Question

10 drops of oleic acid solution of concentration 1/400 cm³ per cm³ of alcohol, are dropped on a water surface. The circular film thus produced has radius 10cm. Find the molecular size of oleic acid, if the radius of each drop is 1.4mm.

Answer 1

$$\begin{gathered} Theradiusofdropofoleicacidconcentrationwithalcohol=1.4\times {10}^{-3}m. \\ Thereforevolumeof10suchdrops=10\times \frac{4}{3}\pi \times (1.4\times {10}^{-3}{)}^3{m}^3. \\ Nowthevolumeoleicacid=\frac{1}{400}\times 10\times \frac{4}{3}\pi \times (1.4\times {10}^{-3}{)}^3{m}^3. \\ Letussupposetherearennumberofoeicacidmoleculesofradiusr. \\ Thereforen\times \frac{4}{3}\pi r^3=\frac{1}{400}\times 10\times \frac{4}{3}\pi \times (1.4\times {10}^{-3}{)}^{3}orn{r}^3=1.4\times 1.4\times 1.4\times {10}^{-10}orn=\frac{4\times 1.4\times 1.4\times 1.4\times {10}^{-10}}{r^3}. \\ Againtheareaofthefilm=areaofnnumberofoleicacidmoleculei.e. \\ \frac{4\times 1.4\times 1.4\times 1.4\times {10}^{-10}}{r^3}\times 4\pi r^2=4\pi \times (10\times {10}^{-2}{)}^{2}orr=4\times 1.4\times 1.4\times 1.4\times {10}^{-10}\times {10}^{2}orr=4\times 0.686\times {10}^{-8}m=2.744\times {10}^{-8}m. \\ orr=0.2744\times {10}^{-7}m. \end{gathered}$$