Question

Why is the `pi` bond between the two central carbon atoms destroyed halfway through the rotation from cis- to trans-2-butene?

Answer 1

Because it's not a rotation of the double bond itself. A cis and trans molecule are geometric isomers, not conformational isomers.

The bond is too rigid to rotate, so the `pi` bond breaks, the `sigma` bonds rotate, and the `pi` bond is reformed. This tends to need some catalysis, sometimes in the form of heat or light.

For example, azo dyes are sensitive to light and experience this effect of trans-cis isomerism, called photoisomerism, with times on the order of `"ps"`.

https://en.wikipedia.org/wiki/Azobenzene#Trans-cis_isomerization