Picture one molecule of methylcyclohexane in a chair with its methyl group axial. A moment later, the same molecule is in its other chair, and the methyl is equatorial. No bond broke and nothing was added: the ring simply flexed. This change from one chair to the other is a ring flip, and at room temperature each molecule makes it about a hundred thousand times a second.
This page shows what a flip changes, what it leaves alone, and how to draw the result. It builds on the chair from Cyclohexanes and on the axial and equatorial positions from Axial/equatorial.
What a ring flip does
Start with cyclohexane itself. Each of its six carbons carries one axial hydrogen, pointing straight up or straight down, and one equatorial hydrogen, pointing outward around the rim. In the left chair below, the six axial hydrogens are highlighted. After the flip, those same six hydrogens are the equatorial ones, and every equatorial hydrogen becomes axial.
A ring flip is also called a chair flip. No bond breaks in a flip: the ring only twists about its C–C single bonds, the same kind of rotation that turns one Newman projection into another. All twelve positions swap: axial becomes equatorial, and equatorial becomes axial.
A flip never changes which face of the ring a group points toward. A ring has two faces, an upper one and a lower one, and moving a group from one face to the other would mean breaking a bond and making a new one. Which face a group is on is a fact about the molecule; whether it is axial or equatorial is a fact about the chair the molecule is in at the moment. A hydrogen that points up before the flip still points up after it; its bond has only turned from vertical to outward, or the reverse.
The methyl of methylcyclohexane shows this clearly. Before the flip it sits on the axial bond of C1, pointing straight up. After the flip, the axial bond of C1 points down, so the methyl ends up on the outward bond that still points up. It went from axial to equatorial and stayed on the upper face.
Faces are what cis and trans describe: two groups on the same face are cis, and two on opposite faces are trans, as Axial/equatorial set out. Since a flip keeps every face, a cis compound is still cis afterward and a trans compound is still trans. Only the axial and equatorial labels change.
Drawing the other chair
You are given the chair on the left of the figure below. The bromine on C1 is axial and points up. The methyl on C2 is equatorial and also points up. Draw the other chair and read the new labels off it.
Step 1 — Write down the faces. Br: up. CH₃: up. The faces are the only thing that carries across the flip, so record them before you draw anything.
Step 2 — Draw the ring the other way up. Draw a chair whose far-right end tips down and whose far-left end tips up. Keep the two ends where they were: C1 stays the far-right carbon, now tipped down, and C4 stays the far-left carbon, now tipped up. A plain top-to-bottom reflection would put the middle carbons in the wrong places, so place them by hand: C2 stays on the top edge next to C1, C6 stays on the lower edge next to it, and the rest follow round the same way. Numbering the other way would draw a different compound; Stereochemistry explains why.
Step 3 — Put each group back on its own face. At C1, find the bond that points up in the new chair and put the bromine on it. At C2, do the same for the methyl. Place each group by its face, not by its old label.
Step 4 — Read the labels. The upward bond of C1 is now the outward one, so the bromine is equatorial. The upward bond of C2 is now the vertical one, so the methyl is axial. Both labels changed, and both groups still point up.
Step 5 — Check. Every group should have swapped between axial and equatorial and kept its face. If a group changed face, you drew a different compound. Both groups started on the upper face, so the compound was cis, and it is still cis.
The example works because axial bonds alternate around the ring: up at C1, down at C2, up at C3, and so on. On each carbon, the equatorial bond angles the opposite way from the axial one. C2 has a downward axial bond, so its equatorial bond angles up. That is how a methyl can be equatorial and up on C2 while the bromine is axial and up on C1.
C1 and C3, with one carbon between them, share an axial direction. In the chair above both point up, so the equatorial bonds of both carbons angle down. No bond on C3 of that chair is both equatorial and pointing up. If a problem seems to need one there, a face or a number has been misread.
The same fact decides what happens to a cis-1,3 pair. In cis-1,3-dimethylcyclohexane both methyls are on the upper face. Because C1 and C3 point their axial bonds the same way, the two methyls are both axial in one chair and both equatorial in the other, never one of each.
The path between the two chairs
A flip is not a jump from one drawing to the other. Follow C1 and C4, the two ends of the chair: C1 starts as the headrest, tipped up, and C4 as the footrest, tipped down. To reach the other chair, C1 has to travel down past its neighbors, and C4 has to travel up.
The ring passes through shapes you met in Cyclohexanes. C1 moves first. Partway down, it lies level with C2, C6 and C5, and the ring is a half-chair, with those four consecutive carbons, C5, C6, C1 and C2, in one plane. Holding four carbons in one plane opens their angles and eclipses the bond in the middle of the four, so the half-chair is the most strained shape on the path.
Next the ring relaxes into a twist-boat, and it can pass through a boat, in which C1 and C4 both sit below the other four carbons. This is the same boat as in Cyclohexanes, seen with its ends pointing down. Then C4 rises in the same way, through a second twist-boat and a second half-chair, and the ring settles into the other chair.
The energies of these shapes, also from Cyclohexanes, set the height of the climb. The half-chair, about 10.8 kcal/mol above the chair, is the transition state between a chair and a twist-boat, and it is the tallest peak on the path. The twist-boat, at about 5.5 kcal/mol, is a shallow dip. The boat, at about 6.5 kcal/mol, is the small peak between the two twist-boats.
How fast the ring flips
The climb to the half-chair, about 10.8 kcal/mol, is the barrier to a flip. Newman projections showed that turning ethane's C–C bond costs only 2.9 kcal/mol.
A process slows down steeply as its barrier rises. At room temperature, every extra 1.4 kcal/mol of barrier makes it about ten times slower. The flip's barrier is about 8 kcal/mol higher than ethane's, and 8 ÷ 1.4 is nearly 6, so the flip is slower by nearly six factors of ten. The C–C bond of ethane turns some 10¹⁰ to 10¹¹ times a second, while a cyclohexane ring flips about 10⁵ times a second. The flip is roughly a million times slower, and still far too fast to watch.
Two chairs in equilibrium
Back to methylcyclohexane. Its two chairs are not equal in energy. In one, the methyl is axial and is crowded by the two axial hydrogens on its own face, the 1,3-diaxial interactions of Axial/equatorial. In the other, the methyl is equatorial and nothing crowds it. The methyl's A-value, 1.7 kcal/mol, is the energy difference between these two chairs, as Axial/equatorial measured.
Because the ring flips so fast, the two chairs are always in equilibrium, and the lower-energy chair holds more of the molecules. For methylcyclohexane, about 95% of the molecules are in the chair that has the methyl equatorial.
So "the methyl is equatorial" describes the chair that most molecules are in at any instant, not a fixed property of the molecule. Each molecule spends most of its time in the equatorial chair and a little in the axial one. Neither chair can be bottled on its own at room temperature, because each turns into the other within microseconds.
When the ring stays in one chair
Two kinds of structure hold a ring in one chair, and chemists use both on purpose.
The first is a very large substituent. Axial/equatorial showed that a tert-butyl group (A-value 4.9 kcal/mol) keeps more than 99.9% of molecules in the chair with it equatorial, which makes it a conformational anchor. The ring still flips; at any moment only about one molecule in 4,000 is in the other chair.
The second is a fused ring, and this one truly cannot flip. Two rings are fused when they share a bond, and with it two carbons. In trans-decalin, two cyclohexane rings, A and B, are fused, and the hydrogens on the two shared carbons point to opposite faces. As a result, ring B joins ring A through two equatorial bonds.
Now try to flip ring A. Its two equatorial bonds to ring B would become axial. On neighboring carbons, axial bonds point in opposite directions, one straight up and one straight down, 180° apart. The two carbons left in ring B cannot bridge ends that far apart, so the flip cannot happen and the system is rigid.
Steroids, such as cholesterol and many hormones, are built on four fused rings, most of them trans-fused (like trans-decalin). That is why a steroid has one fixed three-dimensional shape, and why the shape can fit so precisely into a receptor, the protein in the body that the hormone binds to.
Common questions
What is a ring flip in organic chemistry? A ring flip, also called a chair flip, is the change of a cyclohexane ring from one chair to the other. No bond breaks: the ring only twists about its C–C single bonds. At room temperature each molecule flips about a hundred thousand times a second.
What changes in a ring flip? Every axial position becomes equatorial and every equatorial position becomes axial, hydrogens included. No group changes face, so a cis compound stays cis and a trans compound stays trans.
What is a simple ring flip example? In methylcyclohexane, a methyl that is axial and points up before the flip is equatorial after it, and it still points up.
What carries forward
The next page, Conformational analysis, compares the two chairs of rings with several substituents and picks the lower-energy one. That comparison only matters because the ring can reach both chairs.
Looking ahead: on a ring, the E2 reaction (Substitution & Elimination) needs its leaving group axial. A ring whose favored chair holds that group equatorial can still react, because it flips into the less favored chair, where the group is axial. A strong preference for the other chair does not stop this, but it makes the reaction slower, because fewer molecules are in the right chair at any moment.