Conformational

A Newman projection looks directly along a chosen C–C bond. The front carbon is represented by a dot (or vertex), and its three bonds radiate outward like spokes. The back carbon is represented by a large circle, and its three bonds also radiate from the circle's edge. The angle between a front-carbon bond and a back-carbon bond, measured clockwise from the front, is the dihedral (torsional) angle (ω). This angle completely defines a conformer.

In the staggered conformation of ethane (ω = 60°), each H on the front carbon bisects the H–C–H angle of the back carbon. Electron clouds of C–H bonds are maximally separated, minimising torsional strain. The molecule is at an energy minimum. In the eclipsed conformation (ω = 0°), front and back H atoms perfectly overlap in the Newman projection. Torsional strain raises the energy by approximately 12 kJ mol⁻¹ (the rotational barrier of ethane). There is only one type of staggered and one type of eclipsed conformer for ethane because all substituents are identical (H).

Butane is viewed along the C2–C3 bond. With two methyl groups (CH₃) and two H atoms on the relevant carbons, four distinct conformers emerge as the molecule rotates through 360°: (1) Anti (ω = 180°) — the two CH₃ groups are directly opposite each other; this is the most stable conformer because steric and torsional strain are minimised. (2) Gauche (ω = 60° or 300°) — the two CH₃ groups are 60° apart; approximately 3.8 kJ mol⁻¹ higher in energy than anti due to gauche (steric) interaction. (3) Eclipsed-methyl/H (ω = 120° or 240°) — one CH₃ eclipses an H; about 16 kJ mol⁻¹ above anti. (4) Fully eclipsed (ω = 0°) — both CH₃ groups eclipse each other; the highest-energy conformer at ~19 kJ mol⁻¹ above anti due to severe steric and torsional strain. The energy profile across one full rotation forms a periodic curve with alternating minima (anti, gauche) and maxima (eclipsed forms).

A planar cyclohexane ring would force all C–C–C bond angles to 120°, far from the ideal tetrahedral 109.5°, and would place all adjacent H atoms in eclipsed positions — a doubly unfavourable situation. Instead, cyclohexane puckers out of the plane to relieve both angle strain and torsional strain. The chair conformation (energy minimum) has all C–C–C angles at ~111°, all adjacent C–H bonds perfectly staggered, and zero torsional strain. Each carbon bears one axial bond (pointing straight up or down, parallel to the ring axis) and one equatorial bond (pointing outward at ~109.5° from axial, roughly in the plane of the ring). The boat conformation places four carbons in a plane with two 'prow' carbons above and below; it retains angle strain relief but reintroduces torsional strain along the four 'side' C–C bonds and adds a severe steric clash ('flagpole' interaction) between the two prow hydrogens separated by only ~180 pm. The boat is ~27 kJ mol⁻¹ less stable than the chair.

When a substituent larger than H is present, it strongly prefers the equatorial position to avoid 1,3-diaxial interactions — steric clashes with the two axial H atoms two carbons away on the same face of the ring. For methylcyclohexane, the equatorial methyl conformer is ~7.3 kJ mol⁻¹ more stable than axial, giving >95% equatorial at room temperature. Bulkier groups (e.g., tert-butyl, ~22 kJ mol⁻¹ preference) lock the ring almost entirely in one chair conformation. Ring-flip (chair-to-chair interconversion) swaps all axial bonds to equatorial and vice versa; the more stable conformer is the one placing the largest group equatorial.

• \Delta G^\circ — Standard Gibbs free energy difference (kJ mol⁻¹): Energy difference between the two conformers; negative value means the lower-energy conformer is favoured.
• R — Universal gas constant (J mol⁻¹ K⁻¹): 8.314 J mol⁻¹ K⁻¹; links energy to temperature scale.
• T — Absolute temperature (K): Temperature in kelvin; higher temperature increases population of higher-energy conformers.
• K_{eq} — Conformational equilibrium constant (dimensionless): Ratio of the population of the more stable conformer to the less stable conformer at equilibrium.

Problem. Methylcyclohexane has ΔG° = –7.3 kJ mol⁻¹ favouring the equatorial methyl conformer. Calculate the percentage of molecules in the equatorial conformation at 298 K.

Answer. Approximately 95% of methylcyclohexane molecules adopt the equatorial chair conformation at 298 K.

• Structural Isomerism — Conformational isomers are a subset of the broader category of isomerism; understanding how structural isomers differ in connectivity provides essential context for why conformers — with identical connectivity — are classified separately.
• Geometric (Cis-Trans) Stereoisomerism — Geometric isomerism, like conformational isomerism, involves different spatial arrangements of the same atoms, but geometric isomers cannot interconvert without bond breaking, making the distinction between the two types fundamental to organic chemistry.
• Sigma and Pi Bonds — Conformational rotation occurs exclusively around sigma bonds; understanding that sigma bonds allow free rotation while pi bonds prevent it explains why conformational isomerism arises in alkanes but not in alkenes.
• Gibbs Free Energy and Equilibrium — The relative populations of different conformers at equilibrium are governed by ΔG°, making thermodynamic principles essential for quantitatively predicting conformational preferences.