Conformations and Stereoisomerism

Purpose

To construct and compare the energies of staggered, eclipsed, gauche, and anti conformations of ethane, butane, and 2,3-dimethylbutane using Newman projections; to investigate the chair/ring-flip equilibrium of cyclohexane with substituents of different A-values; to compare the envelope and half-chair forms of cyclopentane; and to classify six pairs of molecules as identical, constitutional isomers, or stereoisomers, with a subsequent sub-classification of the stereoisomers as conformational, geometric, enantiomeric, diastereomeric, or meso.

Theory

Rotation about a C–C single bond interconverts conformations. The energetic cost of eclipsing C–H bonds (torsional strain, ~4 kJ/mol per H–H eclipse) and of bringing large groups close in space (steric strain) sets the energy profile. For ethane, only torsional strain is present and the eclipsed–staggered difference is 12 kJ/mol; for butane, the fully-eclipsed Me–Me conformation costs ~25 kJ/mol because of additional steric strain between the two methyls. Gauche butane is ~3.8 kJ/mol above anti due to a single Me–Me gauche interaction. 2,3-Dimethylbutane has three eclipsed Me–Me pairs in the syn-periplanar conformer, raising the maximum barrier to ~33 kJ/mol.

Cyclohexane's chair is strain-free: all C–C–C angles are 109.5° and every pair of neighbouring C–H bonds is perfectly staggered. Each carbon bears one axial (vertical) and one equatorial (out-of-ring) hydrogen; a ring flip interconverts the two. Substituents prefer equatorial because an axial substituent experiences 1,3-diaxial repulsions with two axial H's on the same face. The energy cost is the A-value: 7.5 kJ/mol for methyl, 2.0 kJ/mol for chloro, 22 kJ/mol for tert-butyl.

Two molecules with the same molecular formula can be classified in one of three ways: identical (same compound), constitutional isomers (different connectivity), or stereoisomers (same connectivity, different spatial arrangement). Stereoisomers sub-divide into conformational (interconvert by rotation, not normally isolable), geometric (cis/trans, cannot interconvert without breaking a bond), enantiomers (non-superimposable mirror images), diastereomers (stereoisomers that are not mirror images), and meso compounds (have stereocentres but an internal mirror plane, so the molecule is achiral overall).

Calculations / Worked Analyses — Sample: methylcyclohexane at 25 °C

Problem: What fraction of methylcyclohexane molecules has the methyl group equatorial at 25 °C?

Given: A-value of –CH₃ = 7.5 kJ/mol = 7500 J/mol.

ΔG = −RT ln K  ⇒   ln K = −ΔG / (RT) = +7500 / (8.314 × 298) = 3.028
K = e^{3.028} = 20.66
Fraction equatorial = K / (1 + K) = 20.66 / 21.66 = 0.954
Fraction axial = 1 / (1 + K) = 1 / 21.66 = 0.046

So at room temperature about 95% of molecules have the methyl group equatorial and only 5% have it axial. This is why equatorial is drawn as the dominant conformation in all teaching representations.

Worked pair classification — (2R,3R)-tartaric acid vs (2S,3S)-tartaric acid:

Both molecules have formula C₄H₆O₆ with identical connectivity (HOOC–CH(OH)–CH(OH)–COOH).
Both have the same functional groups in the same positions, so they are not constitutional.
C2 and C3 are both stereocentres; each has a defined configuration (R or S).
The two structures differ in the configuration at both stereocentres. A mirror-image reflection of (R,R) gives (S,S).
There is no way to superimpose (R,R) onto (S,S) without breaking bonds.
Therefore (2R,3R) and (2S,3S) are enantiomers — non-superimposable mirror images.
(The third and fourth stereoisomers, (2R,3S) and (2S,3R), are actually the same compound — the meso tartaric acid — because the molecule has an internal mirror plane between C2 and C3.)

Results Table

Section I — conformation energies (kJ/mol, relative to most stable conformation of each molecule)

Section II — classification of six pairs

Section III — diene classification, stability ranking, and IUPAC naming

Stability ranking: (2E,4E)-2,4-hexadiene > 1,3-butadiene > 1,4-pentadiene > 1,2-propadiene. The conjugated dienes benefit from π-electron delocalisation; the isolated dienes do not gain or lose energy from the second C=C; the cumulated diene loses energy to sp-hybridisation strain and orthogonal π bonds.

Discussion

The Newman-projection exercise reproduced the textbook energy profiles. For ethane, the only contribution to the 12 kJ/mol barrier is torsional strain from the three pairs of eclipsed C–H bonds; the molecule has identical minima at 60°, 180°, and 300°. Butane's profile adds a steric component: the anti minimum is ~3.8 kJ/mol below each gauche minimum, and the fully-eclipsed Me–Me maximum (~25 kJ/mol) is much higher than the two Me–H eclipsed maxima (~16 kJ/mol each). 2,3-Dimethylbutane has an even larger barrier (~33 kJ/mol) because six methyl groups are involved in three simultaneous eclipsing interactions.

For cyclohexane, the ring-flip demonstration made the axial/equatorial swap tangible. Placing a methyl on an axial position and flipping the ring dropped the total strain by exactly its A-value (7.5 kJ/mol); placing a tert-butyl group showed that the larger A-value (22 kJ/mol) essentially locks the ring with t-Bu equatorial. 1,3-Diaxial interactions also make it possible to predict the favoured conformer for disubstituted rings: cis-1,2 and trans-1,3 cyclohexanes have one axial and one equatorial position regardless of flip, while trans-1,2 and cis-1,3 can place both substituents equatorial. Cyclopentane's envelope and twist forms are very close in energy and interconvert rapidly by pseudorotation, making the ring flexible rather than locked.

The classification exercise emphasised that differences in spatial arrangement alone are not enough to determine the type of isomerism: one must first check connectivity. Butane and 2-methylpropane are constitutional isomers (same C₄H₁₀, different skeletons); cis- and trans-2-butene are geometric isomers (same skeleton, but the C=C forbids interconversion); (R) and (S) 2-chlorobutane are enantiomers; (R,R) and (R,S) tartaric acid are diastereomers — and the (R,S) form, despite bearing two stereocentres, is achiral overall because of its internal mirror plane, making it the meso compound of the tartaric-acid family.

The dienes module extended these ideas to systems with two C=C bonds. Conjugated dienes (alternating single and double bonds, as in 1,3-butadiene and 2,4-hexadiene) benefit from π-electron delocalisation across all four sp² carbons, which lowers the heat of hydrogenation by ~16 kJ/mol relative to two isolated double bonds. Isolated dienes (e.g., 1,4-pentadiene and 1,5-hexadiene) behave as two non-interacting alkenes. Cumulated dienes (allenes, e.g., 1,2-propadiene) suffer from sp-hybridisation at the central carbon and from two orthogonal π bonds that cannot delocalise; they are the least stable class. The IUPAC naming exercise reinforced that E/Z descriptors must accompany every locant where geometry is defined: a diene like 2,4-hexadiene must be written as (2E,4E), (2Z,4E), (2E,4Z), or (2Z,4Z) to be fully specified.

Conclusion

Interactive Newman projections and the chair/flip viewer reproduced the known energy profiles of acyclic and cyclic alkane conformations, confirming that conformational preferences follow directly from torsional strain and 1,3-diaxial / gauche steric repulsions. The classification flowchart — identical vs constitutional vs stereo, with stereo sub-divided into conformational, geometric, enantiomer, diastereomer, and meso — successfully distinguished all six practice pairs and the four unknowns. The experiment illustrated that connectivity is the first diagnostic question for isomerism; only when connectivity is identical does one proceed to spatial comparisons, and only when the spatial comparison yields a non-superimposable mirror-image relationship does one invoke enantiomerism. Meso compounds emerge as a reminder that the presence of stereocentres does not guarantee chirality.