Obviously in SN1 reactions, the compounds that make most stable carbocations react the quickest in the order of tertiary>secondary>primary.
However, if your carbocation is a ring structure with pi bonds, how would you go about comparing carbocation stability? Would we judge stability based on aromaticity/anti-aromaticity such that aromatic carbocations are more stable than antiaromatic carbocations?
If I understand you correctly, you're referring to aromatic carbocations like the cyclopropenium carbocation (three membered ring with one double bond and a carbocation on the other carbon - aromatic) and the cyclohexatrienyl carbocation (seven membered ring, three pi bonds, carbocation on the other carbon - aromatic). These are extremely stable carbocations due to the fact that they obey Huckel's rule and are thus aromatic.
Antiaromatic carbocations (example - cyclopentane with two alkenes and a carbocation on the fifth carbon) are extremely unstable and generally do not form. It's a safe bet you won't see this on your MCAT. These are chemical curiosities only, as they generally do not exist in the wild.
Within the context of comparing carbocation stability, carbocations can be stabilized by resonance. So if you are comparing a tertiary carbocation to a tertiary carbocation with an adjacent alkene, the latter will be more stable [it is unlikely you'd be asked to directly compare a tertiary carbocation to a *secondary* carbocation with an adjacent alkene - that would be changing two variables at once, which is generally not done (leads to confusion).
the more resonance structures available to the carbocation, the greater the stability. the aromatic carbocations you mentioned would be an example of that.
Could have shortened this answer
😉 , but I hope this helps - James
