I know this has multiple parts, which isn\'t really allowed..but these are basic

Question

I know this has multiple parts, which isn't really allowed..but these are basic ideas of thermodynamics that involve little to no calculation (I mainly want to check my work) so I didn't think it would be a problem.

The ideal gas law states that PV = nkbT:

1) Does it matter what the units of T are? Why or why not?

2) What is the avg. volume per molecule for an ideal gas at room temperature and pressure? How far apart on avg. are a pair of molecules in an ideal gas under these circumstances? How does that distance compare to the size of a small molecule like N2?

3) Under what circumstances do you expect the ideal gas law to break down?

Explanation / Answer

1) Yes it matters because all constants like kb were determined using the Kelvin scale of temperature.

So, using any other unit will lead to wrong results.

2)At T = 298 K, P = 1.013x105 Pa, kb = 8.314 kJ/mol-K,

So, V/n = volume/mol = 24.46 dm3

So, per molecule volume = 24.46/NA = 24.46/(6.023x1023) dm3 = 4.06x10-23 dm3 = 4.06x10-26 m3.

So, distance between 2 molecules on an average = (4.06x10-26)1/3 m = 3.437x10-9 m

Size of an N2 molecule = 300 pm = 3x10-10 m

So, the average distance is around 10 times as large as a nitrogen molecule.

3)The ideal gas law will break down when the intermolecular distance becomes similar to the molecular size. That will be under high pressure, low temperature. Then the molecular forces of attraction will be too large to ignore and molecular volume will also have to be accounted for in the gas law.

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