$(1)$ Consider the following two reactions.

$(1$A$)$ Draw the mechanisms for both reactions. Even without rearrangements, you get $8$ different products $(2$ regioisomers, each with $4$ stereoisomers$).$

$(1$B$)$ Based on the mechanisms, state why the reaction with water $($and acid $H_{2}S{O}_4$ or similar TsOH...draw it out$)$ can be accomplished in high conversion using only a catalytic amount of acid, but the other reaction requires at least a stoichiometric amount of $HBr$ to reach "high" conversion? What would be your maximum conversion if you used only $0\mathrm{.}5$ equivalents of $HBr$ plus $0\mathrm{.}5$ equivalents NaBr in the reaction on the left?

$(1$C$)$ You will see $H_{2}S{O}_4$ and TsOH as acid catalysts MANY times in CHE $232.$ Why are these preferred for, e$.$g$.$ an addition of water like above on the right, instead of an acid like $HBr$ or $HI?$ Think about the reactivity$/$stability of the conjugate bases $($and reaction competing with elimination$).$ Look up "spectator ion$.$

$(2)$ Notice the rearrangement in the reaction below $($not to mention no stereocontrol in the addition$).$

$(2$A$)$ Draw the mechanism.

$(2$B$)$ If you don't want carbocation rearrangements or loss of stereocontrol in a substitution, then don't choose reaction conditions that promote mechanisms involving carbocations as intermediates! Draw reaction schemes, with the appropriate reagents, to get Markovnikov, and anti$-$Markovnikov hydration without rearrangements.

$(3)$ Review the mechanism for the addition reaction to form bromohydrins, then consider the reaction scheme below.

$(3$A$)$ NOW...Draw a mechanism for the reaction above. If you can't figure it out, look up halolactonization $($lactone is a cyclic ester$).$ You are cheating yourself if you look it up before trying to apply basically the same mechanism as for bromohydrin formation. Can you see how you can start putting together a "big picture" already from the reactions you've seen so far? I HIGHLY recommend you do your best to compare$/$contrast with each new reaction going forward so that CHE $232$ does not seem like a bewildering slog through countless dissimilar reactions. Write some stuff about the common features of all the addition reactions in Chapter $8.$