Explain the mechanistic basis of the following observations and discuss how the observation provides information about the reaction mechanism.
a. When 1-aryl-2-methyl-2-propyl chlorides (8-A) react with $\mathrm{NaOCH}_{3}$, roughly 1:1 mixtures of internal (8-B) and terminal alkene (8-C) are formed. By using the product ratios, the overall reaction rate can be dissected into the rates for formation of 8-B and 8-C. The rates are found to be substituent dependent for 8-B $(\rho=+1.4)$ but not for $8-C(\rho=-0.1 \pm 0.1)$. All the reactions are second order, first order in reactant and first order in base.
b. When 1,3-pentadiene reacts with DCl, more $E-4$-chloro-5-deuterio-2-pentene $(60-75 \%)$ is formed than $E-4$-chloro-1-deuterio-2-pentene $(40-25 \%)$.
c. When indene (8-D) is brominated in $\mathrm{CCl}_{4}$, it gives some $15 \%$ syn addition, but indenone (8-E) gives only anti addition under these conditions. When the halogenation of indenone is carried out using $\mathrm{Br}-\mathrm{Cl}$, the product is trans-2bromo-3-chloroindenone.
d. The acid-catalyzed hydration of allene gives acetone, not allyl alcohol or propanal.
e. In the addition of HCl to cyclohexene in acetic acid, the ratio of cyclohexyl acetate to cyclohexyl chloride drops significantly when tetramethylammonium chloride is added in increasing concentrations. The rate of the reaction is also accelerated. These effects are not observed with styrene.
f. The $\rho$ value for elimination of $\mathrm{HF}$ using $\mathrm{K}^{+-} \mathrm{O}-t-\mathrm{Bu}$ from a series of 1 -aryl2-fluoroethanes increases from the mono- to di- and trifluoro derivatives, as indicated below.