Hi Chenglin, I am assuming you are referring to the image under section 5.
The *overall* kinetics of these reactions will be dictated by the formation of the carbocation, which is the rate-limiting step. Generally the more stable the carbocation, the lower will be the the activation energy for its formation (“late” transition state) and the faster the overall rate of reaction.

It should not be interpreted to mean that there is a relationship between the stability of the carbocation and the rate of the *second* (i.e. fast addition of nucleophile to carbocation) step.

Cyclopropyl methyl. Cyclopropenyl quickly rearranges to allyl cation.

THANK YOU!!!!

That is an EXCELLENT question and the data contradicts somewhat. Cyclopropylmethyl cations are generally considered to be more stable than benzyl. I’m looking for a better reference than just March 5th ed. p. 222, but the references therein are to good, but somewhat obscure, reviews. Hydrolysis rates suggest cyclopropylmethyl cations are more stable.

However another way to answer that is to look at 13-C NMR to determine the chemical shift of the carbocations. The more negative the chemical shift, the more unstable it is. The 2-cyclopropyl carbocation has a chemical shift of -86.8 ppm and the 2-phenylpropyl cation has a chemical shift of -61.1 indicating that the phenyl group is better at stabilizing. See https://pubs.acs.org/doi/10.1021/ja00731a026

Discussed in the series on rearrangments.

Aromaticity. See: https://www.masterorganicchemistry.com/2017/02/23/rules-for-aromaticity/

It’s far more powerful to look at stabilization from the perspective of hyperconjugation, but it’s far easier to explain it from the perspective of inductive effects. If you are a major in a chemistry program I would take the time to learn hyperconjugation and apply that to your studies. It’s a very powerful concept.