Explain the dehydration reaction of $2$-methylbutan-$1$-ol with concentrated $H_2SO_4$.

(N/A) The dehydration of $2$-methylbutan-$1$-ol with concentrated $H_2SO_4$ at $443 \ K$ proceeds via the formation of a carbocation intermediate.
$1$. Protonation of the alcohol: The hydroxyl group is protonated to form a good leaving group $(-OH_2^+)$.
$2$. Formation of carbocation: Loss of water molecule generates a $1^{\circ}$ carbocation.
$3$. Rearrangement: The $1^{\circ}$ carbocation undergoes a $1,2$-hydride shift to form a more stable $3^{\circ}$ carbocation.
$4$. Elimination: Loss of a proton from the $3^{\circ}$ carbocation yields $2$-methylbut-$2$-ene as the major product,following Saytzeff's rule.