The reactivity of bromocyclopentane compared to bromocyclohexane when heated with sodium iodide in acetone can be understood through the mechanism of the SN2 reaction and the structural differences between these two compounds.
Bromocyclopentane has a five-membered ring, which allows for a more accessible reaction site for the nucleophile, iodide ion. The smaller ring size leads to less steric hindrance, making it easier for the iodide to attack the carbon atom bonded to the bromine atom. In contrast, bromocyclohexane, with its six-membered ring, has more steric bulk due to the larger ring size and is more conformationally strained, creating more hindrance for the nucleophile to approach and react with the carbon center.
Additionally, the triangular geometry of the cyclopentane ring can create more favorable conditions for backside attack during the SN2 mechanism, where the nucleophile approaches from the side opposite to the leaving group (Br). In cyclohexane, the ring is more stable and less reactive due to its chair conformation, which does not provide the same ease of nucleophilic attack.
Moreover, when you consider the solvent – acetone, a polar aprotic solvent – it is particularly good at stabilizing the sodium iodide and facilitating the SN2 reaction. The polar nature of acetone helps to solvate the sodium cation, allowing the iodide anion to remain free and reactive. This reactivity maximizes the difference observed between bromocyclopentane and bromocyclohexane.
In summary, bromocyclopentane is more reactive than bromocyclohexane in SN2 reactions due to its smaller, less hindered structure which allows easier access for the nucleophile, while the larger cyclohexane exhibits more steric hindrance and stability, thus decreasing its reactivity.