Question

The energy barrier for rotation about the \(\mathrm{C}-\mathrm{C}\) bond in ethane is about \(3 \mathrm{kcal}\), which suggests that the energy required to bring one pair of hydrogen into an eclipsed arrangement is 1 kcal. Calculate how many kilocalories the planar form and extreme boat form of cyclohexane are likely to be unstable relative to the chair form on account of \(\mathrm{H}-\mathrm{H}\) eclipsing and flagpole interactions.

Short answer

The planar form of cyclohexane is likely to be unstable by \(3 \mathrm{kcal}\) and the boat form by \(6 \mathrm{kcal}\) relative to the chair form when considering H-H eclipsing and flagpole interactions.

Step-by-step solution

Identify the number of H-H eclipsing interactions in each conformation

Assuming the planar conformation for cyclohexane, the H-H eclipsing interactions would be for every adjacent hydrogens with bond stability of 1 kcal. In a hexagon, there are a total of 6 hydrogen atoms, but since each H-atom participates in 2 interaction, therefore, there would be 3 distinct H-H eclipsing interactions in planar cyclohexane. For the chair conformation, there are no H-H eclipsing interactions since the atoms are staggered, making it more stable than the planar conformation. In the boat conformation, there are 4 H-H eclipsing interactions between hydrogen atoms 1 - 2, 2 - 3, 4 - 5, and 5 - 6 and 2 flagpole interactions between hydrogen atoms 1 - 4 and 3 - 6.

Calculate the instability of the planar and boat forms relative to the chair form

As the chair form doesn't have any H-H eclipsing and flagpole interactions, we simply need to calculate the energy difference between the other 2 forms and chair form. Since we are given an energy barrier of 1 kcal for each H-H eclipsing interaction: In the planar form, there are 3 H-H eclipsing interactions giving a total of \(3\times 1\mathrm{kcal} = 3 \mathrm{kcal}\) of interaction energy. In the boat form, there are 4 H-H eclipsing interactions and 2 flagpole interactions giving a total of \(4 \times 1 \mathrm{kcal} + 2 \times 1 \mathrm{kcal} = 6 \mathrm{kcal}\) of interaction energy.

Present the results

In conclusion, the planar form of cyclohexane is likely to be unstable by \(3 \mathrm{kcal}\) and the boat form by \(6 \mathrm{kcal}\) relative to the chair form when considering H-H eclipsing and flagpole interactions.

Key concepts

Energy Barrier

The concept of the energy barrier is crucial when studying the conformations of cyclohexane, as it affects how easily one conformation can transition to another.
This energy barrier is the amount of energy required to rotate around a bond, like the \(\mathrm{C}-\mathrm{C}\)bond in ethane, where the barrier is about \(3\,\mathrm{kcal}\).
For cyclohexane, the difference in energy between its various forms sets the stage for understanding their stability.
When considering different conformations, such as the planar and boat forms compared to the chair form, we must take into account the interactions that contribute to the energy barrier.
These conformations have specific interactions like H-H eclipsing and flagpole interactions, which increase their energy levels, making them less stable.
The chair form, with no such interactions, is the most stable, acting like a baseline for comparing other conformations.

H-H Eclipsing Interactions

H-H eclipsing interactions occur when hydrogen atoms from neighboring carbon atoms align in such a way that they overlap. This overlap creates tension, because the electron clouds of the hydrogens are repelling each other.
This repulsion contributes to the increased energy levels seen in some conformations of cyclohexane, like the planar and boat forms.
In cyclohexane, the chair form is free of these interactions because it is staggered, meaning atoms are placed diagonally across from one another, minimizing direct overlap.
In contrast, the planar form experiences three H-H eclipsing interactions, each contributing 1 kcal to the overall energy of the molecule.
Meanwhile, the boat form sees four such interactions, resulting in extra energy that accounts for its instability when compared to the chair conformation.
These interactions serve as a fundamental explanation for why the chair form is energetically favorable, without these energy-consuming overlaps.

Flagpole Interactions

In cyclohexane's boat conformation, flagpole interactions occur between hydrogen atoms that are positioned at the bow and stern of the "boat." These hydrogens are often forced into close proximity, resulting in significant steric strain.
The two flagpole interactions in cyclohexane's boat form are akin to points where these hydrogen atoms push against each other, causing instability.
Each flagpole interaction contributes to the heightened energy level of the boat conformation.
This is because the hydrogen atoms at these positions are closer than in the more favorable chair form, creating additional repulsive forces.
Like H-H eclipsing interactions, flagpole interactions are another reason why the chair form is preferred in terms of energy.
By understanding these interactions, students can appreciate why certain conformations are naturally more stable due to reduced internal stress from overlapping or crowded atoms.