Problem 55 - A Complete Resource Book in Chemistry for JEE Main

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) \(17 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

The energy difference is approximately 13 kJ/mol, so the answer is (c) 13 kJ/mol.

Step 1: Understand the Concept of Conformers

In ethane, the 3-bond between the two carbon atoms allows for free rotation about the bond, creating different spatial arrangements of the attached hydrogen atoms. These arrangements are called conformers. The two main conformers of interest are the staggered and eclipsed conformers.

Step 2: Energy Comparison Between Conformers

The staggered conformer is more stable because it minimizes the repulsion between electron clouds of the hydrogen atoms, whereas the eclipsed conformer is less stable due to increased torsional strain from the alignment of hydrogen atoms.

Step 3: Identify the Energy Difference

Empirical studies and quantum chemical calculations have determined that the energy difference between the staggered and eclipsed conformers of ethane is approximately 12-14 kJ/mol. When presented with multiple choice options, select the value that falls within or closest to this range.

Step 4: Select the Correct Answer

Among the provided options, only option (c) 13 kJ/mol falls within the 12-14 kJ/mol range. Therefore, option (c) is the correct answer.

Key Concepts

Sigma Bond

The concept of the sigma bond is fundamental to understanding molecular structures and interactions. In ethane, the carbon-carbon bond is an example of a sigma (\(\sigma\)) bond. A sigma bond is a covalent bond formed by the head-on overlap of atomic orbitals, specifically s-orbitals or hybrids like sp, sp2, or sp3. This type of bond allows for free rotation of the bonded atoms, which is why different conformers- or rotations - can exist.

• Ethane's \(\sigma\)-bond involves the overlap of sp3 hybrid orbitals from each carbon atom, creating a strong and stable bond.
• This single bond has a symmetrical distribution of electron density along the axis connecting the two nuclei.
• Because of this rotational symmetry, the orientation of the bonded hydrogens can change without breaking the bond.

These changes between different rotational forms are crucial in understanding conformers like those found in ethane.

Torsional Strain

Understanding torsional strain is essential when studying molecular conformation, especially in compounds like ethane. Torsional strain arises when atoms or groups closely interact in a molecule and repulsion occurs due to overlapping electron clouds. This form of strain is crucial in determining the stability of a molecule's conformation.

• In ethane, torsional strain is observed when the molecule is in the eclipsed conformation.
• Here, hydrogen atoms align with each other, causing electron repulsion due to their close proximity.
• Conversely, the staggered conformation reduces torsional strain as the hydrogen atoms are positioned further apart, lessening repulsive interactions.

The reduction of torsional strain enhances the stability of the staggered conformer, making it energetically favorable compared to the eclipsed form.

Staggered and Eclipsed Conformers

Ethane can exist in different conformations due to rotation around its sigma bond. These variations are primarily the staggered and eclipsed conformers. Both have distinct energy levels due to their molecular arrangements.

• The staggered conformer of ethane is the most stable form. It occurs when the hydrogen atoms on one carbon atom are positioned between those on the adjacent carbon atom, maximizing distance and minimizing repulsion.
• The eclipsed conformer, on the other hand, occurs when hydrogen atoms on adjacent carbons line up, creating maximum torsional strain from their close proximity and alignment.
• The energy difference between these conformers results from the torsional strain in the eclipsed form and the decreased strain in the staggered conformer.

Empirical studies show that the energy difference between staggered and eclipsed conformers of ethane lies typically between 12 and 14 kJ/mol. This is a pivotal factor when predicting the molecule's behavior and stability.