why can't you convert cis-2-butene into trans-2-butene simply by undergoing a rotation/

The cis and trans isomers of 2-butene involve a pi bond as well as a sigma bond. To "rotate" the molecule, the pi bond must be broken (remember this double bond is planar) and that involves about 70 kcal of energy so a simple interconversion isn't possible; for example, at room temperature.

To understand why you can't convert cis-2-butene into trans-2-butene simply by undergoing a rotation, let's break it down step by step.

1. First, we need to understand the structure of cis-2-butene and trans-2-butene. Both compounds have the same molecular formula, C4H8, but differ in their spatial arrangement of atoms around the double bond.

Cis-2-butene has the two alkyl groups (CH3-CH2-) on the same side of the double bond, while trans-2-butene has the two alkyl groups on opposite sides of the double bond.

2. In order to convert cis-2-butene into trans-2-butene, we would need to move the two alkyl groups from one side of the double bond to the other side. This would involve breaking the pi bond and rearranging the atoms.

3. However, breaking the pi bond requires a significant amount of energy. The double bond between the carbon atoms in 2-butene consists of a sigma bond and a pi bond. The pi bond is formed by the overlap of p-orbitals above and below the plane of the molecule.

4. To rotate the molecule and convert cis-2-butene to trans-2-butene, the pi bond needs to be broken. This would disrupt the overlap of the p-orbitals, resulting in an increase in energy. In fact, breaking the pi bond in 2-butene requires approximately 70 kilocalories (kcal) of energy.

5. At room temperature, the energy required to break the pi bond is not readily available, so a simple rotation or interconversion between cis and trans isomers of 2-butene is not possible under normal conditions.

In conclusion, due to the high energy requirement to break the pi bond in 2-butene, a simple rotation is not sufficient to convert cis-2-butene into trans-2-butene. This is why these isomers cannot be interconverted easily.