Estimating Diameter of an Oil Slick with One Liter of Spilled Oil on a Lake

[mlowery]

The Problem
One liter (1000 cm^3) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of 2 x 10^-10 m.

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My Work
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1. I will first change liters from cm^3 to m^3 so that the units will match up.
1 liter = 1000 cm^3 = 1.0 x 10^-3 m^3

2. I will use the formula for volume of a cylinder (V = h π r^2) where:

V = 1.0 x 10^-3 m^3
h = 2 x 10^-10 m
r = unknown

3. Simply solve for the unknown radius:
(1.0 x 10^-3 m^3) = (2 x 10^-10 m) π r^2
(1.0 x 10^-3 m^3) / (2 x 10^-10 m) = π r^2
[(1.0 x 10^-3 m^3) / (2 x 10^-10 m)] / π = r^2
{[(1.0 x 10^-3 m^3) / (2 x 10^-10 m)] ^ (1/2)} = r = 1.3 x 10^3m

4. Calculate the diameter using the radius:
D = 2r
D = 2(1.3 x 10^3)
D = 2.5 x 10^3m

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Final Answer
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D = 2.5 x 10^3m

I have no idea if this is right or not, but it is as close as I have been able to get. This question has been giving me problems for hours. Can somebody confirm my calculation, or inform me where I went wrong?

Thanks,
Mitch

 

[lightgrav]

Good job - but -
How come you don't know if it is right? Do you have zero confidence?
Why do you think "went wrong"? Here's how to "check" your answer:

If you sliced a 1-liter bottle into disks (10^9 of them)
they'd fill a rectangle 10^5 disks x 10^4 disks , or 10^4 m x 10^3 m

How big an oil slick *** 1 - atom thick *** did you expect 1 liter to make?

Always ry to check answers ROUGHLY, using a different approach

 

[mlowery]

Thanks.

I was having trouble grasping the concept that we assume the oil molecules are perfect spheres. I was thinking, you know, complex branch-chain alkanes and stuff. So even when I did get the correct calculation, I was unsure whether my assumption was valid.

Additionally, I found one flaw in my answer. Significant figures. On the diameter of the molecule, I cannot assume that

2 x 10^-10 m == 2.0 x 10^-10 m.

Therefore, my answer should be D = 3 x 10^3m

Thanks for the response lightgrav,
Mitch