# The Cyclohexane Chair Flip – Energy Diagram

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In the last post,  we showed a video of  a cyclohexane ring flip – turning a cyclohexane chair conformation into a boat and then into the opposite chair.

The key observation we made here was that a chair flip converts all axial groups into equatorial groups and all equatorial groups into axial groups. However all “up” groups remain up and all “down” groups remain down.

Now that we know what “looks” like to do a chair flip, let’s ask a different question: how much does it “cost”? When we say “cost”, of course, we’re talking about energy. Many organic chemists like to use kcal/mol [to convert to kJ/mol, multiply by 4.184].

As you might have noticed while watching the video, converting one cyclohexane into the opposite chair conformation isn’t a matter of doing a simple bond rotation, like it is for, say, “eclipsed” butane into “staggered’ butane. There’s a lot more going on – each C-C bond undergoes rotation of some form.

Let’s walk through it in more detail.

First, we take one end of the cyclohexane chair and push it into the “plane” created by the four carbons, making a “half chair”. This first step is actually the most unfavorable – because of a combination of ring and angle strain, the half-chair lies 10 kcal/mol in energy above the chair conformation.

The next step is to continue pushing that “end” of the half chair up until it is roughly on the same level as the other “end”. This makes a “twist boat”, which is a local energy minimum – we no longer have angle strain (all bonds are again 109°) but there is some torsional strain owing to the fact that there are two pairs of eclipsed C-C bonds. There is also a “flagpole” interaction between the hydrogens on the “prows” but in the twist-boat, they are slightly offset with respect to each other. The twist-boat is 5.5 kcal/mol in energy above the cyclohexane chair.

Where to go from here? Well, the “twist” momentarily passes through a full “boat” conformation (6.5 kcal/mol)  on its way to a different “twist”, which is a bit awkward – in the full boat the two “flagpole” hydrogens are held in very close proximity to each other (within each other’s Van Der Waals radius).  Think of two friends with long Cyrano de Bergerac noses kissing each other on alternate cheeks – there’s an awkward moment when they briefly bang noses in the middle : –  )

From the new twist, we’re merely going backwards to get to the alternate chair – down goes one “prow” to give (momentarily) a half-chair, en route to the new chair.

If we draw an energy diagram, the whole process looks like this. Again, note that the chair on the left has the red hydrogens axial, and in the chair on the right, the red hydrogens are now equatorial.

So what? you might ask. We’ve turned one chair into another. Who cares?

[And you might not care. That’s fine. The following discussion is not crucial for us going forward, but is helpful to understand a key consequence of this energy diagram…. ]

For cyclohexane, I cede your point of “who cares”,  because for all purposes the two chair forms are identical.

However, things start getting interesting once we start putting any type of substituent on our cyclohexane.

For example, let’s take 1-methylcyclohexane. Let’s say we start with the chair on the left (methyl is axial)  and a chair flip converts it into the chair on the right (methyl is equatorial).

First of all, note that these are NOT mirror images of each other – they are different conformations.

Now imagine we have a magical device that can take “snapshots” of molecules, so that we can tell, at any given time, what the structure of a molecule is. Press a button, and presto ! you get pictures of all the molecules in solution.

What would a “snapshot” of a solution of “1-methylcyclohexane” look like? Assume that 1) the molecules will spend >99% of their time in “chair” conformations, and 2) assume (for now) that the two chair forms are equal in energy.

Based on this, we’d expect to see that 50% of the “snapshots” show “axial” 1-methylcyclohexane, and 50% show “equatorial” 1-methylcyclohexane.

[We actually do have a device which does this, and it’s not magic – it’s called an NMR spectrometer – more on that in a later series].

So what do we actually see?

Here’s the cool part.

At very low temperatures (–78°C, which is the temperature of the cheap dry ice/acetone cold bath) our “magic device” does indeed show that there is a mixture of equatorial and axial 1-methylcyclohexane in solution, just like we might expect.

However, when we let it warm up to room temperature, something interesting happens. The “snapshots” of the “axial” and “equatorial” 1-methylcyclohexane start blurring together, until we see a single signal that is an average of those two snapshots.

So what could explain this? Why might we see two “snapshots” at low temperature, but a single, “blended” snapshot at high temperature?

Does it remind you of something? Maybe of the difference between taking pictures of a ceiling fan at rest (where you can see the individual blades) and taking pictures at high speed (where you just see a blur). Or spokes on a bicycle? Or a colour wheel?

We see a “blur” on our magic snapshot machine (i.e. an NMR spectrometer) because, like a camera with a long shutter speed, we see an average of the different states over time.

A similar type of thing is happening here. At low temperatures, we have separate populations of “axial” and “equatorial” 1-methylcyclohexane, which do not have sufficent energy to ascend the 10 kcal/mol barrier (through the “half-chair”) that would allow for their interconversion.

At higher temperature, there is sufficient energy for each molecule to ascend the barrier to half-chair formation, and therefore the interconversion can occur.

Now let’s circle back to one key assumption. Here, we made the assumption that the “equatorial” and “axial” forms of 1-methylcyclohexane are equal in energy.

Is this actually true? If not, why not?