Question

problem sight along the c2 - c1 bond of 2 - methylpropane (isobutane). 3 - 16 (a) draw a newman projection of the most stable conformation. (b) draw a newman projection of the least stable conformation. (c) make a graph of energy versus angle of rotation around the c2 - c1 bond. (d) assign relative values to the maxima and minima in your graph, given that an h→h eclipsing interaction costs 4.0 kj/mol and an h→ch3 eclipsing interaction costs 6.0 kj/mol.

Explanation:

Step1: Analyze most - stable conformation

The most stable conformation of 2 - methylpropane (isobutane) along the C2 - C1 bond is the staggered conformation. In a Newman projection, for the most stable conformation, the large methyl group on C2 is anti - to the methyl group on C1.

Step2: Analyze least - stable conformation

The least stable conformation is the eclipsed conformation where the methyl groups on C2 and C1 are directly eclipsed. In a Newman projection, the two methyl groups are in an eclipsed position.

Step3: Graph energy vs rotation

As the molecule rotates around the C2 - C1 bond, the energy changes. The staggered conformations are minima and the eclipsed conformations are maxima. The rotation is considered in 60 - degree increments.

Step4: Calculate energy values

In the least stable (fully eclipsed) conformation, there are two H - CH₃ eclipsing interactions and one H - H eclipsing interaction. The energy of this conformation is \(2\times6.0\ kJ/mol+ 4.0\ kJ/mol=16.0\ kJ/mol\). The most stable (staggered) conformation has an energy of 0 kJ/mol (by convention as a reference).

Answer:

(a) In the Newman projection of the most stable (staggered) conformation, the large methyl group on C2 is anti - to the methyl group on C1.
(b) In the Newman projection of the least stable (eclipsed) conformation, the two methyl groups are directly eclipsed.
(c) The graph has minima at 60 - degree intervals (staggered conformations) and maxima at 0 - degree and 120 - degree intervals (eclipsed conformations) with rotation around the C2 - C1 bond on the x - axis and energy on the y - axis.
(d) The minimum energy (staggered conformation) is 0 kJ/mol and the maximum energy (fully eclipsed conformation) is 16.0 kJ/mol.