Predict the product(s) and provide the mechanism for each reaction below. What do the mechanisms have in common?

a.

b.

c.

d.

As the base reacts with the epoxide opening of the epoxide occurs and the ether oxygen atomgainsa negative charge.Also, it is apoor leaving group so, the formation of the hydroxyl group occurs followed by a reaction with methanol and follows the mechanism.

As per the given epoxide on reaction with a base, the epoxide opening occurs and the $-{\mathrm{OCH}}_3$group is added from the left side because of the less hindered site and the hydroxy group is formed on another carbon as shown below:

Opening of epoxide ring

The reaction of the epoxide with the Grignard reagent follow ${\mathrm{SN}}_2$mechanism in which Grignard reagent act as a nucleophile and attack occurs from less hindered side and addition of alkyl group occurs on less hindered carbon and MgBr is added on more hindered carbon further followed by hydrolysis MgBr is removed by H and formation of alcohol occur as shown below:

This follow acid catalysed reaction and opening of epoxide occur by the alkyl halide or acid and if the epoxide is tertiary ${\mathrm{SN}}_1$reaction is followed and formation of carbocation occur and the halide ion is attack from more hindered site due to stability of carbocation as shown:

Opening of epoxide ring

The reaction of epoxide with amine is occur by the opening of the epoxide ring on reacting with N having lone pairs which behaves as a nucleophile and formation of hydroxy and addition of amine occur as follow:

Opening of epoxide ring