Absolute alcohol is converted into diethyl ether by heating at $410 \, K$ in the presence of which of the following?

The starting material is $butan-2-ol$. The reaction with $H^+/\Delta$ yields $(x)$ possible products,and the subsequent reaction of these products with $Br_2/CCl_4$ yields $(y)$ possible products. Determine the values of $x$ and $y$.

Write the mechanism of the acid dehydration of ethanol to yield ethene.

Write the main product of the given reactions:
$1$. $(CH_3)_2CHCHBrCH_3 \xrightarrow[ethanol]{KOH, \Delta }$
$2$. $(CH_3)_2CHCH(OH)CH_3 \xrightarrow{H_2SO_4, \Delta }$

When glycerol is treated with an excess of $HI$,it produces:

Write the structures of different isomeric alkyl groups corresponding to the molecular formula $C_{5}H_{11}$. Write the $IUPAC$ names of the alcohols obtained by the attachment of $-OH$ groups at different carbons of the chain.