Conformations of Ethane

Although the carbon-carbon bond in ethane, $\text{H}_3\text{C--CH}_3$, is drawn as a single line,

the two $\text{CH}_3$ groups are free to rotate about that sigma bond, because a sigma bond is

cylindrically symmetric about its axis and rotating one end does not break the orbital overlap

that holds the bond together. As the molecule rotates about the $\text{C1--C2}$ axis it passes

through an infinite number of spatial arrangements called conformations (or conformers), which

are not different compounds -- they interconvert too rapidly at room temperature to be isolated --

but do differ in potential energy.

The two extreme, most useful conformations are best seen in a Newman projection, in which the

molecule is viewed end-on along the $\text{C1--C2}$ bond: the front carbon's three hydrogens are

drawn as lines meeting at the centre, and the back carbon's three hydrogens are drawn as lines

meeting at the circumference of a circle behind it. In the staggered conformation the back

hydrogens sit exactly between the front hydrogens, at a dihedral (torsional) angle of $60^\circ$

to their nearest front hydrogen; in the eclipsed conformation the back hydrogens sit directly

behind the front hydrogens, dihedral angle $0^\circ$.

The staggered conformation is lower in energy -- and therefore more stable and more populated --

than the eclipsed conformation, by about $12.5\ \text{kJ mol}^{-1}$ (the rotational barrier of

ethane). This energy difference is attributed to torsional strain: in the eclipsed form the

carbon-hydrogen bonding electron pairs on the front and back carbons are forced close together

(directly opposite one another), and the resulting electron-electron repulsion destabilises the

molecule relative to the staggered form, where each front C--H bond points into the gap between

two back C--H bonds and electron-pair repulsion is minimised. As the molecule rotates from

staggered to eclipsed and back, six eclipsed and six staggered arrangements alternate every full

$360^\circ$ turn, producing a periodic potential-energy curve with maxima at the eclipsed

angles ($0^\circ, 120^\circ, 240^\circ$) and minima at the staggered angles

($60^\circ, 180^\circ, 300^\circ$).

Because the barrier is so small compared with the thermal energy available at room temperature,

rotation about the $\text{C--C}$ bond is essentially free and rapid (billions of times per …