$(i)$ How will you bring about the following reactions? Write the concerned chemical equations:
$(a)$ Ethanol to Ethene.
$(b)$ Ethanol to Ethanoic acid.

(N/A) Ethanol undergoes dehydration in the presence of hot concentrated sulfuric acid $(H_2SO_4)$ at $443 \ K$ to form ethene:
$CH_3CH_2OH \xrightarrow[Conc. H_2SO_4]{443 \ K} CH_2=CH_2 + H_2O$
$(b)$ Ethanol undergoes oxidation in the presence of alkaline potassium permanganate $(KMnO_4)$ or acidified potassium dichromate $(K_2Cr_2O_7)$ to form ethanoic acid:
$CH_3CH_2OH \xrightarrow[alk. KMnO_4]{Oxidation} CH_3COOH$