Several substituted propyl tosylates with $\gamma$-silicon groups have been studied. For the 2,2 -dimethyl derivatives 24-B, the solvolysis rates are $10^{3}$ to $10^{4}$ greater than for the nonsilyl analogs. The products are rearranged 1,1 -dimethyl derivatives. The reaction shows modest sensitivity to substituents in the aryl group, correlating with a Hammett $\rho$ value of $-1.0$. When the parent system 24-A (without the 2,2-dimethyl substituents) was studied in the nonnucleophilic solvent $97 \%$ TFE, cyclopropane was formed, ranging in yield from $0 \%$ with $\mathrm{EWG}\left(\mathrm{CF}_{3}\right)$ to $100 \%$ with ERG $\left(\mathrm{CH}_{3} \mathrm{O}\right)$. The Hammett correlation gave $\rho=-1.1$ for cyclopropane formation but no significant substituent effect for substitution. Describe a mechanism that is consistent with this information.
a. The stabilization of vinyl cations tends to be somewhat larger than for the corresponding ethyl cation.
b. $\mathrm{F}, \mathrm{OH}$, and $\mathrm{NH}_{2}$ provide less stabilization of vinyl cations than of ethyl cations.
c. $\mathrm{CF}_{3}$ and $\mathrm{CN}$ are less destabilizing of vinyl cations than of ethyl cations.
d. What factors dominate the effect of the $\mathrm{CH}_{2}-\mathrm{X}$ substituents?
e. Compare the $\pi$-donor and polar effects of the $\mathrm{OH}, \mathrm{NH}_{2}$, and $\mathrm{SH}$ substituents.