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

Solvolysis is a type of nucleophilic substitution reaction where the solvent acts as the nucleophile. In this problem, the solvent is aqueous acetic acid. Factors affecting the rate of solvolysis include the stability of the intermediate carbocation, the electronegativity of the leaving group, and any steric hindrances. It is crucial to first analyze each given compound and understand their structures in order to make any comparisons.

Since the compounds are not provided, we will consider three general cases: primary (R-CH2-X), secondary (R2-CH-X), and tertiary (R3-C-X) alkyl halides. The stability of carbocations follows the order: tertiary carbocations > secondary carbocations > primary carbocations. This occurs due to the inductive effect of the alkyl groups, which can stabilize the positive charge on the carbon center. More alkyl groups on the carbon center result in a more stable carbocation intermediate.

A good leaving group is one that can stabilize the negative charge after leaving the substrate. In general, a leaving group with higher electronegativity results in a more stable anion, thus promoting solvolysis. Therefore, comparing different halides, iodide is a better leaving group than bromide, and bromide is better than chloride.

Steric hindrance refers to the spatial arrangement of atoms in a molecule that can inhibit a reaction. In the case of solvolysis, a more hindered substrate can hinder the approach of the nucleophile and slow down the reaction. For alkyl halides, the steric hindrance increases in the order: primary alkyl halides < secondary alkyl halides < tertiary alkyl halides.

Based on the factors discussed above, the following general observations can be made: 1. Tertiary alkyl halides usually have the fastest solvolysis rate due to the high stability of the intermediate carbocations. 2. Secondary alkyl halides have moderate solvolysis rates, as their carbocation stability is intermediate between primary and tertiary alkyl halides. 3. Primary alkyl halides have the slowest solvolysis rates, as their carbocations are the least stable. So, the relative rates of solvolysis for the given compounds in aqueous acetic acid follow the order: tertiary alkyl halides > secondary alkyl halides > primary alkyl halides. Keep in mind that other factors like the specific leaving groups and steric hindrances could also influence the solvolysis rates, but this general trend should apply to most cases.