Rotation about a single bond: conformations

A bond that can turn

Think of a door on its hinge. The door turns about the hinge pin, and nothing breaks. A C-C single bond behaves in the same way. Its electron cloud is the same all round the line joining the two nuclei, so the group at one end can turn against the group at the other.

Because of this turning, one molecule can have many shapes. The shapes that come from turning about a single bond are called conformations, or conformers. They are not different compounds. At room temperature they change into each other so fast that you cannot separate them.

Two ways to draw them

A Newman projection looks straight along one C-C bond. The carbon nearest to you is a point, where its three bonds meet. The carbon behind it is a circle. Its three bonds start at the edge of the circle.

A sawhorse projection looks at the bond from a little above and to one side. The C-C bond is a slanted line, with three bonds drawn at each end.

The angle between a bond on the front carbon and a bond on the back carbon, seen in a Newman projection, is the dihedral angle. It is also called the torsional angle.

Ethane

Ethane has two extreme conformations.

• Staggered. Each hydrogen of the back carbon lies between two hydrogen atoms of the front carbon. The dihedral angle is $60^{\circ}$. The C-H bonds are as far apart as they can be.
• Eclipsed. Each hydrogen of the back carbon is directly behind one of the front carbon. The dihedral angle is $0^{\circ}$. The C-H bonds are as close as they can be.

The eclipsed form has more energy. The bonding pairs of electrons in the nearly aligned C-H bonds repel each other. The extra energy is called torsional strain. For ethane it is about $12\ \text{kJ/mol}$.

NCERT prints $12.5\ \text{kJ/mol}$. The value measured in experiments and used in most reference books is $12\ \text{kJ/mol}$, and we use it here.

Is this a big barrier? Compare it with the thermal energy at room temperature, $RT = 8.314 \times 298\ \text{J/mol} = 2.5\ \text{kJ/mol}$. Collisions at room temperature supply energy of this size easily. So the rotation goes on all the time. It is nothing like the $347\ \text{kJ/mol}$ needed to break the C-C bond.

One full turn passes through three staggered forms and three eclipsed forms, because the three hydrogen atoms are alike. So the curve repeats every $120^{\circ}$.

Butane

Now look along the bond between carbon 2 and carbon 3 of butane. Each of these carbons carries one methyl group and two hydrogen atoms. The dihedral angle that matters is the one between the two methyl groups. There are four kinds of conformation.

• Anti ($180^{\circ}$). The methyl groups are as far apart as possible. This is the most stable form. We take its energy as zero.
• Gauche ($60^{\circ}$). The methyl groups are staggered but close. The energy is $3.8\ \text{kJ/mol}$ higher. The methyl groups crowd each other, which is called steric strain.
• Eclipsed ($120^{\circ}$). A methyl group is behind a hydrogen atom, and the other pairs also eclipse. The energy is $16\ \text{kJ/mol}$.
• Fully eclipsed ($0^{\circ}$). The two methyl groups are right behind each other. This is the least stable form, at $19\ \text{kJ/mol}$.

The order of stability is therefore

You can build these numbers from three small costs for each pair of eclipsed bonds. H with H costs $4\ \text{kJ/mol}$, H with $\text{CH}_{3}$ costs $6\ \text{kJ/mol}$, and $\text{CH}_{3}$ with $\text{CH}_{3}$ costs $11\ \text{kJ/mol}$. Ethane, eclipsed, has three pairs of H with H, which gives $3 \times 4 = 12\ \text{kJ/mol}$. In the fully eclipsed butane there is one pair of methyl groups and two pairs of H with H, which gives $11 + 2 \times 4 = 19\ \text{kJ/mol}$.

How many molecules are in each form

The share of molecules in a form of energy $E$ above the lowest, compared with the lowest, is the Boltzmann factor $e^{-E/RT}$. The gauche form has a mirror form, so we count two of them. At $298\ \text{K}$ this gives about 70 per cent anti and 30 per cent gauche. The eclipsed forms hold only about a quarter of one per cent between them.

Practise with new numbers

Try it in Python

The program turns the energies of butane into percentages of molecules at one temperature.

Common mistakes

• Calling conformations isomers that can be separated. At room temperature they turn into each other too fast.
• Mixing up the dihedral angles. Staggered ethane is $60^{\circ}$ and eclipsed is $0^{\circ}$. Anti butane is $180^{\circ}$.
• Saying gauche has torsional strain. It is staggered. Its extra energy is steric strain between the methyl groups.
• Thinking the anti form is the only one present. About 30 per cent of butane molecules are gauche at room temperature.
• Using kJ with R in J. Change the energy to joules before using $RT$.

Remember these

• A single bond allows rotation. The arrangements are conformations.
• Ethane: staggered ($60^{\circ}$) is stable, eclipsed ($0^{\circ}$) is higher by about $12\ \text{kJ/mol}$ (torsional strain).
• Butane: anti $0$, gauche $3.8$, eclipsed $16$, fully eclipsed $19\ \text{kJ/mol}$.
• Number of molecules in a form is proportional to $e^{-E/RT}$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the dihedral angle between the hydrogen atoms in the staggered form of ethane?

2. Why is eclipsed ethane higher in energy than staggered ethane?

3. Which conformation of butane is the most stable, and why?

4. Why is the gauche form of butane more stable than the eclipsed form but less stable than the anti form?

5. Why can the conformations of ethane not be separated at room temperature?

References

• OpenStax Organic Chemistry (McMurry), chapter 3, the sections "Conformations of Ethane" and "Conformations of Other Alkanes".
• NCERT Chemistry, Class 11, Part II, the chapter "Hydrocarbons" (conformations of ethane).