Methylcyclohexane flips between two chairs. In one chair its methyl group is equatorial, and in the other it is axial. At room temperature about 95% of the molecules are in the equatorial chair at any moment. Working out a split like this for any substituted cyclohexane is called conformational analysis: you decide which chair the molecule prefers, and by how much. This page turns that into a procedure you can run on rings you have never seen.
The procedure uses three earlier ideas: the A-value from Axial/equatorial, the flip between two chairs from Ring flips, and the gauche interaction from Newman projections.
One substituent: equatorial wins
Start with methylcyclohexane and put the methyl on C1. In the axial chair the methyl points straight up. The axial hydrogens on C3 and C5 also point up, right beside it, and crowd it. These are its two 1,3-diaxial interactions. In the equatorial chair the methyl points out from the edge of the ring, where nothing crowds it.
The energy gap between the two chairs is the methyl group's A-value, 1.7 kcal/mol. That gap is what sets the 95:5 split.
A ring with one substituent always behaves this way. The major chair puts the group equatorial, and the size of the preference is the group's A-value. tert-Butylcyclohexane, with an A-value of 4.9 kcal/mol, spends more than 99.9% of its time with the tert-butyl group equatorial.
Two substituents: first find out which chairs are possible
Take 1,2-dimethylcyclohexane. It exists as two different compounds. In the trans isomer the two methyls are on opposite faces of the ring, and in the cis isomer they are on the same face. A ring flip never moves a group to the other face, so each isomer keeps its relationship in both of its chairs.
The faces decide which chairs can exist. Axial bonds alternate as you go round the ring: up at C1, down at C2, up at C3, and so on. Each carbon's equatorial bond tilts the opposite way from its axial bond. So if the groups on C1 and C2 are both equatorial, the C1 group tilts down and the C2 group tilts up. They are on opposite faces, which makes the pair trans.
Move one carbon further and the result reverses. C3's axial bond points up, like C1's, so equatorial groups on C1 and C3 both tilt down. They share a face, which makes the pair cis. C4's axial bond points down, like C2's, so a 1,4 pair with both groups equatorial is trans again.
The other isomer in each case cannot put both groups equatorial. A cis-1,2 pair, a trans-1,3 pair and a cis-1,4 pair each have one group axial and one equatorial in both chairs.
A ring flip shows the same thing for 1,2-dimethylcyclohexane. A flip turns every axial bond into an equatorial one and every equatorial bond into an axial one, and it never changes a face. So the trans isomer's diequatorial chair flips into a diaxial one, and trans-1,2-dimethylcyclohexane has both methyls equatorial or both axial. The cis isomer starts with one methyl axial and one equatorial, and the flip only swaps which is which. In cis-1,2-dimethylcyclohexane one methyl is axial in every chair. Worked examples for both isomers follow below.
Add up the axial penalties
The two groups are cis and sit on C1 and C4, so one of them is axial in either chair. The only question is which one.
One chair puts the tert-butyl group axial. Its penalty is the tert-butyl A-value, 4.9 kcal/mol. The other chair puts the methyl axial instead, for a penalty of 1.7 kcal/mol.
The methyl-axial chair wins by 4.9 − 1.7 = 3.2 kcal/mol.
That example is the whole method. Draw both chairs and note which groups are axial in each. Add up the A-values of the axial groups to get each chair's penalty. The chair with the smaller penalty wins, and the difference between the two penalties is the size of its preference. When the groups cannot all be equatorial, this arithmetic always gives the equatorial position to the group with the larger A-value.
When the two groups touch each other
An A-value measures how much a group is crowded by hydrogens. When two substituents sit close together, they also crowd each other, and adding A-values misses that. Two such contacts are common enough to learn. Each of the next two examples shows one.
This example runs the whole procedure, one step at a time. The name alone does not give the answer; the drawing does.
Step 1 — turn the name into faces. Trans means opposite faces, so put the C1 methyl down and the C2 methyl up. If you are given a flat ring drawn with wedges and hashes instead, read the faces straight off it: a wedge is up and a hash is down.
Step 2 — draw one chair and number it. Pick any carbon as C1 and number round to C6 in either direction. Write the numbers on the drawing instead of keeping them in your head.
Step 3 — put each group on its face. On C1, find the bond that points down and put a methyl on it. On C2, find the bond that points up and put the other methyl on it. Because axial directions alternate, the down bond on C1 and the up bond on C2 are the same kind of bond: both axial, or both equatorial.
Step 4 — read the labels. In the chair drawn below on the left, both methyls are equatorial. Call this chair ee, for equatorial–equatorial.
Step 5 — flip and read again. The faces stay the same and the labels reverse, so in the other chair both methyls are axial. Call it aa.
Step 6 — add up, then look for contacts. The aa chair has two axial methyls: 1.7 + 1.7 = 3.4 kcal/mol. The ee chair has no axial group, but its two methyls sit on neighboring carbons. Look down the C1–C2 bond and they are 60° apart. That is the gauche interaction of butane, carried onto the ring, and it costs 0.9 kcal/mol. In the aa chair the methyls are 180° apart (anti), so they do not touch.
Result. The ee chair wins by 3.4 − 0.9 = 2.5 kcal/mol, roughly 70:1. The measured value is 2.7. Plain A-value addition would have said 3.4, so the gauche correction is what brings the estimate close to the measurement.
Faces. Cis means the same face, so put both methyls up.
Place them. C1 and C3 have the same axial direction, so two groups on the same face are either both axial or both equatorial, never one of each. That gives an ee chair and an aa chair.
The ee chair. Neither methyl is axial, so its penalty is 0. There is no gauche correction either, because the methyls are not on neighboring carbons.
The aa chair. C1, C3 and C5 all have axial bonds pointing up, so both methyls and the axial hydrogen on C5 share the upper face. The two methyls sit side by side, much closer together than a gauche pair, and this contact costs about 3.7 kcal/mol. It is called a syn-pentane interaction. The two methyls are the ends of a five-carbon chain, CH₃–C1–C2–C3–CH₃, and the chair holds those ends side by side on the same side of the chain; syn means “same side”, as in the syn form in Newman projections.
Add it up. Plain A-value addition would charge 1.7 + 1.7 = 3.4 kcal/mol. That sum assumes each axial methyl has two axial hydrogens beside it. Here each methyl has only one, on C5, and the other neighbor is the second methyl. An axial methyl's 1.7 comes from its two hydrogen contacts, about 0.9 each, as in Axial/equatorial. The 3.7 contact replaces one of those per methyl, so the aa chair's real total is 3.7 + 0.9 + 0.9 ≈ 5.5 kcal/mol.
Result. The ee chair wins by about 5.5 kcal/mol, so cis-1,3-dimethylcyclohexane is almost entirely diequatorial.
The table collects the two corrections. Add the A-values first. Then check the drawing for either pattern. For a gauche pair, add 0.9. For a syn-pentane pair, leave out those two groups’ A-values. Instead, count 3.7 for the pair and 0.9 for each hydrogen contact the two groups still have.
| Direct interaction | Where it appears | Cost (kcal/mol) |
|---|---|---|
| CH₃/CH₃ gauche | neighboring carbons, both equatorial or one axial and one equatorial | 0.9 |
| CH₃/CH₃ 1,3-diaxial (syn-pentane) | two axial groups on the same face, on C1 and C3 | 3.7 for the pair, plus 0.9 for each remaining hydrogen contact, in place of the two A-values |
Comparing a cis isomer with its trans isomer
Both methyls are on the upper face, so, as shown above, one is axial and one equatorial in either chair.
In one chair the C1 methyl is axial and the C2 methyl is equatorial. In the other it is the reverse. Each chair pays 1.7 kcal/mol for its axial methyl. Each also pays 0.9 for a gauche contact, because an axial and an equatorial group on neighboring carbons are 60° apart too. Both chairs total 2.6 kcal/mol.
The two chairs are equal in energy, so each holds half the molecules, and the molecule always carries one axial methyl it cannot get rid of.
That makes the cis isomer less stable than the trans isomer. The trans isomer's best chair carries only its 0.9 gauche contact, so the gap is about 2.6 − 0.9 = 1.7 kcal/mol, and the measured difference is close to 2. The two compounds have the same formula and the same connections, and differ only in which face one methyl is on. Even so, the difference shows up in their heats of combustion (see Cyclohexanes): when burned completely, the cis isomer releases more heat.
What carries forward
Looking ahead (nothing on this page depends on this section): which chair a molecule sits in also decides what it can do, because a reaction can only happen if the molecule can reach the shape its mechanism needs. The E2 reaction in Substitution & Elimination makes a C=C double bond by removing an H and a second group from neighboring carbons. It needs those two to be anti-periplanar, the 180° arrangement from Newman projections. On a cyclohexane ring that means both must be axial. So the chair analysis on this page decides how fast an elimination on a ring goes and which alkene it gives.
The same question returns later, wherever geometry controls a reaction: the one-step substitution in Substitution & Elimination, where the incoming group must arrive on the side opposite the departing one, and the opening of three-membered rings fused to a cyclohexane in Alkenes & Alkynes and Alcohols, Ethers & Related Chemistry, which puts the two new groups trans and diaxial. When a reaction's outcome seems arbitrary, check whether the molecule can physically reach the geometry its mechanism requires.