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

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Br2/CCl4; then 2 NaNH2; then Li/liq. NH3

The reason why you can't convert cis-2-butene into trans-2-butene simply by undergoing a rotation is because the difference between cis and trans is not just about the spatial orientation of the molecule, but also about the arrangement of the atoms attached to the double bond.

In cis-2-butene, the two methyl groups (CH3) are on the same side of the double bond, while in trans-2-butene, they are on opposite sides. If you were to rotate the cis-2-butene molecule, the spatial orientation would change, but the methyl groups would still be on the same side of the double bond. This rotation wouldn't result in the formation of trans-2-butene.

To convert cis-2-butene into trans-2-butene, you would need to break the double bond and rearrange the atoms attached to it. This can be achieved through a chemical reaction called an isomerization, where the atoms are rearranged to form a new compound with a different spatial orientation.