(i) butan-1-ol
You would expect the acid-catalyzed dehydration to be an #E2# elimination, but the conjugate base of the strong acid is very weak.
So we get a slow #E1# elimination to give a 1° cation.
#"CH"_3"CH"_2"CH"_2"CH"_2"-OH" → "CH"_3"CH"_2"CH"_2stackrel(+)("C")"H"_2 "#
The cation undergoes a hydride shift to form the more stable 2° carbocation, which can lose a proton to form but-1-ene.
#"CH"_3"CH"_2"CH"_2stackrel(+)("C")"H"_2 stackrel ("hydride shift")(→) "CH"_3"CH"_2stackrel(+)("C")"HCH"_3 → underbrace("CH"_3"CH"_2"CH=CH"_2)_color(red)("but-1-ene")#
or the more stable but-2-ene (cis and trans isomers).
#"CH"_3"CH"_2stackrel(+)("C")"HCH"_3→ underbrace("CH"_3"CH=CHCH"_3)_color(red)("but-2-ene")#
The observed products are 12 % but-1-ene, 32 % cis-but-2-ene, and 56 % trans-but-2-ene.
(ii) #("CH"_3)_3"COH"#
#("CH"_3)_3"COH" → ("CH"_3)_3stackrelcolor (blue)(+)("C") → underbrace("CH"_2"=C"("CH"_3)_2)_color(red)("2-methylpropene")#
(iii) #"HO-CH"_2"CH"("CH"_3)"CH"_2"CH"_3 → stackrelcolor(blue)(+)("C")"H"_2"CH"("CH"_3)"CH"_2"CH"_3 stackrelcolor (blue)("hydride shift")(→) "CH"_3stackrelcolor(blue)(+)("C")("CH"_3)"CH"_2"CH"_3 → underbrace("CH"_2"=C"("CH"_3)"CH"_2"CH"_3)_color(red)("2-methylbut-1-ene") + underbrace(("CH"_3)_2"C=CHCH"_3)_color(red)("2-methylbut-2-ene")#
(iv) #"CH"_3"CH(OH)CH"("CH"_3)_2#
#"CH"_3"CH(OH)CH"("CH"_3)_2 → "CH"_3stackrelcolor (blue)(+)("C")"CH"("CH"_3)_2 → underbrace("CH"_2"=CHCH"("CH"_3)_2)_color(red)("3-methylbut-1-ene") + underbrace("CH"_3"CH=C"("CH"_3)_2)_color(red)("2 methylbut-2-ene") #
#"CH"_3stackrelcolor (blue)(+)("C")"CH"("CH"_3)_2 stackrelcolor (blue)("hydride shift")(→) "CH"_3"CH"_2stackrelcolor (blue)(+)("C")("CH"_3)_2 → underbrace("CH"_3"CH"_2"C"("CH"_3)"=CH"_2)_color(red)("2-methylbut-1-ene") + underbrace("CH"_3"CH=C"("CH"_3)_2)_color(red)("2-methylbut-2-ene")#
