Question

How many different staggered conformations are there for 2-methylpropane? How many different eclipsed conformations are there?

Short answer

Short Answer: In 2-methylpropane, there are 3 different staggered conformations and 3 different eclipsed conformations.

Step-by-step solution

Understand the structure of 2-methylpropane

2-methylpropane is an organic compound which contains four carbon atoms and ten hydrogen atoms. It is an isomer of butane. In 2-methylpropane, there are three carbons in the main chain and one side chain (methyl group) on the second carbon. Considering the main carbon-carbon bond between central carbon and the methyl group as C1-C2 bond, we need to rotate around this bond to determine the different conformations.

Determine the possible staggered conformations

To find the possible staggered conformations, we need to consider the dihedral angle between the front and back carbon atoms in the Newman projection. For staggered conformations, the dihedral angles should be 60, 180, and 300 degrees. In a Newman projection, let's place the large substituent at the front (i.e., methyl group attached to C1) at the top position as a reference. Here are the possible staggered conformations: 1. First staggered conformation: Methyl group (C2) is at the bottom of C1 (60° dihedral angle). 2. Second staggered conformation: The eclipsed conformation (C2) goes to the bottom C1 position (dihedral angle of 180°). Since both front and back positions have large substituents (methyl groups), this conformation is also a gauche conformation. 3. Third staggered conformation: The staggered conformation again, with C2 at the bottom right of C1 (dihedral angle of 300°). So, there are \boxed{3} different staggered conformations for 2-methylpropane.

Determine the possible eclipsed conformations

For eclipsed conformations, the dihedral angle between front and back carbon atoms in the Newman projection is 0, 120, and 240 degrees. Following the same method as in step 2, we place the large front substituent as a reference point in each case. 1. First eclipsed conformation: C2 at the top position overlapping with the C1 methyl group (dihedral angle of 0°). 2. Second eclipsed conformation: C2 at the middle right position of C1 (dihedral angle of 120°). 3. Third eclipsed conformation: C2 at the middle left position of C1 (dihedral angle of 240°). So, there are \boxed{3} different eclipsed conformations for 2-methylpropane.