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

• The diameter of the molecule of oil is
  `1.405 10 ^(-9) \ m`

Step-by-step explanation:

We define density as

`\rho = (mass)/(volume)`

So, the volume for our oil will be

`volume = (mass)/(\rho)`

`volume = (7.62 \ 10^(-7) \ kg)/( 912 \ (kg)/(m^3)  )`

`volume = (7.62 \ 10^(-7) \ kg)/( 912 \ (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 = (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.