Solving the ideal gas law for volume -> length

[jaded18]

[SOLVED] solving the ideal gas law for volume --> length

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

 

[hage567]

I think you've done it properly. You get 3.44 x 10^-9 m. That's the right magnitude anyway. Maybe ask your teacher?

 

[Blueshift5]

Yes, you are correct in using the ideal gas law to solve for volume and then using that to calculate the volume per molecule. However, the volume of one mole of gas that you calculated is not accurate. It should be V= 0.0246 m^3, not 2.46(10^-2) m^3. This is because the value of R in the ideal gas law is in units of m^3 (atm/mol*K), not cm^3 (atm/mol*K).

Using the correct value of V=0.0246 m^3, the volume per molecule would be V=4.09*10^-29 m^3. Then, taking the cube root of this value would give you the length of one side of the cube as 3.8*10^-10 m. This is a very small value, as expected for the size of gas molecules.

It is important to pay attention to units when using equations and to always double check your calculations to ensure accuracy. I hope this helps and clarifies the solution for you.