What is the molecular formula of ethyl acetate?

$(a)$ Why is hard water not suitable for washing clothes with soap?
$(b)$ Why does micelle formation take place when soap is added to water?
$(c)$ What is saponification?

Complete the following chemical reactions and write the chemical name of the products obtained.
$(i)$ $CH_{2}=CH_{2} + H_{2}O \longrightarrow$
$(ii)$ $CH_{3}COOH + NaOH \longrightarrow$
$(iii)$ $CH_{3}CH_{2}OH \xrightarrow{H_{2}SO_{4}} $
$(iv)$ $HCOOH + Na \longrightarrow$
$(v)$ $C_{2}H_{5}OH \xrightarrow{\text{Alk. } KMnO_{4}} $

With the help of a diagram,explain the cleansing action of soap.

Which functional group is present in alcohol?

$(a)$ Differentiate between soap and detergent.
$(b)$ Explain why soaps form scum with hard water,whereas detergents do not.