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Why is chlopropyl chloride less reactive...

Why is chlopropyl chloride less reactive than cyclopentyl chloride towards `S_(N^(1))` reaction?

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In `S_(N^(1))` reaction, a carbocation intermediate is formed in the slow or rate determining step by the cleavage of `C-Cl` bond. Now, this means that the cyclopropyl carbocation intermediate formed is less stable than cyclopentyl carbocation due to greater strain. therefore, cyclopropyl chloride is less reactive than cyclopentyl chloride towards `S_(N^(1))` reaction.
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