Question

Account for the relative rates of solvolysis of these compounds in aqueous acetic acid.

Short answer

Answer: tert-Butyl iodide will have the fastest solvolysis rate in aqueous acetic acid.

Step-by-step solution

Identify the nucleophile and the mechanism

Aqueous acetic acid acts as a weak nucleophile and favors the formation of stable carbocations. Thus, the most likely reaction mechanism in this case will be Unimolecular Nucleophilic Substitution (SN1). The nucleophile in this reaction is the acetate ion (CH3COO-) from acetic acid. We should also take the identity of the leaving group (X) into account, as it may influence the rate of solvolysis. Generally, better leaving groups will lead to faster solvolysis rates.

Analyzing the effect of alkyl group on the solvolysis rate

In the SN1 mechanism, the rate of solvolysis depends on the stability of the carbocation intermediate formed upon leaving group departure. Carbocation stability generally follows the order: \[3^{\circ} > 2^{\circ} > 1^{\circ} \] A 3° (tertiary) carbocation is more stable than a 2° (secondary) carbocation, which is more stable than a 1° (primary) carbocation. This is due to hyperconjugation and inductive effects that help to stabilize positive charge on the carbocation. Thus, the solvolysis rate will be faster with a more substituted alkyl group (R).

Analyzing the effect of the leaving group on the solvolysis rate

The leaving group's ability to depart from the alkyl halide influences the rate of solvolysis. Better leaving groups will have a more significant effect on the solvolysis rate. The leaving ability generally follows the order: \[I^- > Br^- > Cl^- > F^- \] So, alkyl iodides will undergo solvolysis faster than alkyl bromides, which will be faster than alkyl chlorides and alkyl fluorides.

Comparing the relative rates of solvolysis

Now that we understand the factors affecting solvolysis, we can compare the relative rates for three compounds of differing alkyl groups (R) and leaving groups (X). For instance, let's consider the following compounds: 1. tert-Butyl iodide (R= tert-butyl, X=I) 2. sec-Butyl bromide (R= sec-butyl, X=Br) 3. Isopropyl chloride (R= isopropyl, X=Cl) The relative solvolysis rates can be compared based on the stability of carbocations and leaving group ability: 1. tert-Butyl iodide is expected to have the fastest solvolysis rate, since it has a 3° alkyl group (forming a more stable carbocation) and iodine as the leaving group (a good leaving group). 2. sec-Butyl bromide will have an intermediate solvolysis rate, as it has a 2° alkyl group (forming a less stable carbocation than tert-butyl) and bromine as the leaving group (a less effective leaving group than iodine). 3. Isopropyl chloride will have the slowest solvolysis rate, as it has a 2° alkyl group (comparable to sec-butyl) but chlorine as the leaving group (a less effective leaving group than both iodine and bromine). In conclusion, the relative rates of solvolysis for the given compounds in aqueous acetic acid can be ranked as: tert-Butyl iodide > sec-Butyl bromide > Isopropyl chloride