Which one of the following compounds can exist as cis-trans isomers?

CONCEPT:

Cis-Trans Isomerism

• Cis-trans isomerism (or geometric isomerism) occurs when a molecule has restricted rotation, typically due to the presence of a double bond or a ring structure, and two distinct groups are attached to the atoms involved in the restricted rotation.
• For cis-trans isomerism to exist:
  • In alkenes: The carbon atoms in the double bond must each have two different groups attached to them.
  • In cyclic compounds: The ring restricts rotation, and two substituents attached to different carbons in the ring can be oriented on the same side (cis) or opposite sides (trans).

EXPLANATION:

• Pent-1-ene:
  • Pent-1-ene has a terminal double bond (C₁=C₂), and one of the carbons in the double bond (C₁) has two identical hydrogen atoms. Therefore, it cannot exhibit cis-trans isomerism.
    
• 2-Methylhex-2-ene:
  • The double bond in 2-methylhex-2-ene (C₂=C₃) has two same groups attached to both C₂. Therefore, it can not exhibit cis-trans isomerism.
    
• 1,1-Dimethylcyclopropane:
  • In 1,1-dimethylcyclopropane, both methyl groups are attached to the same carbon atom in the ring. Since the substituents are not on different carbons, cis-trans isomerism is not possible.
    
• 1,2-Dimethylcyclohexane:
  • In 1,2-dimethylcyclohexane, the methyl groups are attached to different carbons in the ring, and the ring restricts rotation. Therefore, it can exhibit cis-trans isomerism.

Therefore, the compounds that can exhibit cis-trans isomerism is 1,2-Dimethylcyclohexane