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We've learned in class that epoxide ring openings can be catalyized with acids, and I seem to recall either the professor or a classmate mentioning that they also react with bases, but some quick internet searching didn't turn up anything useful. Do epoxide rings react with bases, and if so, what is the mechanism?
(Dis)claimer: this is just for my own curiosity/learning, and not being asked as a homework/test question (yet).
Do epoxied rings react with bases
Yes, they can be opened, e.g. with alkoxides.
what is the mechanism?
In principle, this is a $S_N2$ reaction, with the typical approach of the nucleophile from the back side. The difference to a non-epoxide case is that removal of the leaving group (bond breaking, ring opening) is facilitated by the ring strain.
But the general rules for the reactivity of alkyl-substituted centres in $S_N2$ nevertheless apply: the higher the substitution, the lower the rate. This is attributed to the steric hindrance of the respective centre.
Note that the regioselectivity is different under acidic conditions!
