I would really appreciate some assistance on this problem. I can't seem to get the correct answer. Thank you so much!
You can obtain a rough estimate of the size o f a molecule with the following simple experiment: Let a droplet of oil spread out on a fairly large but smooth water surface. The resulting "oil slick" that forms on the surface of the water will be approximately one molecule thick.
Given an oil droplet with a mass of 9.03 x 10^-7 kg and a density of 911 kg/m^3 that spreads out to form a circle with a radius of 43.8 cm on the water surface, what is the approximate diameter of an oil molecule? Answer in units of m.
2007-08-16 10:40:50 · 5 answers · asked by sg88 1 in Science & Mathematics ➔ Mathematics
density = mass / volume
volume = mass / density
volume = 9.03x10^-7 kg / 911 kg/m^3 = 9.912x10^-10 m^3
Now the radius is 43.8 cm, you want this in meters because you have to work with the same units. So this is 43.8 cm / 100 cm/m = .438 m
The area of the resulting circle is just then pi*r^2 = 3.141*.438^2 = .602 m^2
Now just divide the volume by the area to get the height, or diameter of a molecule.
9.912x10^-10 m^3 / .602 m^2 = 1.645 x 10^-9 m
2007-08-16 10:51:40 · answer #1 · answered by Jon G 4 · 2⤊ 0⤋
You can think of the oil slick as a cylinder, whose "height" is the diameter of one molecule.
Use the formula for cylinder volume (V = Ï r^2 h) to find the volume of this in terms of d, and set this equal to the known volume of the oil droplet (which you can calculate from the mass and density). Make sure you're using the same units! Now just solve the equation for d.
2007-08-16 17:52:18 · answer #2 · answered by Anonymous · 0⤊ 0⤋
D = m/V
911 kg/m^3 = 9.03*10^-7 kg/V
V = m/D = 9.03*10^-7 kg/911 kg/m^3 = 9.91 * 10^-10 m^3
Let us assume the spherical drop flattens out into a cylinder one molecule high. Thus the volume will be h*Ïr^2, where r = 43.8 cm = 0.438 m. This volume is still equal to 9.91 * 10^-10 m^3/(Ï*0.438^2) = h
This is 1.64 *10^-9 m or 16.4 angstroms.
So the molecule is ~16.4 angstroms in diameter.
2007-08-16 17:55:23 · answer #3 · answered by Edgar Greenberg 5 · 0⤊ 0⤋
Volume = (9.03 X 10^-7)/911 = 9.91 x 10^-10 m^3
Area of circular oil slick is pi*.438^2 = .6027 m^2
So diameter of oil molecule must be (9.91X10^-10)/.6027 =
1.64 X 10^-11 meters
2007-08-16 17:58:18 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋
The height of the slick times the area of the slick give the volume of the slick. This times the density of the slick gives its mass:
h(pi*r^2)(density)= m
h=m/((pi*r^2)(density)) = 1.644 nanometers
2007-08-16 17:54:05 · answer #5 · answered by supastremph 6 · 0⤊ 0⤋