Quick question regarding Final Pressure of a mixture of (inert) gases

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boxbrown

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According to TPR (from hyperlearning science workbook, Chemistry Passage 50, #3),

It states that for equal volume of inert gases A and B, the Final Total pressure is equal to the average of the pressure of each component, so: Final Total Pressure= (P flask A +P flask B)/2.
Specifically, the problem stated that Flask A has pressure of 450 torr, and B was 620 torr, so the inert mixture of the two gases would yield Final Total Pressure of (450 + 620)/2 = 535 torr.
If the gases were not inert and reacted with one another, you would have a different Final Total Pressure.

What I don't understand is (1) why are we allowed to take the average of these individual gases to get the final pressure? In other words, does equal volume of each imply equal moles of gas for each flask- but I thought this would only be in the case if there is constant pressure (which clearly isn't the case- flasks A and B have different pressures!), volume, and temperature.
2 Which gas law applies here? I thought perhaps Raoult's Law which says Pi=(X)(Pvapor) or Dalton's law which states Pi=(X)(Ptotal). Even if the Mole fraction is X=1/2 for each gas, I'm not sure how we get TPR's "Average formula" above.

This problem/concept has confused me, and I would really be grateful for any help I can get. Thanks!
 
If you smooshed both gases into one flask, the total pressure would be (450 + 620). If you then let this mix expand into both flasks, the total volume of the mix would double, therefore the pressure would go down by half.

Final pressure is (450 + 620) / 2.
 
If you smooshed both gases into one flask, the total pressure would be (450 + 620). If you then let this mix expand into both flasks, the total volume of the mix would double, therefore the pressure would go down by half.

Final pressure is (450 + 620) / 2.

I think that makes sense; so it's essentially an application of Boyle's law. It just seemed weird, because I thought some how you would have to apply Dalton's Law of Partial Pressure in these kind of problems, but I guess not. Thanks a bunch Sazerac!
 
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