Wlien oil is spilled on water, it forms a very thin layer with a thickness of ap

Question

Wlien oil is spilled on water, it forms a very thin layer with a thickness of approximately 1 molecule. Assume an oil molecule has a diameter of 65 Aringngstrom, and 1.0 gallon of oil is spilled on the ocean. For this problem you may treat each molecule as a perfect sphere. How many molecules will be spilled in the ocean? Each molecule covers an area equal to pir^2. Demonstrate with calculations that the area covered by all the oil molecules equals 0.34 mi^2, (if you were unable to obtain an answer for part a. assume 7.05middot10^24 molecules. In this case you need to prove that the answer is 90. Mi^2)

Explanation / Answer

A) a molecule has 65 A, this in meters is 65x10-10 m.

Now, assuming the volume of an sphere, we can say that one molecule has a Volume of:
V = 4/3 * 3.1416 * (65x10-10/2)3
V = 1.44x10-25 m3

In gallon we have 3.78 L, or simply 3.78x10-3 m3 so:
3.78x10-3 / 1.44x10-25 = 2.63x1022 molecules

To do part b) we already know that volume is 3.78x10-3m3 so, calculating r:
r = (3V/4*3.1416)1/3
r = (3*3.78x10-3 / 4*3.1416)1/3
r = 0.0966 m
r = 0.0966 m * 1 mi/1609m = 6.01x10-5 mi

From here solve for A and replace. You should get the 0.34 mi.

Hope this helps

PS: if for any reason you don't get the value given, then check for the molecules I calculated. I assumed a volume of an sphere, maybe it's not a sphere. Hopefully you will get the correct answer.

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