D12.4 Energy and Isomerism

The energy needed for rotations about a single bond is relatively small because the molecular orbital of a σ covalent bond has cylindrical symmetry along the internuclear axis (Section: Molecular Orbital (MO) Diagram, Section: Formation of a Sigma Bond). This cylindrical symmetry means that regardless of how two σ-bonded atoms are rotated with respect to each other around the internuclear axis, the σ bond remains unbroken between them.

Therefore, most of the energy needed are for overcoming the increased electron-electron repulsions between the substituents bonded to the two atoms when they get closer to each other. For example, consider the rotation around the C-C single bond in 1,2-dichloroethane:

Figure: Rotation around the C-C bond in 1,2-Dichloroethane. Energy (indicated by the readout and the green dot on the graph) varies with angle of rotation. Expanding the animation to full screen makes the graph easier to see. You can pause the video and adjust to various angles of rotation to find the corresponding energy. (Animation by Michael Aristov.)

The three maxima in energy (top of the hill) correspond to when C-H or C-Cl bond on one carbon is spatially close to the C-H or C-Cl bond on the other carbon due to the rotation angle. (The highest energy point correspond to when the two C-Cl bonds are closest.)

Notice in the above figure that complete 360° rotation around the C–C bond requires an energy input of 40 kJ/mol. This means that at room temperature, it will only take 2 μs (2 × 10-6 seconds) for half of a sample of 1,2-dichloroethane to rotate fully about the C-C bond. Therefore, if you could see all the molecules in a room-temperature sample of 1,2-dichloroethane at a specific instant in time, you would find all three of these structures:

Each structure corresponds to one of the minima (bottom of the valley) in the energy curve in the figure above. If, instead, you followed one molecule over time, you would see it go from one structure to the next in microseconds as the C-C bond rotates (as seen in the animation in the figure). There is no way to separate one structure from the others at room temperature, hence they are all conformers of the same molecule. You can draw any of them as a representation of 1,2-dichlororethane.

In contrast to bond rotation, the average bond enthalpy of a C–C single bond is 346 kJ/mol. If we imagine a 1,2-dichloroethane molecule simply falling apart into two equal pieces, breaking at the C-C bond, it would need an energy input of 346 kJ/mol. This means that at room temperature, it will take 1 × 1040 years, much longer than the lifetime of our universe, for half of a sample of 1,2-dichloroethane to have its C-C bond broken.

For the simpler ethane molecule (H3C-CH3), the energy needed for C-C bond rotation is lower, only 12.1 kJ/mol. Hence, ethane’s C-C bond rotation happens faster, needing only 30 ps (30 × 10-12 seconds) for half of a sample of ethane to change conformation. (These reaction time scale considerations will be delved into in detail later on in our course.) While the exact energy requirement for rotation about a single bond will vary depending on the groups bonded to the two atoms, in general, the timescale for rotation about a single bond is short enough that conformers cannot be separated from each other.

 

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Chemistry 109 Fall 2021 by John Moore, Jia Zhou, and Etienne Garand is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.