Question

There is free rotation about the carbon-carbon \(\sigma\) -bond in ethane. This means that the energy difference between the staggered and eclipsed conformers is: (a) \(3 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(23 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(13 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(17 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Short answer

The energy difference is approximately \(13 \mathrm{~kJ} \mathrm{~mol}^{-1}\), so the answer is (c).

Step-by-step solution

Understand Ethane's Bond Rotation

In ethane, the rotation about the carbon-carbon single bond (\(\sigma\)-bond) causes different spatial arrangements of hydrogen atoms, known as conformers. The two primary conformations are staggered, where hydrogens are as far apart as possible, and eclipsed, where hydrogens line up with each other.

Compare Staggered and Eclipsed Conformers

Staggered conformers are lower in energy because they minimize repulsive interactions between electron clouds of adjacent hydrogens. Eclipsed conformers have higher energy due to these interactions.

Know the Energy Difference

The energy difference between staggered and eclipsed conformations of ethane is well-documented through experimentation and theoretical calculations. This difference represents the barrier to rotation around the carbon-carbon bond.

Identify the Correct Energy Difference

Recall or lookup the precise energy difference between staggered and eclipsed conformers of ethane, which is a known value from molecular physics and thermodynamics. The difference is approximately \(12-14\,\text{kJ/mol}\).

Select the Closest Answer

With the known energy difference range between \(12-14\) kJ/mol, compare the options. Option (c) \(13 \mathrm{~kJ} \mathrm{~mol}^{-1}\) is within that range.

Key concepts

Sigma Bond Rotation

In ethane, the carbon-carbon single bond is referred to as a \(\sigma\)-bond. This type of bond allows for free rotation around its axis. Imagine it like a hinge or a flexible axle connecting the two carbon atoms. This rotation results in different spatial arrangements of the attached hydrogen atoms, leading to variations known as conformers. The concept of free rotation essentially means these variations can occur without breaking the \(\sigma\)-bond.

Conformers result from the angle between hydrogens attached to each carbon. During \(\sigma\)-bond rotation, you can visualize ethane constantly switching through different states or arrangements. This is a key feature of single bonds and a fundamental aspect of molecular dynamics, giving rise to varied chemical and physical properties in molecules.

Staggered and Eclipsed Conformations

As the \(\sigma\)-bond rotates, ethane can exist in different conformations, primarily staggered and eclipsed. Each conformation describes the relative positions of hydrogens attached to the carbon atoms.

The staggered conformation is the most stable arrangement. Here, hydrogen atoms are positioned as far apart from each other as possible, reducing electron cloud repulsions. This spatial arrangement minimizes the energy, making the staggered conformation energetically favorable.

On the other hand, the eclipsed conformation occurs when hydrogens align with one another. Imagine them standing in a straight line behind each other. In this state, the repulsive interactions between adjacent hydrogen atom electron clouds are maximized. As a result, the eclipsed conformation is less stable and possesses higher energy.

Energy Difference in Conformations

Rotating around the \(\sigma\)-bond in ethane alters its energy. Typically, moving from one conformation to another means navigating through energy landscapes. The staggered conformation is by far more favorable than the eclipsed conformation, because it involves less repulsion among electron clouds.

The energy difference between these conformers is not just academic—it directly affects molecular behavior and reactions. For ethane, this energy difference is approximately \(12-14\, \text{kJ/mol}\). The staggered form experiences the lowest energy, while the eclipsed state represents a higher energy plateau.

Calculating or experimentally determining these energy differences helps chemists understand the dynamics of molecules. This information is crucial in predicting how molecules will interact, react, and change shape under different conditions.

Bond Rotation Barrier

The concept of a bond rotation barrier refers to the energy required to overcome to switch between conformations. In ethane, this barrier is characterized by the energy difference between the staggered and eclipsed conformations.

Even though the \(\sigma\)-bond allows for rotation, it isn't entirely unrestricted. To move from a staggered to an eclipsed state, a molecule must have enough energy to overcome this barrier. The magnitude of this barrier for ethane, around \(12-14\, \text{kJ/mol}\), reflects how much energy you need to surpass these electron repulsions.

Understanding these barriers is essential, as it illustrates the flexibility or rigidity of molecular structures. In simpler terms, it tells us how easily a molecule can twist and turn in response to environmental factors or reactions.