Torsional Strain and the Energy Profile of Ethane

Introduction

Ethane rotates around its C–C single bond, but the motion is not energetically flat. A graph of energy against H–C–C–H dihedral angle displays alternating high eclipsed and low staggered arrangements. The difference, about 12 kJ mol⁻¹ for ethane, is called the rotational barrier.

Core explanation

In a staggered Newman projection, the bonds of the rear carbon sit between the bonds of the front carbon, with a nearest H–C–C–H dihedral angle of 60°. In an eclipsed projection, front and rear C–H bonds align at 0°. The eclipsed geometry has greater torsional strain and is approximately 12 kJ mol⁻¹ higher than the staggered minimum. Start a potential-energy graph at 0° with an eclipsed maximum; it falls to a staggered minimum at 60°, rises to the next eclipsed maximum at 120°, and repeats at 180°, 240°, 300° and 360°. Because ethane has three equivalent hydrogens on each end, all staggered minima have equal energy and all eclipsed maxima have equal energy. The approximate barrier is small enough that ethane rotates readily at ordinary temperature; it is not a bond dissociation energy. The physical explanation involves repulsion and electronic stabilisation that depend on orbital alignment. For introductory analysis it is sufficient to associate eclipsing with increased torsional strain, while recognising that a detailed quantum-chemical energy decomposition is more nuanced. The graph describes an energy landscape, not a sequence of new molecular formulas or separate bottled compounds.

Step-by-step reasoning

Draw a Newman projection at 0° and label it eclipsed. Rotate only the rear carbon in 60° increments, classifying each arrangement. Mark maxima at 0°, 120° and 240° and minima at 60°, 180° and 300°. Draw a smooth periodic curve and label the vertical difference of roughly 12 kJ mol⁻¹.

Visual explanation

Imagine six equally spaced marks around a circle representing rear rotation. Alternate a red high point for bond alignment and a blue low point for bond offset. Unroll the circle into a horizontal angle axis from 0° to 360° to produce the wave-shaped energy profile.

Real-world analogy

A three-bladed fan passes the blades of a second fan. When blades align in the viewing direction, the arrangement is crowded; halfway between those positions it is more open. The analogy tracks periodic geometry, not actual collisions between atoms.

Real-world example

Chemists use conformational energy profiles to predict which molecular shapes a reactant occupies before a reaction. Ethane is a calibration example: its regular threefold profile teaches how to read the more complicated profiles of butane and substituted chains.

Why?

The C–C sigma bond remains intact throughout rotation, so bond breaking is unnecessary. Yet adjacent bond electrons and substituents interact differently as the angle changes. The eclipsed arrangement costs energy, creating a finite barrier between staggered minima.

Common misconception

The 12 kJ mol⁻¹ barrier is not the energy required to break a C–C bond. It is only the energy needed to rotate from a staggered minimum through the eclipsed maximum while the C–C sigma bond remains present.

Worked example

Question: If staggered ethane is assigned zero relative energy, estimate the energy at 120° and classify the structure. Reasoning: With an eclipsed arrangement at 0°, each 120° rotation gives another equivalent eclipsed arrangement. Its energy is about 12 kJ mol⁻¹ above a staggered minimum. Answer: Approximately +12 kJ mol⁻¹; the geometry is eclipsed.

Quick check

1. Which ethane conformation lies at a local energy minimum? Answer: A staggered conformation, with adjacent C–H bonds offset by 60°.

Exam focus

On the plot, label the axes and identify maxima, minima, periodicity and barrier height. Avoid drawing a monotonic rise with angle: equivalent geometries recur every 120° because of ethane's threefold symmetry.

Advanced insight

The measured or calculated barrier depends slightly on the method and conditions, so 12 kJ mol⁻¹ is an approximate teaching value. The population of high-energy eclipsed geometries is smaller, but rapid passage through them enables continual interconversion among equivalent staggered arrangements.

Summary

Ethane's potential energy oscillates as it rotates: eclipsed structures at 0°, 120° and 240° are higher, staggered structures at 60°, 180° and 300° are lower. The approximate 12 kJ mol⁻¹ gap is a rotational barrier associated with torsional strain, not a C–C bond-breaking energy.

Practice questions

1. At what dihedral angle is ethane eclipsed if the nearest front and rear C–H bonds align? Answer: At 0°; equivalent eclipsed forms recur after 120° rotations.

2. Where is a staggered minimum between 0° and 120°? Answer: At 60°, halfway between the eclipsed positions.

3. If the staggered minimum is zero, what approximate energy is the eclipsed maximum? Answer: About +12 kJ mol⁻¹ relative to the minimum.

4. Why are there three identical maxima over one full ethane rotation? Answer: Each carbon has three equivalent hydrogens, so bond alignment repeats every 120°.