• Sep 3rd 2007, 05:41 PM
help1
This is the problem:

"Suppose 300 cubic meters of oil is spilled into the ocean. Find the area of the resulting slick, assuming that it is one molecule thick and that each molecule occupies a cube 0.50 µm on a side."

• Sep 3rd 2007, 06:56 PM
TKHunny
You have assumed that the molecues fit together perfectly. This is only a division problem.

$\displaystyle \frac{300 m^{3}}{0.5 \mu^{3}}$ = Number of Molecules

Where are you struggling, this setup or the unit conversion?
• Sep 4th 2007, 11:47 AM
topsquark
Quote:

Originally Posted by TKHunny
You have assumed that the molecues fit together perfectly. This is only a division problem.

$\displaystyle \frac{300 m^{3}}{0.5 \mu^{3}}$ = Number of Molecules

Where are you struggling, this setup or the unit conversion?

(This is from the other thread.)
Quote:

Originally Posted by help1
You suggested that the answer is 300/.5 so that equals 600. So are you saying that the answer is that the area is 600? That doesn't make sense at all to me! How do I find the area?

No. The area of the spill is not 600 $\displaystyle m^2$. Keep track of your units.

The volume of the spill is
$\displaystyle V = \text{Area} \times \text{thickness}$

So
$\displaystyle \text{Area} = \frac{V}{\text{thickness}}$

We know the volume of the spill and we know that the spill is one molecule thick, so
$\displaystyle \text{Area} = \frac{300~m^3}{0.50~\mu m}$
as TKHunny said.

Now get the units on top and bottom to be similar:

$\displaystyle \frac{300~m^3}{0.50~\mu m} \cdot \frac{1~\mu m}{1 \times 10^{-6}~m} = \frac{300~m^3}{0.5 \times 10^{-6}~m} = 600 \times 10^6~m^2 = 6 \times 10^8~m^2$

Always always always keep track of your units!

-Dan