Final answer:
Cis-1,2-dichlorocyclohexane is less stable than its trans isomer due to steric hindrance when the chlorines are positioned on the same side of the ring. Trans-1,2-dichlorocyclohexane allows both chlorines to adopt the more stable equatorial positions in the chair conformation, thus minimizing steric strain.
Step-by-step explanation:
The question asks why cis-1,2-dichlorocyclohexane is less stable than its trans isomer. This is a question of steric hindrance and the distribution of electron clouds within the molecule. In the cis isomer, two chlorine atoms are on the same side of the cyclohexane ring, which places their large electron clouds in close proximity and creates steric strain. This strain leads to destabilization. In the trans isomer, however, the chlorine atoms are on opposite sides of the ring, which minimizes steric interactions and leads to greater stability.
The chair conformation is the most stable conformation for cyclohexane and its derivatives due to the bond angles approximating 109.5°, minimizing both angle and torsional strain. When substituents like chlorine atoms are added, their positions will either be axial (pointing up or down from the plane of the ring) or equatorial (pointing outwards, parallel to the plane of the ring). Typically, large groups like chlorine prefer the equatorial position due to less steric strain compared to the axial position. In the cis-conformation of 1,2-dichlorocyclohexane, both chlorine atoms can't be in the equatorial positions simultaneously due to their proximity, leading to at least one chlorine atom being in the less favorable axial position. Conversely, in the trans-conformation, it's possible for both chlorines to occupy equatorial positions in the chair conformation, thereby minimizing steric hindrance and resultingly, being more stable.