# By what mechanisms can molecules with the same empirical formula be so different?

I understand the difference between empirical and chemical formula. But I always thought that compounds and molecules took their specific shape because it's the lowest energy configuration. How then, can fructose ($\ce{C6H12O6}$) and formaldehyde ($\ce{CH2O}$) both exist? If for example formaldehyde had overall the smaller energy, why then wouldn't fructose just decompose in 6 $\ce{CH2O}$ molecules? What makes both of those molecules so stable?

I guess this is a very general question of what makes certain elements combine the way they do to form compounds.

What makes both of those molecules so stable?

This is a fundamental question. Let's start by looking at the following diagram; a chemist would call it a "potential energy diagram." The y-axis shows the energy of a molecule as it travels along the reaction coordinate (x-axis; transforms, reacts) from the starting material on the left to the product on the right.

Notice that there are 3 "potential energy wells" (valleys) in the diagram, these reflect molecules that are stable enough to have a finite lifetime. Notice too that to move from one well to another, an energy barrier must be surmounted.

So to return to your question, a molecule would be "kinetically stable" if it was protected on all sides by high energy barriers. A molecule would be "thermodynamically stable" if its potential energy well was located at an energy that had a very low value on the y-axis. A molecule that is very stable in a thermodynamic sense, could still be kinetically unstable (and therefore very reactive) if it was surrounded by low energy barriers. By the same token, a molecule that is very unstable in a thermodynamic sense (exists at a high energy value on the y-axis) could be kinetically stable if it were surrounded by high energy barriers to reduce the likelihood of further reaction.

Millions of molecules are stable at room temperature, but if you supply enough energy to the system (heat them for example) they can all transform into other compounds. At room temperature there are high enough energy barriers separating fructose and formaldehyde and they will both be stable in a jar, but under more energetic conditions such transformations might be feasible.

• Just a small correction: a chemist would, of course, call the diagram in your post potential energy curve. It is the variable along the abscissa which chemist would call reaction coordinate. – Wildcat Sep 25 '14 at 15:31
• @Wildcat Good point Wildcat, I'll edit my answer accordingly. Thanks! – ron Sep 25 '14 at 15:33
• Thanks for this! Very helpful! Now I'm wondering: if you just dump a whole bunch of atoms in a box at a certain temperature, so a couple of C,H and O, is there a deterministic solution to which compound will be formed? Also: do we know enough about chemistry and physics to synthesise any molecule we want if we had all the atoms separated and could add those to a mix at will? – Moppentapper Sep 28 '14 at 6:54
• @Moppentapper, answer to your first question is, I think, yes. Roughly speaking, you have to calculate potential energy surface which will presumably have many minima corresponding to different (meta)stable combinations of these atoms and many maxima connecting those minima. Then given a temperature you can estimate the average amount of kinetic energy atoms and forming (meta)stable molecules possess, so that you can predict which maxima will eventually be crossed and which minima will be popoulated. – Wildcat Sep 28 '14 at 7:10
• @Moppentapper, your second question sounds for me like it is about molecular assemblers - hypothetical devices that are a popular topic in the area of molecular nanotechnology and science fiction. :D – Wildcat Sep 28 '14 at 7:31

I guess this is a very general question of what makes certain elements combine the way they do to form compounds.

At the fundamental level, I think, a good answer to this question would be the principle of minimum potential energy, which basically states that a system has a tendency to be in a configuration that minimizes its total potential energy. (Please, note the word tendency!) For the case of molecules it means that if forming a molecule out of atoms lowers the potential energy comparing to the situation when these atoms are infinitely far apart of each other, than there is a natural tendency for this molecule to be formed.

But there is a one important detail that complicates matters: given some set of atoms, there is no guarantee that there exist only one possible arrangement of them which minimizes the potential energy. In fact, the situation is usually the opposite: there are many different minima in the potential energy corresponding to different possible arrangements of the same set atoms. Often we can clearly identify one global minimum (the lowest one) and call all other minima local minima.

Any local minima in potential energy (directly on indirectly, i.e. through other local minima) is connected with the global minimum in a sense that there exist some way for a system to transit from a local local minima to the global one. But on it is way to the global minimum from a local one potential energy first rises and only then falls. It falls to the lower value, but first the system need to overcome a barrier. Thus, we say that a structure that corresponds to a global minimum is stable, while structures that correspond to local minima are metastable in a sense that a system (a molecule) actually may reside in these local minima for quite a long time if the barriers are relatively high. Relatively to what? Basically, to the amount of kinetic energy a molecule posses so that it can be converted to the potential energy to overcome the barrier.

A good analogy may be drawn with a ball resting in a hollow on a slope (image below courtesy of Wikipedia)

If the ball being in a hollow (1) does not have enough kinetic energy to be converted into potential with the aim to overcame the barrier (2) and move on to the lower energy minimum (3) it will stay at (1) for ages. But if the ball has enough kinetic energy it will roll to the lower level. Here (3) might be just another local minimum or the global minimum, it does not matter. If (3) is not the global minimum then this process is just one of the steps on a way to the global minimum.

Now, back to molecules, think about (1) as of 6 molecules of formaldehyde being far apart of each other and about (3) as of 1 molecule of fructose. Both these different combinations of atoms correspond to minima in potential energy, and here I assumed that fructose is lower in potential energy. Note that I could not guarantee that, as well as, I could not guarantee that of of these minima is the global minimum for a system composed of 6 atoms of $\ce{C}$, 12 atoms of $\ce{H}$, and 6 atoms of $\ce{O}$. Apriori we do not know what form is lower in potential energy, so we have to do some calculations, say. But here let me just assume that $\ce{C6H12O6}$ is lower in potential energy than $\ce{6 CH2O}$.

Now recall that (as I noted at the very beginning) the principle of minimum potential energy only tells us that there is a tendency for a system to favour a configuration with the lowest potential energy (i.e. $\ce{C6H12O6}$ out of two choices we discuss). But starting from $\ce{6 CH2O}$ the natural tendency to form $\ce{C6H12O6}$ would not necessarily be realized in reality if the barrier between these configurations is relatively high in a sense already mentioned. So, it might be the case that at, say, room temperature, most of the $\ce{CH2O}$ molecules do not posses enough kinetic energy to be converted to potential energy to overcame the barrier. But you can increase the amount if kinetic energy of $\ce{CH2O}$ molecules by rising the temperature, so that the system will roll to overcome the barrier. Chemical reaction will take place, although, I'm not sure that these two ($\ce{6 CH2O}$ and $\ce{C6H12O6}$ are directly connected). But conceptually, the situation is similar to just pushing the ball from the picture above. :D