Substituted Cyclohexanes – Axial vs Equatorial

Equatorial vs Axial Groups: Why The Equatorial Position Is Of Lower Energy

Just to bring you up to speed,  let’s quickly review the last post.  And at the bottom, I’ll also correct a little fib I made in the last article.

Table Of Contents

1. Brief Review On The Cyclohexane Chair Conformation
2. In 1-Methylcyclohexane, The Ratio Of Equatorial Methyl Conformer To Axial Methyl Conformer Is About 95:5
3. The “Equatorial Methyl” Conformation Encounters Fewer Gauche Interactions Than The “Axial Methyl” Conformation
4. The Experimentally Determined Equilibrium Ratio Of Conformers Can Be Used to Calculate The Energy Difference
5. Summary: Axial Vs Equatorial Groups
6. Notes
7. (Advanced) References and Further Reading

1. Brief Review On The Cyclohexane Chair Conformation

• Cyclohexane Undergoes A Conformational Interconversion Known As A Chair Flip.  In this chair flip, all axial groups become equatorial, and all equatorial groups become axial. [but all “up” groups remain up, and all “down” groups remain down].
• The two chair forms of cyclohexane itself are completely indistinguishable, but this is not true in most cases. For example, in 1-methylcyclohexane, one chair conformer has an axial methyl group, and in the other the methyl group is equatorial. These are conformational isomers, or simply, “conformers”.
• At room temperature, these two conformations are in rapid equilibrium with each other. There is an activation barrier of about 10 kcal/mol for this interconversion, since the high-energy “half-chair” conformer is an intermediate in this process. Trying to observe both conformations of 1-methylcyclohexane at room temperature with a device for taking “molecular snapshots” (an NMR spectrometer is what we use – more precise details on this in future posts) results in a blurred picture. Like an old camera trying to take pictures of spokes on a moving bicycle wheel, the “shutter speed” is too slow, and the result is that the images blend together to give an average. Using this device, it’s simply not possible to see both cyclohexane conformers of 1-methylcyclohexane at room temperature.
• At very low temperatures (about 80 degrees above absolute zero) equilibrium between the two chair forms stops, because there isn’t enough thermal energy available to ascend the activation barrier of 10 kcal/mol. Now,  when we try to take “molecular snapshots” of 1-methylcyclohexane, we do indeed see the two conformations separately. [Note 1]

Now, the correction to the fib.

In the last post, we assumed that these two conformations would be equal in energy, and therefore we would see a 50:50 mixture of the two conformations.

Is this true? No.

2. In 1-Methylcyclohexane, The Ratio of the Equatorial Methyl Conformer to the Axial Methyl Conformer Is 95:5 .

There’s only one way to find out. Do the experiment with a substituted cyclohexane such as 1-methylcyclohexane.

When we do this, here’s what we find. Instead of being equal, the ratio of “equatorial methyl” to “axial methyl” conformers is about 95:5  favouring the conformation where the methyl group is equatorial. [Note 2]

Very interesting! This must mean that the equatorial conformation is of lower energy than the “axial” conformation.

Why might that be?

3. The “Equatorial” Methyl Conformation Encounters Fewer Gauche Interactions Than the Axial Methyl Conformation

Let’s look at the Newman projection of the chair. Imagine looking along the C-1 to C-2 bond (which is coplanar with the C-4 to C-5 bond). Here’s what you’d see.

Note that in the conformation where methyl is axial,  there is a gauche interaction between the axial methyl group and C-3. This is absent in the conformation where methyl is equatorial.  This gauche interaction is an example of van der Waals strain, which is what makes the axial conformer higher in energy.

There is actually a second gauche interaction if you look along C-1 to C-6 . This gauche interaction is with C-5.
A simple way to keep track is to think of it as the methyl group interacting with the other ‘axial’ hydrogens, at C-3 and C-5. These are called “diaxial interactions” since they are steric interactions between axial substituents.

Bottom line: in two unequal conformations of a cyclohexane ring, the conformation where steric interactions are minimized will be favoured.  [Note 2]

4. The Experimentally Determined Equilibrium Ratio Of Conformers Can Be Used To Calculate The Energy Difference

Now here’s a neat consequence of this knowledge. Since this ratio of conformers (95:5) represents a system at equilibrium, we can actually use it to calculate the difference in energy of these two conformers using the following equation:

For a 50:50 mixture (K = 1) the energy difference ΔG would be zero.

For methylcyclohexane at room temperature (298 K) the 95:5 ratio of equatorial to axial conformers translates to an energy difference of 1.74 kcal/mol. 

In other words, the equatorial conformer is more stable by 1.74 kcal/mol.

Since there are two gauche interactions, and the strain energy is 1.74 kcal/mol, it’s easy to calculate the value of each interaction: 0.87 kcal/mol .

5. Summary: Axial Vs Equatorial Groups

Now this opens up all kinds of questions. If a methyl group (CH₃) leads to an energy difference of 1.70 kcal/mol, then what effect would an ethyl group (CH₂CH₃) have? Or a Cl? Or OH ? Or tert-butyl ?

We can use the same approach to measure all of these numbers. More about that in the next post.

Next Post: Substituted Cyclohexanes: A-Values

Notes

Note 1.  This is a bit of a cheat. In the equation  ΔG = –RT ln K  , the value of K is related to T, so the equilibrium ratio at –80 °C will be a bit different than the value at room temperature.  However, one can then solve for ΔG and use this number to calculate what K is at room temperature.

Note 2. Enterprising students might ask what happens if the axial hydrogens on C-3 and C-5 are removed. Would this change the equilibrium? Absolutely!

In the molecule above, the CH₂ groups at C-3 and C-5 have been replaced by oxygen. Since there are no longer any significant diaxial interactions between the methyl group and substitutents on the ring, there is no significant energy difference between the equatorial and axial conformations of this molecule.

(Advanced) References and Further Reading

This is a topic commonly taught to undergraduates in Organic Chemistry, and goes along with the discussion on A-values. Substituents in cyclohexane can take two positions, axial and equatorial, and the preferred conformation is dictated by stereoelectronic effects.

1. Electron Diffraction Investigations of Molecular Structures. II. Results Obtained by the Rotating Sector Method.
   Hassel, O.; Viervoll, H.
   Acta Chem. Scand. 1947, 1, 149-168
   DOI: 3891/acta.chem.scand.01-0149
2. The Structure of Molecules Containing Cyclohexane or Pyranose Rings.
   Hassel, O.; Ottar, B.
   Acta Chem. Scand. 1947, 1, 929-943
   DOI: 3891/acta.chem.scand.01-0929
   Odd Hassel first confirmed that cyclohexane exists in the now commonly accepted chair confirmation. He also proposed that substituents can take two different types of positions on the ring, which he called c- and e-bonds. He also showed that the conformational analysis of cyclohexanes can be extended to other unsaturated 6-membered rings, such as the pyranoses commonly found in carbohydrates. Odd Hassel later shared the Nobel Prize in Chemistry with Prof. D. H. R. Barton for his work on conformational analysis.
3. The Thermodynamic Properties and Molecular Structure of Cyclohexane, Methylcyclohexane, Ethylcyclohexane and the Seven Dimethylcyclohexanes
   Charles W. Beckett, Kenneth S. Pitzer, and Ralph Spitzer
   Journal of the American Chemical Society 1947, 69 (10), 2488-2495
   DOI: 1021/ja01202a070
   This paper first proposes the terms ‘polar’ and ‘equatorial’ for the two types of positions substituents can take in cyclohexane.
4. Nomenclature of cycloHexane Bonds
   BARTON, D., HASSEL, O., PITZER, K., PRELOG, V.
   Nature 1953, 172, 1096–1097
   DOI: 1038/1721096b0
5. Nomenclature of Cyclohexane Bonds
   H. R. Barton, O. Hassel, K. S. Pitzer, V. Prelog
   Science 1954, 119, 49
   DOI: 10.1126/science.119.3079.49
   These are the first instances of the terms ‘axial’ and ‘equatorial’ being used to denote the two positions substituents can take in cyclohexane. This was also back in the day when scientists could safely cross-publish to get better visibility – pretty much the same article is published in both Science and Nature, considered top journals.
6. Neighboring Carbon and Hydrogen. XIX. t-Butylcyclohexyl Derivatives. Quantitative Conformational Analysis
   S. Winstein and N. J. Holness
   Journal of the American Chemical Society 1955, 77 (21), 5562-5578
   DOI: 10.1021/ja01626a037
   This is the paper that first introduced the concept of A-values (see Table XII) and how to determine them through kinetic (solvolytic) measurements, which is what Prof. Winstein was well known for. The introduction features a summary of how A-values are determined, and later on, Prof. Winstein states “The energy quantity by which a t-butyl group favors the equatorial position is sufficiently large to guarantee conformational homogeneity to most 4-t-butylcyclohexyl derivatives”, which is commonly taught in organic chemistry classes today.
7. STUDIES OF RATES OF CONVERSION AND POPULATIONS OF VARIOUS CONFORMATIONS OF SATURATED RING COMPOUNDS BY N.M.R.: I. CHLOROCYCLOHEXANE AND BROMOCYCLOHEXANE
   W. Reeves, K. O. Strømme
   Canadian Journal of Chemistry, 1960, 38 (8): 1241-1248
   DOI: 10.1139/v60-176
   This might be the first paper to actually use NMR to determine axial:equatorial ratios of substituted cyclohexanes. However, the authors do not explicitly calculate A-values here, which is why this paper is less well-known compared to the JACS publication of Jensen, Bushweller, and Beck below.
8. Conformational Analysis‐The Fundamental Contributions of D. H. R. Barton and O. Hassel
   Topics in Stereochemistry 1967, 1, 1-17
   DOI: 10.1002/9780470147153.ch1
   A summary of the key papers that Profs. Barton and Hassel published in confirmation analysis, earning them the Nobel Prize in Chemistry in 1969.
9. Conformational preferences in monosubstituted cyclohexanes determined by nuclear magnetic resonance spectroscopy
   Frederick R. Jensen, C. Hackett Bushweller, and Barbara H. Beck
   Journal of the American Chemical Society 1969, 91 (2), 344-351
   DOI: 10.1021/ja01030a023
   This is the first paper to actually determine A-values through NMR, by measuring the equatorial:axial ratio of various monosubstituted cyclohexanes.
10. The experimental determination of the conformational free energy, enthalpy, and entropy differences for alkyl groups in alkylcyclohexanes by low temperature carbon-13 magnetic resonance spectroscopy
    Harold Booth and Jeremy R. Everett
    J. Chem. Soc., Perkin Trans. 2, 1980, 255-259
    DOI: 10.1039/P29800000255
    This paper covers the use of ¹³C NMR to determine the free energy differences between axial- and equatorial-subtituted alkylcyclohexanes (in essence, A-values).