The reaction shown is a Markovnikov addition of a hydracid (HX) across a double bond. According to Markovnikov's rule, the hydrogen gets added to the lesser-substituted carbon in the double bond, and the halide (in this case, ) gets added to the more-substituted carbon. Thus, the correct answer is .

SN1 reactions occur in two steps. First, the leaving group leaves, forming a carbocation. Next, the weak nucleophile attacks the carbocation (beware of rearrangements during this step). The protic solvent stabilizes the carbocation intermediate. 

SN2 reactions undergo substitution via a concerted mechanism. Thus, no carbocation is formed, and an aprotic solvent is favored. Furthermore, tertiary substituted substrates have lowest reactivity for SN2 reaction mechanisms due to steric hindrance.

SN2 reaction mechanisms are favored by methyl/primary substrates because of reduced steric hindrance. No carbocation is formed via an SN2 mechanism since the mechanism is concerted; thus a strong nuclephile is used.

All of the given answers reflect SN1 reactions, except the claim that SN1 reactions are favored by weak nucleophiles.

SN1 reactions occur in two steps and involve a carbocation intermediate. The product demonstrates inverted stereochemistry (no racemic mixture). Tertiary substrates are preferred in this mechanism because they provide stabilization of the carbocation.

Substitution reactions—regardless of the mechanism—involve breaking one sigma bond, and forming another sigma bond (to another group).

 is an extremely useful reagent for organic synthesis in instances where an alcohol needs to be converted to a good leaving group (bromine is an excellent leaving group).  reacts selectively with alcohols, without altering any other common functional groups. This makes it ideal for situations in which a molecule contains acid-sensitive components that prevent the use of a strong acid to protonate a target alcohol.

While the mechanisms differ,  reactions are similar to S_N2 reactions in that they both invert the configuration at the site of attack. The configuration about the carbon adjacent to the alcohol in the given reactant is S. After substitution, the configuration of the major product is R, as is the case in molecule IV.

Based on the given reagents and the specification that the reaction takes place in a single step, it may be concluded that the reaction occurs by an S_N2 or E2 mechanism. Since the compound lacks any moderately acidic hydrogen, an S_N2 reaction is more likely. The absolute configuration at the reaction site in the initial compound is S, which is converted to R as a result of the "back-side attack" characteristic of all S_N2 reactions. The major product is shown below:

This problem involves the synthesis of a Grignard reagent. Grignard reagents are easily created in the presence of halo-alkanes by adding magnesium in an inert solvent (in this case ). Once we have created our Gringard, it can readily attack a carbonyl. In this case, our Grignard attacks carbon dioxide to create our desired product.

An  reaction is most efficiently carried out in a protic solvent. An inverted configuration site is characteristic of an  reaction and the substituted nucleophile does not form a pi bond in an  reaction.