Indicate the products of the following reactions and point out the mechanism as $\mathrm{S}_{\mathrm{N}} 1, \mathrm{~S}_{\mathrm{N}} 2$, E1 or E2.
(a) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Br}+\mathrm{LiAlH}_4$ (source of : $\mathrm{H}^{-}$)
(d) $\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{Br}+\mathrm{Mg}$ (ether)
(b) $\left(\mathrm{CH}_3\right)_3 \mathrm{CBr}+\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}$, heat at $60^{\circ} \mathrm{C}$
(e) $\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Br}+\mathrm{Mg}$ (ether)
(c) $\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHCl}+\mathrm{NaNH}_2$
(f) $\mathrm{CH}_3 \mathrm{CHBrCH}_3+\mathrm{NaOCH}_3$ in $\mathrm{CH}_3 \mathrm{OH}$
(a) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_3$; an $\mathrm{S}_{\mathrm{N}} 2$ reaction, : $\mathrm{H}^{-}$of $\mathrm{AlH}_4^{-}$replaces $\mathrm{Br}^{-}$.
(b)
(c) $\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHCl}+\mathrm{NaNH}_2 \longrightarrow \mathrm{CH}_3 \mathrm{C} \equiv \mathrm{CH}+\mathrm{NH}_3+\mathrm{NaCl}$
Vinyl halides are quite inert toward $\mathrm{S}_{\mathrm{N}} 2$ reactions.
(d) $\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{Br}+\mathrm{Mg} \longrightarrow \mathrm{H}_2 \mathrm{C}=\mathrm{CH}_2+\mathrm{MgBr}_2$
This is an $\mathrm{E} 2$ type of $\beta$-elimination via an alkyl magnesium iodide.
$$
\mathrm{Mg}+\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{Br} \longrightarrow \mathrm{BrMg}^{-} \overparen{\mathrm{CH}_2}-\mathrm{CH}_2-\bigodot_{\mathrm{Br}} \longrightarrow \mathrm{MgBr}_2+\mathrm{H}_2 \mathrm{C}=\mathrm{CH}_2
$$
(e) This reaction resembles that in $(d)$ and is an internal $\mathrm{S}_{\mathrm{N}} 2$ reaction.
(f) This $2^{\circ} \mathrm{RBr}$ undergoes both $\mathrm{E} 2$ and $\mathrm{S}_{\mathrm{N}} 2$ reactions to form propylene and isopropyl methyl ether.
$$
\mathrm{CH}_3 \mathrm{CHBrCH}_3+\stackrel{+}{\mathrm{NaO}}-\overline{C H} \mathrm{CH}_3\left(\mathrm{CH}_3 \mathrm{OH}\right) \longrightarrow \underset{\mathrm{OCH}_3}{\mathrm{CH}_3 \mathrm{CH}=\mathrm{CH}_2}+\underset{\mathrm{CH}_3 \mathrm{CHCH}_3}{\mathrm{CH}_3}
$$