The General (Bond) Energy Curve

Over the summer, I contemplated re-thinking the way chemical bonding is introduced in General Chemistry. I decided to try the approach proposed by Nahum and co-workers, at least partially. We spent the first four weeks discussing models of the atom, the interaction of light and matter and atomic orbitals. This week we started the section of chemical bonding (approximately five weeks long).

I devoted my first class on chemical bonding to discussing the general energy curve shown above. We first discussed how the energy changes when two hydrogen atoms approach each other without discussing why. I then proposed that this curve isn’t just true for hydrogen, but it works for any atom. The equilibrium bond distances and bond energies (sometimes called bond length and bond strength) will differ for different atoms, but the overall curve is roughly similar. We then discussed the sign convention for bond breaking (energy change is positive) and bond forming (energy change is negative) relative to the zero reference state of infinitely separated atoms. The students had recently seen something similar when we discussed the orbital energies of the hydrogen atom and the Rydberg equation. I emphasized the counter-intuitive notion that energy is released when chemical bonds are formed, in analogy to conservation of energy principles when we talked about atomic emission spectra two weeks ago.

After H₂, I covered N₂ and O₂, and we contrasted the equilibrium bond distances and energies. Again, we left out the why question for now, although I alluded to atomic size being one of the factors. N₂ is a nice contrast because the bond strength is more than twice that of H₂ even though it is a longer bond. O₂ provides another interesting contrast because even though the O atom is smaller than the N atom; O₂ has a longer bond length than N₂, while its bond energy is closer to that of H₂.

Then we looked at argon. One normally doesn’t think of two Ar atoms forming a “bond” but the general energy curve still holds when two Ar atoms approach each other. The equilibrium bond distance is much longer and the bond energy is tiny (less than 1 kJ/mol compared to 436 kJ/mol in H₂). I talked about how words we use such as “bond” and “attractive force” often overlap, and technically there is no clear-cut distinction between the two. This was illustrated in the next few examples.

What if instead of atoms you had two molecules approaching each other? We used the example of two O₂ molecules – the equilibrium bond length and strength are not too different from the case of two Ar atoms. In General Chemistry this would normally be covered later in the semester under the topic of Intermolecular Forces. But I wanted to introduce them here in the context of the general energy curve. Again, we did not cover the why. The final example was the approach of the two ions K(+) and Cl(-). I chose these because they are isoelectronic to Ar. So you have a situation of two argon-like atoms (actually ions) approaching each other, but the bond energy (using Coulomb’s Law) is now closer to that of H₂ or O₂ even though the ion-pair has a somewhat longer equilibrium bond distance.

Next we talked about the source of attraction as two chemical “species” (atoms, molecules, ions) approach each other. Without going into details, we discussed electrostatics per Coulomb’s law, one-electron orbital overlap, and I briefly mentioned the idea of a dipole with scant details. I promised the students we would delve into these concepts in-depth over the next several weeks. Finally we talked about the source of the repulsion (the steep part of the curve near the left). Most instructors leave this out, or hand-wave a quick argument about nuclear-nuclear repulsion. I made it a point to talk about repulsion due to the Pauli Principle and how this would show up time and again when we discuss molecular shape and steric effects. Students often confuse the much weaker electrostatic repulsion between electrons with the much stronger Pauli repulsion. (They use the former as an explanative argument in cases when they should be using the latter.) In General Chemistry, the Pauli Principle is often treated as a quantum number rule that leads to two electrons per orbital. But it is so much more important in chemistry!

As I’ve been planning the next several classes, I’ve been inserting elements of the (Un)Happy Atoms story into the flow of my course material. I guess those hours I spent making the figures and outlining the story paid off – since I’m actually going to make use of it. How will my new approach work out? I don’t know yet, but I explained to my students why there was no assigned textbook reading for yesterday’s class, why I chose to cover the material in the way that I did with the generic energy curve, and what they should expect to see in the coming weeks. One thing I’ve learned about teaching: Context, context, context.