# Free energy, heat, and potential

I thought I was setting the record straight on energy yesterday, but upon reflection, I made an egregious mistake. Well, I probably made several, but there’s only one that I’m currently aware of.

In drawing a distinction between free energy (G) and enthalpy (H), I unintentionally conflated enthalpy with potential energy. Fortunately, the situation is easily corrected.
As I pointed our yesterday, free energy is the “available” energy. Entropy is what sets free energy and enthalpy apart.

And, as I also pointed out, enthalpy is the “total” energy in the sense that it includes all of the different forms of energy that we need to consider when looking at a molecular structure. It includes all of the energies created by interparticle forces (electron-electron, nucleus-electron, nucleus-nucleus) and particle motions (electron, nuclear).

So far, so good.

I got myself into trouble, however, when I said that the energy graph for internal rotation showed dihedral angle vs. enthalpy, not free energy (as Loudon seems to think). The graph actually shows dihedral angle vs. potential energy. To make things worse, this so-called “potential” energy is different from all of the potential energies associated with interparticle forces (see above).

Physicists describe an object’s energy as “potential” when it depends only on the object’s location in space. For example, if you think about the gravitational attraction that exists between our planet and your backpack, you realize that your pack’s potential energy is higher when its slung over your shoulder and lower after you drop it on your toe.

And so it is with molecules. If a molecule’s energy depends only the locations of its atoms, i.e., the molecular geometry, it is “potential” energy. Therefore, when I draw a graph showing how geometry (dihedral angle) and energy are related, I am most likely referring to “potential” energy.

To summarize:

• potential energy – energy of molecule(s) with geometry completely specified (atoms do not move)
• enthalpy – potential energy + energy of atom (nucleus) motions
• free energy – enthalpy + entropy correction
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