Question

You can obtain a rough estimate of the size of a molecule by the following simple experiment. Let a droplet of oil spread out on a smooth water surface. The resulting oil slick will be approximately one molecule thick. Given an oil droplet of mass of 7.61 × 10−7 kg and density of 912 kg/m3 that spreads out into a circle of radius 43.5 cm on the water surface, estimate the diameter of an oil molecule. Answer in units of m. Your answer must

Answer 1

Answer:

• The diameter of the molecule of oil is $1.405 10 ^{-9} \ m$

Explanation:

We define density as

$\rho = \frac{mass}{volume}$

So, the volume for our oil will be

$volume = \frac{mass}{\rho}$

$volume = \frac{7.62 \ 10^{-7} \ kg}{ 912 \ \frac{kg}{m^3} }$

$volume = \frac{7.62 \ 10^{-7} \ kg}{ 912 \ \frac{kg}{m^3} }$

$volume = 8.355 \ 10 ^{-10} \ m^3$

the volume for a cylinder with radius r and height h is

$volume = \pi r^2 h$

So, we can obtain the height of the droplet of oil as:

$h = \frac{volume}{\pi r^2}$

the radius is

$r=43.5 \ cm = 0.435 \ m$

$h = 1.405 10 ^{-9} \ m^3$

And this is the diameter of the oil molecule.