Cyclohexane

Today's post is slightly inspired by two old ones:

Modelling Compounds and Molecules: "Cyclohexane might look like a hexagon, but that's only from one angle. It looks like a discarded crisp packet in its chair conformation (one of the shapes cyclohexane takes) for example."

Aromatisation and Hückel's rule: "So cyclohexane may be cyclic and planar"

Neither of those are particularly correct. Cyclohexane isn't planar, for one. And that's where the chair conformation comes from.

The hexagon is a lie...

Although actually, in that first post, I did say this: 

The shape of cyclohexane might convince you one bonding angle is 120°, but it's actually 109.5° - but all the angles are of an equal size at least.

Which is elite ball knowledge considering I was 16 at the time, and sort of mediocre at chemistry at the time. Because I'd completely forgotten I'd ever written this by the time I had a lecture a few months ago, and the lecturer mentioned how cyclohexane isn't actually planar, and instead takes on various chair conformations.

The first obvious sign that 120° is a lie is when you consider how many bonds each carbon atom makes in a cyclohexane molecule - it's four - two bonds to adjacent carbons, and two bonds to adjacent hydrogens. This means each carbon atom will prefer to be in a tetrahedral configuration, that keeps the atoms as far from each other as possible - the electrons love repelling themselves - and so we get a bond angle of 109.5°, as expected. This is also in part due to all the carbon atoms being sp³ hybridised, but I'd rather not go into more detail - that's for another time.

This is generally the case with most cycloalkanes like cyclohexane - the carbons are all tetrahedral, so if you want a bond angle of 109.5°, you're going to need the bonds to bend a bit and live in 3D space. That's why cyclohexane isn't planar - instead, it takes up specific conformations, which vary in terms of stability. The most stable is the chair conformation, by 99.99%.

The chair conformation

Here, the carbons are in black. The red atoms are axial hydrogens - that is, they're out of the plane of carbon atoms. The blue atoms are also hydrogens, but this time they're equatorial - in the plane of carbon atoms. The axial and equatorial hydrogens cannot exchange position with each other just by rotating a bond around - they're chemically inequivalent to each other. But you can go from axial to equatorial or vice versa by performing a ring flip. Think of it like having a jumper and turning it inside out, but instead of a jumper you have a series of carbon atoms. What was on the inside is now on the outside, and vice versa - same with the hydrogens and their axial/equatorial orientation.

There are other conformations, like the boat conformation, but these are high in energy. Why the chair conformation works so well is that it minimises steric repulsion between the axial and equatorial hydrogens - there is a reduced electron clash between them. In the boat conformation, there is far greater interference between the hydrogen atoms, and you get greater repulsive effects. 

(All this time, I've been saying hydrogen atoms, but bear in mind all this applies for any other substituent groups, say an alcohol group. The main exception is that due to the steric effects from before, some groups prefer being in an axial or equatorial environment - a tert-butyl group (also known as 2-methylpropane) almost always wants to be equatorial, as it takes up loads of space and the methyl groups interfere loads).

Now, compared to other cycloalkanes, cyclohexane is especially stable, since its conformations are closest in bond angle to 109.5°, which you'll remember was the optimum arrangement. It's not quite 109.5°, it's more like 111°, but who's measuring? It's even more unique because the stability of cycloalkanes naturally increases as the size of the molecule increases, so a cyclodecane ring will be more stable than cyclopropane, since it's more flexible.

Yet cyclohexane is an anomaly. The chair conformation minimises any steric or torsional repulsion which would arise from a planar hexagonal molecule so well that it's more stable than cycloheptane or cyclooctane. 

All hail the humble chair.