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Understanding how a real gas differs from an ideal gas

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In an industrial process, nitrogen has to be heated to 500K at constant volume. If it enters the system at 300 K and 100 atm, what pressure does it exert at its final working temperature? Treat it as a van der Waals gas. Assume the volume is 1 m^3 (where "^" means "to the exponent").

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Finding Molar Mass Through Dumas Method

We are trying to determine the molar mass of an unknown liquid through Dumas Method: measure density (mass/volume) of its vapor at a known temperature and pressure. I am having trouble answering question 3 and question 4 as attached.

1) I did the calculations for question 3 but am really lost on whether I plugged in the right numbers eg whether I use the # of moles calculated from the ideal gas equation in question C. If I do that, wouldn't the response make no sense? We're trying to determine the difference between the known between an ideal or non-ideal gas but if the moles of the gas is derived from the ideal gas equation to plug into non-ideal gas equation, wouldn't the results be wrong? Also, it says you can determine the actual volume of the gas molecules from the volume of the liquid, because in a liquid, the molecules are compressed about as close together as possible - what does this mean? I had no idea how to solve this so I just used the volume of a liquid - is this wrong? Are my calculations correct?
2) I'm having trouble with question 4: part a&b, have to eplain why chemically (not just b/c of mathematics as I already did. Also, question c&d - please advise.

thank you!

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