Final answer:
The anti-conformation of ethane is the most stable staggered conformation, while the gauche-conformation has more energy due to steric repulsion, and eclipsed conformations have the highest energy due to torsional strain.
Step-by-step explanation:
The relative energy levels of the three staggered conformations of alkanes, like ethane and butane, are determined by the torsional strain present due to the dihedral angle between atoms or groups attached to adjacent carbons. In the case of ethane, there is an anti-conformation which is the most stable, a gauche-conformation which is less stable, and an eclipsed conformation which is the least stable and highest in energy. Specifically, the anti-conformation of ethane is the reference with the lowest energy.
Upon rotation by 60°, it changes to the eclipsed conformation with an increase in energy of 12.5 kJ/mol. Another 60° rotation leads to the gauche-conformation, which is a local energy minimum but is still 3.8 kJ/mol higher in energy than the anti-conformation. The gauche-conformation is less stable due to steric repulsion between the bulky groups that are now closer to each other. After yet another rotation of 60°, it reverts back to an eclipsed conformation, with the highest energy increase of all conformations considered.