Part 7: MECHANISMS

I.
This reaction converts an alcohol into an alkyl chloride, usually via an SN2 type mechanism. Remember -OH is a poor leaving group. Here the O becomes attached to the S and eventually leaves as part of sulfur dioxide, SO2 when the chloride ion attacks as a nucleophile.
mechanism
II.
Alcohol to an alkene is an elimination, a dehydration. With a strong acid this is an E1 reaction. Here the intermediate carbocation has also rearranged via a 1,2-alkyl shift.
mechanism
In the final step, the base, B: could be the conjugate base of the acid (HSO4-), or H2O or the original alcohol.
III.
Ether syntheses.  1 and 2 are both Williamson type reactions.  1 is the most efficient because the alkyl halide is a methyl system and hence can't undergo a competing elimination since the is no H beta (i.e. 1,2-) with respect to the bromide leaving group. In  2 where methoxide is reacting with a tertiary alkyl halide, it's likely to cause a significant amount of elimination as well as the desired substitution due the the steric hinderance at the C-Br center. Reaction 3 will lead to a mixture ot three ethers, dimethyl ether, t-butyl methyl ether and di-t-butyl ether (depending if R = R' or not).

mechanism
IV.
Radical halogenation reactions. First step is the formation of the halogen radical by dissociation of the halogen.  Cl radicals are more reactive than Br this means that Cl is less selective in its reactions. Radical halogenation is a balance between stability and statistics.  Cl is more reactive because of the greater affinity to complete it's octet (as reflected by Cl being more electronegative than Br).  Cl is only 5.2 times as likely to react at a tertiary H compared to primary H. For Br it is 1640 times more reactive towards the tertiary site.

In the reaction with Br2, the Br radical abstracts the tertiary H to give the more stable tertiary radical and this in turn leads to the tertiary bromide.

mechanism

In contrast, in the reaction with Cl2, the Cl radical is more likely to react with the primary H to give the primary radical and this in turn leads to the primary chloride.