Answer to Question #179526 in Physics for EGG

Question

 A typical oil molecule has an effective diameter of 0.25 nm. If 25 L (1 L is the same as 1000 cm3) of oil is spilled on a lake, and if the oil is spread so that it is only a single molecule thick, what will be the approximate area of the oil slick? Assume that the oil molecules are just touching.

Answer 1

First, find the volume of one molecule:

$$v=\frac 16 \pi d^3.$$

Find the number of molecules in 25 L of oil:

$$N=\frac Vv=\frac{6V}{\pi d^3}=\\\space\\=\frac{25·10^{-3}}{3.14·(0.25)}$$

One molecule takes an area on the surface of water of

$$a=\pi\frac{d^2}{4}.$$

N molecules will give an approximate area of

$$A=Na=\frac{6V}{\pi d^3}·\pi\frac{d^2}{4}=\frac{3V}{2d},\\\space\\ A=\frac{3·25·10^{-3}}{2·0.25·10^{-9}}=150·10^6\text{ m}^2.$$