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Consider an ideal gas at 27.0 degrees Celsius and 1.00 atmosphere pressure. Imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube.

What is the length L of an edge of each small cube if adjacent cubes touch but don't overlap?

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I know that the ideal gas law states V=nRT/p and that in this case R=8.2057(10^-5) m^3 (atm/mol*K), p=1atm, T=27+273K. What is n? Well if I calculate the volume of one mole of the gas, I get V=2.46(10^-2) m^3. And then when I use this result to find the volume of one molecule (the volume of the imaginary cube that is assumed to surround each molecule, I get V=( 1/(6.02*10^23))(8.2057)(27+273)= 4.09*10^-26 m^3

Then don't I just use this volume per molecule that I just calculated to find the length of a side of the cube by taking the cube root of it?! Why isn't the answer 0.000000003m?!

No one at the physics forum could help, so if you know how to do this prob correctly, any feedback will be awesome

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# Solving the ideal gas law for volume -> length

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