Question

Let's compare the staggered conformations. We've already determined that the 60° Newman projection has 3 gauche interactions. What can be said about the other staggered conformations?

1) They have more gauche interactions than the 60° Newman projection
2) They have fewer gauche interactions than the 60° Newman projection
3) They have the same number of gauche interactions as the 60° Newman projection
4) The number of gauche interactions cannot be determined

Answer 1

The other staggered conformations have fewer gauche interactions than the 60° Newman projection.

Step-by-step explanation:

The question asks about the other staggered conformations and their potential number of gauche interactions compared to the 60° Newman projection. The answer is that the other staggered conformations have fewer gauche interactions than the 60° Newman projection.

Here's an explanation:

The 60° Newman projection of butane has 3 gauche interactions, which are steric repulsions between the bulky (-CH3) groups at a torsion angle of 60°. When the molecule rotates by 60°, it converts to another staggered conformation called gauche-conformation. In this conformation, one gauche interaction is eliminated because the bulky groups are now at a torsion angle of 120°. However, two new gauche interactions are introduced. Therefore, the number of gauche interactions is reduced by 1.

Similarly, when the molecule rotates by another 60°, it converts to the eclipsed conformation called cis. In this conformation, all three gauche interactions are eliminated because the bulky groups are now at a torsion angle of 180°. Therefore, the number of gauche interactions is reduced to zero.

In summary, the other staggered conformations have fewer gauche interactions than the 60° Newman projection.