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Organic Chemistry I · Conformations

Chair conformation practice problems, with answers

Cyclohexane spends almost all its time in a chair shape, and the chair flips back and forth fast at room temperature. Every flip swaps axial and equatorial positions. The one big idea: a substituent is happier equatorial, because axial groups crowd the axial hydrogens two carbons away, and the bigger the group, the stronger the preference.

Already know the basics? Jump to the 8 practice questions or the worked examples.

Axial, equatorial, and the ring flip

Each of the six ring carbons has one axial and one equatorial position: six of each. Axial bonds point straight up or down, parallel to the ring's axis, and they alternate around the ring. Equatorial bonds point outward around the ring's "equator."

Axial and equatorial bonds on a cyclohexane chairA chair cyclohexane viewed at an angle from above. Every carbon has one vertical axial bond, labeled a, and one equatorial bond, labeled e, that points outward around the ring. The axial bonds alternate up and down around the ring.aeaeaeaeaeae
Every ring carbon has one axial bond (a, straight up or down) and one equatorial bond (e, pointing out around the ring). Going around the ring, the axial bonds alternate up, down, up. On each carbon the equatorial bond tilts slightly opposite to its axial bond. The drawing is a projection of real chair geometry, so equatorial bonds run parallel to ring bonds one carbon away.

A ring flip turns one chair into the other. Every axial group becomes equatorial and every equatorial group becomes axial. What does not change: which face of the ring a group is on. A group pointing up stays up, so a cis compound stays cis. The barrier to flipping is only about 45 kJ/mol, so at room temperature the two chairs interconvert rapidly.

An axial group bumps into the axial hydrogens on the carbons two positions away (1,3-diaxial interactions). For methylcyclohexane that costs 7.6 kJ/mol, so about 95% of the molecules have the methyl equatorial at any moment. A tert-butyl group costs about 22.8 kJ/mol axial, so it stays equatorial essentially all the time. Chemists say it "locks" the ring.

Cis/trans on a chair: the pattern table

For two groups on a ring, cis means both on the same face (both up or both down) and trans means opposite faces. Because axial bonds alternate up and down, the same cis or trans isomer can look different depending on the spacing. Memorize this table or rebuild it from the alternating up/down rule.

Axial (a) and equatorial (e) options for each disubstituted cyclohexane
Patterncistrans
1,2(a,e) or (e,a)(e,e) or (a,a)
1,3(e,e) or (a,a)(a,e) or (e,a)
1,4(a,e) or (e,a)(e,e) or (a,a)
  1. Find the pattern. Use the table to list both chairs.
  2. If one chair is (e,e) and the other (a,a), the diequatorial chair wins.
  3. If both chairs are one-axial, one-equatorial, put the bigger group equatorial. Same groups: the two chairs are equal in energy.
  4. Comparing isomers? The isomer that can put both groups equatorial is usually the more stable one.

Worked examples

Example 1: methylcyclohexane

Which chair of methylcyclohexane is favored, and by how much?

  1. Axial methyl: it has two 1,3-diaxial interactions, one with the axial H on each of C3 and C5. OpenStax lists 3.8 kJ/mol per H–CH₃ interaction, so 2 × 3.8 = 7.6 kJ/mol.
  2. Equatorial methyl: it points away from the ring, with no 1,3-diaxial interactions.
  3. Population: a 7.6 kJ/mol difference at room temperature gives an equilibrium ratio of about 21:1, or about 95% equatorial.

Answer: the equatorial chair, by 7.6 kJ/mol; about 95% of molecules have the methyl equatorial.

Example 2: trans-1,2-dimethylcyclohexane

Draw both chairs and decide which one dominates.

  1. Pattern: trans-1,2 gives (e,e) or (a,a).
  2. Diaxial chair: each axial methyl has two 1,3-diaxial interactions with H, so 4 × 3.8 = 15.2 kJ/mol.
  3. Diequatorial chair: no 1,3-diaxial interactions, but the two adjacent methyls are gauche to each other, which costs about 3.8 kJ/mol.
  4. Difference: 15.2 − 3.8 = 11.4 kJ/mol in favor of (e,e).

Answer: the diequatorial chair, by about 11.4 kJ/mol. The compound is almost entirely in that chair.

Example 3: cis-1-tert-butyl-4-chlorocyclohexane

Which group ends up axial in the favored chair?

  1. Pattern: cis-1,4 gives (a,e) or (e,a). One group must be axial in either chair.
  2. Chair with axial Cl: 2 × 1.0 = 2.0 kJ/mol.
  3. Chair with axial tert-butyl: 2 × 11.4 = 22.8 kJ/mol.
  4. Difference: 22.8 − 2.0 = 20.8 kJ/mol, so tert-butyl stays equatorial.

Answer: the chair with chlorine axial and tert-butyl equatorial, favored by about 20.8 kJ/mol.

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Chair pattern tool

Pick a disubstituted cyclohexane. The tool lists the axial/equatorial pattern for both chairs and estimates each chair's 1,3-diaxial strain from OpenStax Table 4.1 (each value doubled, since an axial group meets two axial hydrogens).

Practice questions

Pick an answer, then check it. A wrong answer tells you what went wrong, so you can try again. Every question also has a full solution.

Question 1On a cyclohexane chair, C1 has its axial bond pointing up. Which way does the axial bond on C2 point?

Show solution

All six axial bonds are parallel to the ring's axis, and they alternate: up on C1, down on C2, up on C3, and so on. So C1, C3, C5 have axial-up bonds and C2, C4, C6 have axial-down bonds.

Question 2A methyl group is axial and points up. After a ring flip, where is it?

Show solution

A ring flip rotates around C–C bonds without breaking any. Each axial group becomes equatorial and vice versa, but a group on the top face stays on the top face. So the axial-up methyl becomes equatorial, tilted slightly up.

Question 3Which statement about trans-1,3-dimethylcyclohexane is correct?

Show solution

On C1 and C3, the axial bonds point the same way (both up, say). Trans means one group up and one down, so one group is axial and the other is equatorial. The ring flip swaps them, giving another (a,e) chair. With identical groups, both chairs have one axial methyl (7.6 kJ/mol), so they're equal in energy.

Question 4What is the most stable chair of cis-1,3-dimethylcyclohexane?

Show solution

On C1 and C3, the two axial bonds point the same way. Cis means same face, so the groups are both axial or both equatorial. Ring flip connects (e,e) and (a,a). The diequatorial chair has no 1,3-diaxial interactions, while the diaxial one has a severe methyl–methyl clash plus methyl–H interactions. Diequatorial wins by a lot.

Question 5Which is more stable, cis- or trans-1,4-dimethylcyclohexane?

Show solution

Trans-1,4: (e,e) or (a,a). Its best chair has both methyls equatorial, with no 1,3-diaxial strain. Cis-1,4: (a,e) or (e,a). Either chair has one axial methyl, about 7.6 kJ/mol. So trans-1,4-dimethylcyclohexane is more stable by roughly 7.6 kJ/mol.

Question 6In the favored chair of trans-1-tert-butyl-3-methylcyclohexane, where are the two groups?

Show solution

Trans-1,3 means one group axial and one equatorial in each chair. The options are tert-butyl axial (about 22.8 kJ/mol) or methyl axial (about 7.6 kJ/mol). The chair with the methyl axial wins by about 15 kJ/mol, so tert-butyl stays equatorial.

Question 7OpenStax lists 4.6 kJ/mol of strain for each 1,3-diaxial interaction between an isopropyl group and a hydrogen. How much strain does an axial isopropyl group add to cyclohexane?

Show solution

An axial group on C1 sits near the axial hydrogens on C3 and C5, which point the same way. That's two interactions: 2 × 4.6 = 9.2 kJ/mol. Compare methyl (7.6) and tert-butyl (22.8).

Question 8How do the two chairs of cis-1,2-dimethylcyclohexane compare?

Show solution

Cis-1,2: (a,e) or (e,a). Each chair has one axial methyl (two 1,3-diaxial interactions, 7.6 kJ/mol) and a gauche interaction between the adjacent methyls (3.8 kJ/mol). OpenStax totals this as 3 × 3.8 = 11.4 kJ/mol for each chair. Same strain, so the two chairs are equally populated.

Answer key

  1. B, down: axial bonds alternate up and down.
  2. A, equatorial and still up: flips change a/e, never the face.
  3. D, (a,e) and (e,a), equal energy.
  4. C, diequatorial: cis-1,3 is (e,e) or (a,a).
  5. B, trans: only trans-1,4 can be diequatorial.
  6. D, tert-butyl equatorial, methyl axial: tert-butyl locks the ring.
  7. B, 9.2 kJ/mol: two 1,3-diaxial interactions.
  8. B, equal: both chairs are (a,e).

Frequently asked questions

Why is equatorial more stable than axial?

An axial group points straight up or down, right next to the axial hydrogens on the carbons two positions away. Those 1,3-diaxial interactions are steric strain. An equatorial group points outward, away from the ring, so it avoids them.

Does a ring flip change cis to trans?

No. A ring flip only rotates bonds, so every group stays on the same face of the ring. Axial and equatorial swap, but cis stays cis and trans stays trans.

What does it mean that tert-butyl locks the ring?

An axial tert-butyl group costs about 22.8 kJ/mol of strain, so the chair with tert-butyl equatorial is overwhelmingly favored. Chemists use tert-butyl to hold a ring in one chair so they can study a second group in a fixed axial or equatorial position.

Are chair conformations on the MCAT?

Conformations of cyclohexane, including axial versus equatorial positions, are standard organic content and can appear in MCAT passages. Detailed strain calculations are less likely. Check the current AAMC content outline for the exact topic list.

Sources

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