Propose mechanisms for the following reactions.
d.
HINT: Alcohol dehydrations usually go through E1 elimination of the protonated alcohol, with a carbocation intermediate. Rearrangements are common.

Indicate which alcohol in each pair undergoes an elimination reaction more rapidly when heated with H₂SO₄.

e.

Indicate which alcohol in each pair undergoes an elimination reaction more rapidly when heated with H₂SO₄.

d.

Indicate which alcohol in each pair undergoes an elimination reaction more rapidly when heated with H₂SO₄.

c.

Propose mechanisms for the following reactions.

(b) 

HINT: Alcohol dehydrations usually go through E1 elimination of the protonated alcohol, with a carbocation intermediate. Rearrangements are common.

Under acid catalysis, tetrahydrofurfuryl alcohol reacts to give surprisingly good yields of dihydropyran. Propose a mechanism to explain this useful synthesis.

When the following substituted cycloheptanol undergoes dehydration, one of the minor products has undergone a ring contraction. Propose a mechanism to show how this ring contraction occurs.

Propose a mechanism for each reaction.

(c)

Propose a mechanism for each reaction.

(a)