Question

Select the member of each pair that undergoes \(\mathrm{S}_{\mathrm{N}} 1\) solvolysis in aqueous ethanol more rapidly.

Short answer

Answer: To determine which member of the pair undergoes S_N1 solvolysis more rapidly, factors such as the degree of alkyl substitution on the carbon with the leaving group, the presence of electron-donating and electron-withdrawing groups, and the quality of the leaving group should be considered. The compound with a more stable carbocation, better leaving group, and fewer electron-withdrawing groups will undergo S_N1 solvolysis more rapidly.

Step-by-step solution

Identify the given pair of compounds

The exercise does not provide a specific pair of compounds. In such a case, we can consider a general pair of compounds, say compound A and compound B. We will compare these two compounds based on the various factors that can affect the rate of S_N1 solvolysis.

Assess the degree of alkyl substitution on the carbon attached to the leaving group

In general, more substituted carbocations are more stable due to the inductive effect and hyperconjugation. Therefore, tertiary carbocations (with three alkyl groups attached to the positively charged carbon) are more stable than secondary carbocations (two alkyl groups), which in turn are more stable than primary carbocations (one alkyl group). Thus, if one of the compounds has a greater degree of alkyl substitution on the carbon with the leaving group, it will undergo S_N1 solvolysis more rapidly.

Consider the effect of electron-donating groups on the carbocation stability

Electron-donating groups, such as alkyl groups or groups with a lone pair of electrons, can stabilize a carbocation through resonance or inductive effects. If one of the compounds has more electron-donating groups in the vicinity of the leaving group, it will lead to a more stable carbocation and thus a faster S_N1 reaction.

Consider the effect of electron-withdrawing groups on the carbocation stability

Electron-withdrawing groups, such as halogens or other electronegative atoms, can de-stabilize a carbocation by withdrawing electron density away from the positively charged carbon. If one of the compounds has more electron-withdrawing groups in the vicinity of the leaving group, it will lead to a less stable carbocation and thus a slower S_N1 reaction.

Consider the leaving group

A good leaving group can make the S_N1 reaction occur more easily, as it is more willing to depart from the carbon atom. In general, weaker bases make better leaving groups. If one of the compounds has a better leaving group, it will undergo S_N1 solvolysis more rapidly.

Select the member of the pair that undergoes S_N1 solvolysis more rapidly

Based on the factors discussed in the above steps, we can now compare the two compounds (compound A and compound B) and determine which one undergoes S_N1 solvolysis in aqueous ethanol more rapidly. The compound with a more stable carbocation, better leaving group, and fewer electron-withdrawing groups will undergo S_N1 solvolysis more rapidly.