How would you bring about the following conversions? Name the process and write the reaction involved.
$(a)$ Ethanol to ethene.
$(b)$ Propanol to propanoic acid.
Write the reactions.

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(N/A) This conversion is achieved by the dehydration of ethanol using hot concentrated $H_2SO_4$,which acts as a dehydrating agent.
Reaction: $CH_3CH_2OH \xrightarrow[conc. H_2SO_4]{Hot} CH_2=CH_2 + H_2O$
$(b)$ This conversion is achieved by the oxidation of propanol using an oxidizing agent such as alkaline $KMnO_4$ or acidified $K_2Cr_2O_7$.
Reaction: $CH_3CH_2CH_2OH \xrightarrow[Heat]{Alk. KMnO_4} CH_3CH_2COOH$

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