issue at stake. Subsequently, I will look at some examples at the introductory chemistry level.

 

Here’s Rosen: “… the complexity of organisms, in the conventional view, is interpreted as a measure of how special they are… Complexity is measured in a system by counting the number of distinguishable ingredients it contains and the interactions that constrain them, by how complicated it looks to us… Moreover, it is conventional to suppose a kind of gradient of complexity in the material world, and to suppose that we move in this gradient from generic simplicity to sparse, non-generic complexity by simple accretion, by a rote addition operation… Conversely, a reduction of one of these rare complex systems is merely an inverse rote operation of subtracting… Also presumably, these rote operations of adding and subtracting do not change the material basis of the systems themselves: simple systems are the same whether they are alone or whether they have been added to a larger one.”

 

Rosen then asserts: “This kind of context independence of simple systems is one central feature of scientific objectivity; its main corollary is that one must never pass to a larger system (i.e., a context) in trying to understand a given one but must only invoke simpler subsystems, specifically those that manifest a complete independence of context in their properties and behaviors.” Rosen thinks this is wrong. Instead, “complex systems are far more generic than simple, context-independent ones… analysis and synthesis are not simple rote operations, nor are they in any sense inverses of one another… context-independence with objectivity is itself far too special and cannot be [foundational].”

 

In my view, chemistry is fundamentally about explaining phenomena at a particular scale: the level of atoms and molecules. And a chemical reaction is about making and breaking chemical bonds between atoms and molecules. That’s a tiny scale, typically at the level of tenths of nanometers (or 10^-9 to 10^-10 meters). Most small molecules, and even medium-sized ones (from a student’s perspective), have sizes in this rage. Larger (macro)molecules and polymers with thousands of subunits might extend into the micron range, just barely visible by a light microscope.

 

Are there seemingly immutable context-independent features of chemistry? Setting aside nuclear reactions for now, my students would (correctly) say that elements do not change identity in a chemical reaction or interaction. Hydrogen remains hydrogen; it doesn’t change into helium. Oxygen remains oxygen; it doesn’t change into nitrogen. Since an element’s identity (a label, a name) is only dependent on the number of protons, and since the number of protons does not change in any chemical reactions (chemistry is about the movement and interaction of electrons!), that the atom identities are in some sense, context independent. The number of protons never changes – so that’s a context independent feature.

 

What else might be context independent? The number of neutrons probably, and anything else that involves the nucleus. So maybe anything involving the nucleus is context independent. What about the electrons? An atom can gain or lose electrons without changing its elemental identity – its name (but what does a name really mean?) – although for practical purposes, these are just the outer electrons or the ones furthest away from the nucleus. The inner electrons are held very strongly by the nucleus, and most chemical reactions (and interactions) that chemists care about under most conditions do not involve energies strong enough to extract these electrons.

 

The rightmost column of the periodic table consists of the noble gases, the only elements that exist as isolated atoms under standard conditions (room temperature and sea-level pressure). Under these conditions, one could surmise that individual atoms can be context independent. Therefore, properties of isolated atoms should also be context independent. Examples might be the ionization energies and electron affinities encountered by students in general chemistry. We can measure these properties for any element, not just for the noble gases, by vaporizing and breaking any chemical bonds between the atoms. Imagining an isolated atom, another property we might be able to measure is polarizability – the ability for the electron cloud to be distorted away from spherical symmetry. But would these properties change in non-isolated atoms? Probably. And that’s why we’re careful to define the ionization energy as referring to the atom, while the analogous work function refers to a bulk metal. The two values are different, but they do correlate. (Students often confuse ionization energy and work function because of their closely similar definitions.)

 

Sticking with pure elements for the moment, properties unique to each element can be found from their phase diagrams. The two properties most familiar to students are the melting point and the boiling point. Let’s be careful in our definition. These should be the normal melting point and the normal boiling point, i.e., at sea-level atmospheric pressure. To be even more specific, these temperatures are when the two phases are at equilibrium. Hence, the point in melting or boiling point. What we’ve done, in fact, is defined the context, and once we’ve done so, we can start to define properties. But now we’re straying into context dependence rather than independence.

 

What about the holy grail of what defines chemistry, the chemical bond? Students learn in general chemistry that there are broadly three kinds of chemical bonds (ionic, covalent, metallic) depending on the elements involved – whether they are metals or non-metals. On top of that there are several types of “intermolecular” forces: dispersion (temporary dipole, related to polarizability), permanent dipole (related to polarity), and hydrogen-bonding (a misnomer that adds to student confusion). It’s why I didn’t list atomic size as a property earlier. The actual measurement of atomic size on the same objective scale for all elements is tricky because of the different bonds and interactions between atoms when they get together. (Good luck trying to measure the size of an isolated atom other than a noble gas!)

 

You might hope that after defining the two elements in a chemical bond, that the bond lengths and bond strengths can be tabulated and used. They are! And they’re useful, which I try to impress upon my students. But I also tell them the caveats – many of these tabulated values are averages. The information on the H–H covalent bond probably does refer to the H₂ molecule but the information on the C–C covalent bond might, or might not, be accurate for the particular molecule you’re considering. The students see this starkly in their textbooks for the C=O bond where both the average value (~730 kJ/mol) and the very different specific value (~800 kJ/mol) in CO₂ are provided. And if you want to go wild thinking about this, how might these change when Ant-Man resizes?

 

The bugbear illustrating the difference between context dependence and context independence in G-Chem is electronegativity. Because the students learn about electronegativity trends across the periodic table, and because they are often exposed to the Pauling values, they think that electronegativity is a context independent property. This leads to them making spurious arguments invoking electronegativity in a variety of contexts. Every time I hear one of these spurious arguments, I ask the students for the definition of electronegativity and try to emphasize its context dependence. Electronegativity is an extremely useful context, and it is invoked throughout the curriculum: organic chemistry, inorganic chemistry, biochemistry, and even physical chemistry (although I hope that here students see the physical basis for context dependence). The attempt to replace Pauling values by the seemingly less context dependent Mulliken values doesn’t work as well. (I think the Allred-Rochow values are an improvement, but they require more work and context.)

 

Ultimately the issue of context independence is about defining two regimes: an inside and an outside separated by a boundary of some sort. In thermodynamic models, we refer to these as the system and the surroundings. But the cutoff has to be made somewhere if you’re trying to establish some independence of the system (inside) from its surroundings (outside). The key word here is ‘some’. The degree of independence will depend on how and where the boundary is placed. In small-molecule chemistry, I’d argue that a practical separation is the nucleus plus core electrons versus the outer electrons. Others might draw the boundaries differently depending on context. To return to Rosen, in a truly complex system, there is no largest model, and therefore any boundary you draw is inadequate and there is no context independence.

Study Guides Revisited

Early in my career as a professor, a student asked for a study guide before the final exam. This was in a chemistry for non-science majors course. I obliged by creating a three-page document with bullet points of what the students should know and be able to do. I used action verbs (e.g. explain, define, solve) to make each point clear and simple; this was before they became the standard practice for “learning outcomes”. As an aside, I think the use of action verbs is useful for small and specific chunks of information, but NOT so useful when it comes to complex concepts. To quote H. L. Mencken: “For every complex problem, there is a clear and simple solution that is wrong.” But that’s another story.

 

I devote the last day of class (before the Final) to answering questions about the final exam and any course content we’ve covered. The students, armed with the study guide, essentially wanted me to go over the guide point-by-point. There’s no way to cram a semester’s worth of material into a single class session. But I tried to oblige by briefly hitting each major point. Within 30 minutes, everyone was exhausted, and it was unclear if I helped the students or just made them more stressed out.

 

The following year (in the same course) I included the study guide at the beginning of the semester, and encouraged student to use it as a guide throughout the semester. The vast majority of them did not. Very close to finals, students finally started looking at the guide, and got stressed out at what they perceived as a mountain of material. My perspective had been “look at how much you’ve learned!” but theirs was “look at how much I don’t know, I’m going to fail.” Waiting until the last minute and attempting to cram does NOT work well in chemistry. Despite my exhortations, my study guide was a bust, at least for many of the students. (There are always a number of students who ace the class but they might have still done so without my provided study guide. Maybe they have good study practices?)

 

I scrapped having these “final exam study guides” and pivoted to a different approach that I’ve used for many years. For each class, I tell them what to read, what to pay attention to, the main points we’ll cover in class. There’s often a statement akin to “you should be able to…” followed by some action verbs relating to course material. (I also did this for my general chemistry for science majors course.) Occasionally, close to finals, a student would ask if there was a study guide for the final exam. I would respond by pointing back to the information I gave for each class session, and that it essentially functions as a study guide. The student was usually disappointed by this, clearly it was not the answer they were looking for. I should also say that since I started teaching, I always spend the first few minutes of every class highlighting “here’s what was important from last time” and write keywords on the board.

 

This semester I’m piloting something new in my G-Chem class. I’m retaining the same setup of telling students how to prepare for each class meeting and what the key points will be. In class, I still have my regular low-stakes short quizzes, and highlight what was important from last time. But I’ve now added a half-page “Study Guide” for each class that includes some bullet points with action verbs, and a “Test Yourself” practice question or two that weaves a numerical problem with conceptual material. Why am I doing this? A decade ago we transitioned to online homework problems (this is now standard in introductory college chemistry) that are bundled with the e-textbook. There are a number of advantages to the online homework system for both students and instructors. But I want to highlight two challenges: (1) these systems do not handle conceptual questions sufficiently well, and (2) the way questions are phrased do not match how I would ask questions on an exam.

 

What I’m hoping that my study guide will do (if the students take them seriously) is to remind them, if they pay attention to it, of the conceptual parts of the course. Being able to solve numerical problems is important, and the ability to solve such problems on an exam indicates some conceptual knowledge. But my experience of grading exams over the years and helping students in office hours is that a lack of conceptual understanding trips students up in solving the numerical problems. And the numerical problem isn’t the end-all. It should lead to a conceptual point of knowledge. One might say that concepts are the bookends of numerical problems, the introduction and the conclusion – both very important parts! Furthermore, there is also much about chemical knowledge and understanding that is conceptual that does not translate into numerical problems.

 

Students also need to be prepared for their knowledge to be assessed through my exams, and that means getting them used to the way I phrase my questions and what I’m looking to see that they can demonstrate knowledge-wise. The online-homework-textbook isn’t sufficient; I daresay it has glaring holes in some areas. So students need to see how I ask questions and work problems. This is much of what takes place in class. They see questions that I ask and how I answer them. They take many of those low-stakes quizzes at the beginning of class. I used to provide previous year exams for practice, and then I pivoted to required self-tests essentially to make sure every student gets practice, not just the conscientious ones. The new “study guides for each class” are my latest experiment. I just sent an e-mail to my class yesterday reminding them to go through them after each class, while it’s still early in the semester. I keep trying new things. But at the end of the day, you can lead a horse to water but you can’t force it to drink.