Cyclohexane- Calculating Flip Energy

In regards to cyclohexane chair flips, for most classes all you will need to know how to do is use equatorial preference to predict the most stable chair conformation.

However, some crazy professors are going to want you to use energetics to calculate the exact percentages of each chair in solution. This is a multistep process, so here I’m going to walk you through it from scratch. 

Calculating Flip Energy

First we have to introduce the concept of an A-value, which is simply the energy difference between the equatorial (most stable) and axial (least stable) positions.

We can use these values to calculate how much energy it is going to take to flip a chair into its least stable form.

Note: Emily from FSU pointed out that I actually flipped my chair INCORRECTLY in this video- and she is absolutely right :/ 

Notice that my methyl group was faced down equatorial before and after I flipped it to up axial. Remember that down's should stay down and up's should stay up. 

Anyway, all the math is still correct here, but I should have drawn the groups down instead of up on the second chair. Sorry about that!

Example: Calculate the difference in Gibbs free energy between the alternative chair conformations of cis-2-ethyl-1-phenylcyclohexane. 

5m

Calculating Chair Equilibrium

Now that we know how to calculate the difference in flip energy, we can plug that information into the famous Equilibrium Constant equation to determine exact Ke of the reaction. 

Once we have the Ke of the equilibria, we can solve for x, which will be the percentage of my most favored chair.   

Example: Estimate the equilibrium composition of the chair conformers of cis-1,3-diethylcyclohexane at room temperature.

8m

Example: Estimate the equilibrium composition of the chair conformers of trans-1-methyl-3-phenylcyclohexane at room temperature.

5m