How would you bring about the following conversions ? Name the process and write the reaction involved

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.

(a) By the dehydration of ethanol in the presence of concentrated $H_{2}SO_{4}$

C$H_{3}$C$H_{2}$OH $\xrightarrow [Conc.H_{2}SO_{4} ]{ Hot}$ C$H_{2}$ = C$H_{2}$ + $H_{2}$O

(b) By the oxidation of propanol using oxidising agent such as alkaline KMn$O_{4}$.

C$H_{3}$C$H_{2}$C$H_{2}$OH $\xrightarrow [ Heat ]{ alk.KMn{ O }_{ 4 } }$

C$H_{3}$C$H_{2}$COOH