What are the major products?
The first reaction is SN2, the giveaways are the strong nucleophile, the polar aprotic solvent (which inhibits E2, usually competitive with SN2), and the secondary substrate.
Some students might overlook the inversion of configuration in the product.
The second is E1, which also has a secondary substrate which will stabilize its intermediate, and a weak nucleophile that will deprotonate the product. I won't do it, because this is a graded assignment and I want you to convince yourself you know what you're doing!
The product from the second mechanism is 2,3-diphenylbut-2-ene.
The mechanism is indeed
Step 1. Loss of
Step 2. Migration of a methyl group
Whenever a carbocation can become more stable by rearranging, it will do so.
Here, the migration of a methyl group generates a highly stable tertiary benzylic carbocation.
Step 3. Loss of the α-hydrogen
I show here the more stable (
It is probably the major product, but the (