In an experiment to estimate the size of a molecule of oleic acid,$1\, mL$ of oleic acid is dissolved in $19\, mL$ of alcohol. Then $1\, mL$ of this solution is diluted to $20\, mL$ by adding alcohol. Now,$1$ drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water,forming a one-molecule-thick layer. Lycopodium powder is sprinkled evenly over the film,and its diameter is measured. Knowing the volume of the drop and the area of the film,we can calculate the thickness of the film,which gives us the size of the oleic acid molecule.
Read the passage carefully and answer the following questions.
$(a)$ Why do we dissolve oleic acid in alcohol?
$(b)$ What is the role of lycopodium powder?
$(c)$ What would be the volume of oleic acid in each $mL$ of the solution prepared?
$(d)$ How will you calculate the volume of $n$ drops of this solution of oleic acid?
$(e)$ What will be the volume of oleic acid in one drop of this solution?

(C) Oleic acid is dissolved in alcohol because it does not dissolve in water,allowing it to form a distinct film on the water surface.
$(b)$ Lycopodium powder is sprinkled on the water surface to make the boundary of the oleic acid film visible. As the oleic acid spreads,it pushes the powder aside,creating a clear circular area that can be measured.
$(c)$ The concentration of the solution is: First dilution: $1\, mL$ in $20\, mL$ total. Second dilution: $1\, mL$ of the first solution in $20\, mL$ total. Thus,the volume of oleic acid per $mL$ of the final solution is $\frac{1}{20} \times \frac{1}{20} = \frac{1}{400}\, mL$.
$(d)$ The volume of $n$ drops can be calculated by using a burette or a measuring cylinder to find the total volume of a known number of drops and then dividing by $n$.
$(e)$ If $n$ drops make $1\, mL$,then the volume of one drop is $\frac{1}{n}\, mL$. Since the concentration is $\frac{1}{400}\, mL$ of oleic acid per $mL$ of solution,the volume of oleic acid in one drop is $\frac{1}{400n}\, mL$.