Draw a reaction energy profile (energy vs dihedral angle) for rotation about the c-c bond in ethane. show the newman projections for the minima and maxima in the reaction energy profile.

The energy profile for rotation about the C-C bond in ethane is shown in the image, along with the Newman projections of the corresponding ethane conformer.

Explanation:

If you see the ethane molecule (second image) from the C-C bond axis (third image), as in the Newman projections, it's easy to draw an angle between one of the hydrogen atoms of the visible carbon, the carbon itself, and one of the hydrogens of the hidden carbon.

When you make a rotation about the C-C bond, the angle between those hydrogens will change. If you start with an eclipsed conformation, with each hydrogen of the hidden C exactly behind the hydrogens of the visible C, the angle will be 0°, or also 120° or 240°, as this rotations will be equivalent. On the other hand, if the angle is 60° (or 180°, or 300°), you will have a staggered conformation. The eclipsed conformation is less stable than the staggered one, because the interactions between hydrogens will be bigger (the repulsion between their electrons), and because of that the eclipsed conformations will be found in the maxima, while the staggered one will be found in the minima.