S_N1 substitution and E1 elimination frequently compete in the same reaction.
a. Propose a mechanism and predict the products for the solvolysis of 2-bromo-2,3,3-trimethylbutane in methanol.

Verified step by step guidance

1. Identify the substrate: The compound 2-bromo-2,3,3-trimethylbutane is a tertiary alkyl halide. Tertiary alkyl halides are prone to undergoing SN1 and E1 mechanisms due to the stability of the carbocation intermediate formed during the reaction.
2. Determine the reaction conditions: The reaction occurs in methanol, which is a polar protic solvent. Polar protic solvents stabilize carbocations and favor SN1 and E1 mechanisms. Methanol can also act as a nucleophile in the SN1 pathway.
3. Propose the first step of the mechanism: The reaction begins with the departure of the bromide ion (Br⁻), forming a tertiary carbocation at the 2-position. This step is the rate-determining step for both SN1 and E1 mechanisms. Represent this step as: $R-\mathrm{Br}\to R++\mathrm{Br}-$.
4. Propose the SN1 pathway: In the SN1 mechanism, methanol acts as a nucleophile and attacks the carbocation, forming an intermediate oxonium ion. This intermediate is then deprotonated by another methanol molecule to yield the substitution product, 2-methoxy-2,3,3-trimethylbutane.
5. Propose the E1 pathway: In the E1 mechanism, a base (methanol or another molecule) abstracts a proton from a β-hydrogen (on the 3-position), leading to the formation of a double bond. This results in the elimination product, 2,3,3-trimethyl-2-butene. Note that the E1 product is favored at higher temperatures due to the entropy increase associated with elimination.

Key Concepts

SN1 Mechanism

The SN1 mechanism is a type of nucleophilic substitution reaction that occurs in two steps. First, the leaving group departs, forming a carbocation intermediate. This is followed by the nucleophile attacking the carbocation. The rate of the reaction depends only on the concentration of the substrate, making it unimolecular.

E1 Mechanism

The E1 mechanism is an elimination reaction that also proceeds in two steps. Similar to SN1, the first step involves the formation of a carbocation after the leaving group departs. In the second step, a base abstracts a proton from a neighboring carbon, resulting in the formation of a double bond. The E1 reaction competes with SN1 when conditions favor elimination.

Carbocation Stability

Carbocation stability is crucial in determining the pathway of reactions involving SN1 and E1 mechanisms. Tertiary carbocations, like the one formed from 2-bromo-2,3,3-trimethylbutane, are more stable due to hyperconjugation and inductive effects from surrounding alkyl groups. This stability influences the likelihood of substitution versus elimination reactions occurring.