Question

Conformation obtained on \(60^{\circ}\) clockwise rotation of \(C_{1}\) and then \(180^{\circ}\) anticlockwise rotaiv of \(\mathrm{C}_{2}\) is (A) Eclipsed (B) Gauche (C) Partially eclipsed (D) Staggered

Short answer

The conformation of the molecule obtained after a 60° clockwise rotation of C1 and a 180° anticlockwise rotation of C2 is (B) Gauche.

Step-by-step solution

Identify the initial conformation of the molecule

At the beginning, we have a molecule (C1-C2) in an undefined conformation, and we are asked about its conformation after two rotations: 60 degrees clockwise rotation of C1 and 180 degrees anticlockwise rotation of C2.

Perform the 60° clockwise rotation of C1

Rotate C1 by 60 degrees in the clockwise direction. To visualize this, imagine each bond around C1 rotates 60°. This would turn any staggered conformation around C1 into a gauche conformation, and an eclipsed conformation into a partially eclipsed conformation.

Perform the 180° anticlockwise rotation of C2

Next, rotate C2 by 180 degrees in the anticlockwise direction. The 180° rotation would swap the positions of any two groups around the C2 carbon. Keep in mind that C1 is stationary, only the groups attached to C2 are rotating. For example, if after the 60° rotation, C1-C2 had a gauche conformation, then after 180° rotation around C2, it would still be gauche. Similarly, if after the 60° rotation, C1-C2 had a partially eclipsed conformation, then after 180° rotation around C2, it would still be partially eclipsed.

Determine the final conformation

Given the two rotations described above, the final conformation of the molecule after both rotations would be the same as the conformation after the first rotation. As mentioned earlier, any staggered conformation around C1 would be turned into a gauche conformation after the 60-degree rotation, and any eclipsed conformation would be turned into a partially eclipsed conformation. Therefore, the correct answer is: (B) Gauche

Key concepts

Rotation Around Bonds

In organic chemistry, molecules consist of atoms bonded together. These bonds can rotate, allowing different spatial arrangements termed conformations. This ability to rotate is most prominent in single bonds, like in simple carbon chains. Rotation occurs because single bonds lack the rigidity present in double or triple bonds.
Rotation is measured in degrees around the bond axis. For instance, a bond can rotate in either a clockwise or anticlockwise direction. Each specific angle results in a unique conformation of the molecule. This potential for rotation around bonds helps explain the dynamic nature of molecular structures. It also aids understanding how different conformations impact properties like energy and reactivity. With the right visualization, imagining this rotation as moving gears can clarify how these conformations change.

Gauche Conformation

The gauche conformation is a specific arrangement where substituents on adjacent carbons are staggered by approximately 60 degrees from each other. This is neither the most stable nor the highest energy conformation but occupies a middle ground.
In a molecule like butane, a gauche conformation occurs when the methyl groups on the molecules are 60 degrees apart. In this conformation, the substituents do not directly overlap, which lowers the energy compared to eclipsed conformations where atoms or groups face each other. Though not the lowest energy option, gauche conformation is prevalent due to its relative ease of access during molecular rotation.

Eclipsed Conformation

In the eclipsed conformation, atoms or groups on adjacent carbons are directly aligned. This means they overlap when looking down the bond axis. Such oppositional alignment leads to high steric strain because of the repulsion between the electron clouds of the overlapping substituents.
This conformation is higher in energy compared to staggered arrangements like gauche. The energy difference is due to torsional strain where electrons in the bonds repel each other. Because of these energy dynamics, most molecules prefer not to stay in an eclipsed conformation unless forced by external factors or pressures in reactions.

Staggered Conformation

Staggered conformations occur when substituents on adjacent carbons are perfectly offset, reaching the maximal separation of 180 degrees when fully staggered. This separation minimizes electron cloud interactions, hence, it is energetically favorable. In contexts like ethane, or simple carbon chains, staggered conformation is often the most stable configuration.
One of the specific staggered conformations, the anti conformation, has groups 180 degrees apart and is the least energy-consuming form. In dynamic conditions or room temperature, most molecules naturally tend to fluctuate toward this state, as it offers reduced steric hindrance and torsional strain.