Question

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes $0.01{\text{cm}}^3$ of oleic acid per ${\text{cm}}^3$ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area $4{\text{cm}}^2$ by considering $100$ spherical drops of radius${\left(\frac{3}{40\pi }\right)}^{\frac{1}{3}}\times {10}^{-3}\text{cm}$. Then the thickness of oleic acid layer will be $x\times {10}^{-14}\text{m}$ where $x$ is

Answer 1

Volume of film $=$ Area of film $\times$ thickness
Also from the question, Volume of film $=$ Volume of 100 spherical drops
So, Volume of film $=$ Area of film $\times$ thickness $\times$Volume of 100 spherical drops

So, $4t=100\times \frac{4}{3}\pi r^3$
where $t$ is the thickness of the solution.
$4t=100\times \frac{4\pi }{3}\times \frac{3}{40\pi }\times {10}^{-9}$
$t=\frac{{10}^{-8}}{4}\text{cm}=25\times {10}^{-12}\text{m}$

Now, thickness of oleic acid layer:
$t_0=0.01t$ ($\because$ concentration of oleic acid is $0.01{\text{cm}}^3$ per $1{\text{cm}}^3$)

$t_0=25\times {10}^{-14}\text{m}=x\times {10}^{-14}\text{m}$
$\therefore x=25$