Skipping Work?

In a previous blog post, I pondered whether we need to discuss Orbitals at the general chemistry level. Today, I will ponder whether we need to discuss Work. Where does Work show up in G-Chem? Usually when we begin thermochemistry.

 

Here’s what I typically do in my course. I introduce the thermodynamic universe with its three parts (chemical system, thermal surrounding, mechanical surroundings). I’ve been stressing the role of models in conceptualizing scientific knowledge, and this simplistic universe is a model. The universe is isolated: nothing goes in or out. The chemical system is closed: it can exchange energy (but not matter) with the surroundings. Planet Earth is mostly a closed system. We receive energy in the form of photons from the sun, and dissipate it as heat to the coldness of space. By and large, not much mass enters or leaves the system. Yes, there is the occasional meteorite that enters or helium that floats away. And we do launch rockets and we do have falling debris. This is contrasted with living organisms on our planet that are open systems, exchanging energy and matter with their surroundings.

 

The three-part model of the universe allows us to keep track of the energy. Typically, we cannot measure what’s going on in the chemical system directly. Tiny atoms and molecules might be doing chemistry – making and breaking chemical bonds. This results in a change in energy (and energy is a key consideration in any chemical reaction). But how do we quantify that change? We can measure energy changes in both the thermal and mechanical surroundings. To do so, we represent them as models. The simple model for the thermal surroundings is an insulated water bath, essentially a calorimeter. The simple model for the mechanical surroundings is a piston-and-shaft system, like a syringe.

 

The calorimeter determines “heat energy” by measuring the change in temperature of the water in the bath when a chemical reaction takes place. The quantity heat (usually given by the symbol q) can be calculated by knowing the amount of water in the bath, the heat capacity of water, and its change in temperature. Conceptually an increase in any of these three things will mean an increase in heat. Hence, we can use the formula q = mcΔT. But we’re doing this for the calorimeter. If the calorimeter gains energy, the chemical system is losing energy, and vice versa. Thus, q of the system is equal and opposite to q of the calorimeter.

 

The piston-and-shaft system determines “PV work” by measuring the distance moved by the piston due to a chemical reaction. Given the surface area of the piston and the distance moved, we can calculate the change in volume of the system as it expands or contracts. The piston will keep moving until the pressure in the system is equal to the pressure outside (usually atmospheric pressure for most chemical reactions). Whenever there is a change in volume, energy is exchanged between the chemical system and the mechanical surroundings. Using the standard definition of work as force multiplied by distance, we can derive the formula w = –PΔV. The magnitude of P is the constant external pressure, and the volume change is for the chemical system. The negative sign is because an expanding system will transfer energy from the system to the mechanical surroundings, while a contracting system does the opposite.

 

This leads to the first law of thermodynamics, encapsulated by the equation ΔE = q + w, where ΔE is the change in internal energy of the system. Importantly, the internal energy is a state function which essentially means that it doesn’t matter how you carry out the chemical reaction. If you use the same reactants and it leads to the same products, ΔE will be the same regardless of what actual experimental method you use to make the chemical reaction happen. This makes sense, chemically speaking. Once you’ve broken the old bonds and made the new bonds, it doesn’t matter how you did it. The old bonds had some quantity of energy; the new bonds have some other quantity; and the difference between the two quantities is the change in internal energy of the chemical system. The full picture gets built up into the one below over the course of two class periods.

 

Magnitude-wise in a chemical reaction, ΔE is much larger than w, i.e., ΔE and q are close to the same value. This is because the change in energy due to bonds breaking and forming is much larger than the change in energy due to any volume changes. If one mole of gas is released in a chemical reaction, that’s roughly 2.5 kJ of energy. But typical covalent chemical bonds are hundreds of kJ per mole. So unless the chemical bonds you break are almost exactly the same as the chemical bonds you make, you’d expect ΔE of a chemical reaction is typically in the tens to hundreds of kJ per mole, dwarfing w. We do a sample calculation in class to illustrate this.

 

Currently in G-Chem, I briefly discuss the difference between bomb calorimetry and coffee-cup calorimetry. The latter is carried out at constant pressure and very easy to use practically-speaking. In particular, the q determined by coffee-cup calorimetry includes both the internal energy change and the change in volume. Instead of trying to separate the two (by using constant volume bomb calorimetry), chemists lump the two quantities together and give it a new name: Enthalpy. Most G-Chem textbooks refer to enthalpy as heat-energy, and use “enthalpy” and “heat” interchangeably, for example the “standard enthalpy of formation” (an important and useful quantity that scientists have tabulated) of a substance is often referred to as the “heat of formation” for short. This sleight of hand is actually confusing to students because technically while enthalpy H is a state function, heat q is not. We might tell the students that for all intents and purposes, ΔH = q, and this is true regardless of the type of calorimetry employed, but they don’t know get why this is so even though they can push symbols around and do algebra. I go into much more detail when I teach this in upper division P-Chem, but at the G-Chem level, going into the minute details will just confuse students, and there isn’t enough time in our already tight semester.

 

We could avoid all this by jettisoning Work. Let’s get rid of the mechanical surroundings, or actually we are subsuming the PV-work into the chemical system. The energy of the system including the volume it occupies, let’s just call that the enthalpy, H. We won’t bother about any equations that involve w. We no longer have to use E to specifically mean the internal energy of the system and can just use it as a generic shorthand for “energy”. (In P-Chem we use U for internal energy to avoid using the symbol E.) We can then directly talk about ΔH = q and state functions for a single generic calorimeter without splitting the difference between constant pressure versus constant volume processes. At the G-Chem level, the students don’t have to worry about the piston-and-shaft model and doing PV calculations (that trip them up units-wise or sign-convention-wise).

 

Even better, when we get to Free Energy, we don’t have to try and distinguish useful work you can extract from the system from the PV-work inherent to the system. Thus whenever you refer to “work”, it is in this more generic sense that matches how students think about the word, rather than the very specific PV-work encapsulated by w = –PΔV. By this point in the semester, we’re pretty much doing everything in terms of system thermodynamic properties anyway, and we aren’t talking about q and w very much. While I’ve typically used the diagrams below to show what is happening when we introduce enthalpy and free energy to the thermodynamic universe, I could simplify this model by starting with a two-part universe and then introducing “useful work” as the third constituent when we cover free energy.

 

Jettisoning PV-work in G-Chem means I will have more work to do (pun intended) in P-Chem. But I do this all carefully and slowly in P-Chem anyway. And most of our G-Chem students aren’t going to be chemistry or biochemistry majors which means they won’t be taking P-Chem. The percentage of students taking G-Chem II (where we cover thermodynamics) who go on to take P-Chem II (thermodynamics in gory detail) is 12% from the average over the last five years. How much time will skipping PV-work in G-Chem save me in class? Barely one lecture’s worth if I combine everywhere I make reference to it throughout the semester. But I think the reduction in cognitive load for the students might be worth it. Every time I teach G-Chem II, students get tripped up over what w is, how to calculate it with the right units, how to distinguish it from useful work and the concept of free energy, and they get muddled about what enthalpy is. Enthalpy is not heat. Furthermore, we can skip trying to distinguish Enthalpy from Internal Energy.

 

One drawback if we skipped PV-work is that students will get confused as they read their G-Chem textbook. There is a cognitive load cost as we help students navigate the things we care that they know from their textbook versus the things deemed less crucial. But this happens for other topics as well. Our G-Chem textbooks are too bloated because they try to serve the desires of many different instructors who might differ in what they deem important and in how much detail. If you’re trying to sell textbooks, more sort-of looks better. More rigorous! Maybe I should just write my own textbook and use it. Ah, but that would be way too much work!