Question

an olive oil drop having diameter 6*10-4 spred into a circular film of radius 12cm.estimate molecular size of the oile oil

Answer 1

Question:-

An Olive oil drop having Diameter $\sf 6\times 10^{-4}m$ spreads into a Circular film of Radius 12cm.Estimate the Molecular size of the olive oil.

Solution:-

• Diameter of the olive drop=$\sf 6\times 10^{-4}m$

Radius:-

$\\ \sf\longmapsto \dfrac{Diameter}{2}$

$\\ \sf\longmapsto \dfrac{6\times 10^{-4}}{2}$

$\\ \sf\longmapsto 3\times 10^-4m$

$\\ \sf\longmapsto Radius\:of\:oil\:drop=0.3mm$

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• Radius of the film=12cm=r

$\boxed{\sf Area\:of\:the\:Film=\pi r^2}$

$\\ \sf\longmapsto (12)^2π$

$\\ \sf\longmapsto A=144\pi cm^2$

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• Volume of drop=V

$\\ \pmb{\sf\longmapsto V=\dfrac{4}{3}\pi (Radius\;of\:oil\:drop)^3}$

$\\ \sf\longmapsto \dfrac{4}{3}\pi (0.3mm)^3$

$\\ \sf\longmapsto \dfrac{4}{3}\pi (\dfrac{3}{10})^3mm^3$

$\\ \sf\longmapsto \dfrac{4}{3}\pi 0.27mm^3$

$\\ \sf\longmapsto \dfrac{4}{3}\pi 27\times 10^{-2}mm^3$

$\\ \pmb{\sf\longmapsto V=\dfrac{4}{3}\pi 27\times 10^{-5}cm^3}$

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$\boxed{\sf Molecular\:Size=Thickness\:of\:the\:film}$

$\\ \sf\longmapsto \dfrac{V}{A}$

$\\ \sf\longmapsto \dfrac{\dfrac{4}{3}\pi\times 27\times 10^{-6}}{144\pi}$

$\\ \sf\longmapsto \dfrac{4\cancel{\pi}\times \bcancel{27}\times 10^{-6}}{\bcancel{3}\times 144\cancel{\pi}}$

$\\ \sf\longmapsto \dfrac{4\times 9\times 10^{-6}}{144}$

$\\ \sf\longmapsto \dfrac{36\times 10^{-6}}{144}$

$\\ \sf\longmapsto 0.4\times 10^{-6}cm$

$\\ \sf\longmapsto 4\times 10^{-7}cm$

$\\ \sf\longmapsto \underline{\boxed{\pmb{\sf Molecular\:size\:of\:Olive\;oil\:drop=4\times 10^{-9}m}}}$

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You can directly calculate the Thickness of the film using the formula given below

if

• Volume of n drops of solution=nVcm$^3$
• t be thickness of film
• A be Area of film

Formula:-

$\boxed{\pmb{\sf t=\dfrac{nV}{A\times 400}cm}}$