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### Topic: Finding the percent space occupied by oxygen in a unit cell  (Read 6246 times)

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#### zxwut?

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• Gender:  ##### Finding the percent space occupied by oxygen in a unit cell
« on: February 01, 2010, 12:42:10 AM »

"Consider solid O2 (molecules assumed spherical) which uses the simple cubic unit cell. What percentage of the space in the unit cell is actually occupied by oxygen molecules?
With the only given: Volume of the sphere=4/3*pi*r^3"

I figured out how to compute edge length earlier but I don't know where to start with this one. I'm not given the density so I'm not sure where to go with it. I know that the a=2r because a simple cubic has 1 atom per unit cell and that the volume occupied is equal to the volume of the sphere and that the volume occupied is the volume of the sphere subtracted from the total volume. I don't know where to start or what sort of plan to follow to figure out this sort of problem. I have been flipping through my book for a while now and all I've found is how to compute edge length and radius of the molecules where density is known. Thank you for your time.

Very Respectfully,

Robert
« Last Edit: February 01, 2010, 12:58:50 AM by zxwut? »

#### AWK

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« Reply #1 on: February 01, 2010, 02:01:34 AM »
Just sketch the unit cell. How much molecules is in this cell?
AWK

#### zxwut?

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« Reply #2 on: February 01, 2010, 02:05:07 AM »
There is one molecule in each cell, I believe. Each corner has an 1/8th of an atom so added up I have one.

#### zxwut?

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« Reply #3 on: February 01, 2010, 02:11:28 AM »
What I tried to do initially was to take the atomic mass of one oxygen molecule and multiply that by Avagadro's number to get the grams per atom and then multiplied that by one atom per unit cell to get grams per cell. At this point I would have then found the volume by dividing by the density but as I said before, I don't have density as a given.

#### zxwut?

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« Reply #4 on: February 01, 2010, 03:10:39 AM »
I think I had a revelation. Since my professor is asking for a percentage, any radius for the sphere is going to be the same as the radius of an edge of the cube. Therefore, assuming an r=2, Volume of the sphere=4/3*pi and
Volume of the cube=2^3 so Vsphere/Vcube x 100 = 52.4%

#### AWK

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« Reply #5 on: February 01, 2010, 08:53:40 AM »
OK
V(ball)/V(cube) = π/6
AWK