First, We want to make one of the Hydroxyl groups a better leaving group. Sulfuric acid will protonate the Hydroxyl group so that later in the mechanism it can leave as water.
Since primary alcohols are present, an SN2 reaction will occur in the next step since a primary carbocation will not be stable for an SN1. In this step, the electrons of the oxygen of the hydroxyl group that was not protonated will attack the alpha carbon of the protonated hydroxyl group and the protonated hydroxyl group will leave as the leaving group, forming the ring-like structure. (This is a concerted reaction)
During the final step, water deprotonates the oxygen, completing the epoxide ring formation.
Below is a picture of the mechanism.
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