Volume of Two Gases: Does Adding Apply?

[Drakkith]

I had an exam question where I had to find the volume taken up by a gas consisting of 32 grams of oxygen and 4 grams of helium at STP conditions. I ended up getting a supposedly incorrect answer of about 44.8 liters by finding the volume of both gases and adding them together. However, my instructor said that it's actually half that, 22.4 liters, and that you don't add the volume of two gases together in this situation. When I asked why, he couldn't really explain it in any way that made sense to me and we got into a confusing discussion over when the ideal gas law applies and when it doesn't. The whole thing ended up confusing me.

So, in this situation do you add the volume taken up by the two gases together or not?

 

[Borek]

The only thing that matters is number of moles. 4 gram of helium is 1 moles, 32 grams of oxygen is another mole. All in all there are two moles of gas, and the volume is that of two moles - so 44.8 L at STP.

Unless the question was worded differently, 44.8 L is a correct answer.

 

[Bystander]

So, in this situation do you add the volume taken up by the two gases together or not?

Sadly, people get PhDs, teaching positions, and other jobs and recognition as "scientists/experts" without ever understanding the difference between mole fraction and partial pressure, and when to use each.

 

[Drakkith]

I remember part of his reasoning was that he thought that two different gases don't interact with each other under the assumptions of an ideal gas. Even assuming this, wouldn't the pressure on the container walls still be the same as when they are interacting with each other? If one gas exerts X pressure on the walls of a container, and another gas exerts Y pressure on the walls of a container, then the pressure when you combine them would seem to be X+Y even if the two gases passed right through each other.

 

[Bystander]

he thought that two different gases don't interact with each other under the assumptions of an ideal gas.

This misunderstanding of the properties of "ideal gases" is as good a root cause for "partial pressure - mole fraction" confusion as any; "point masses" imply no intermolecular collisions, however, it has never been necessary to exclude collisions from discussion of ideal gas properties, one need only constrain collisions to being perfectly elastic. Never get any good chemical kinetics from the model, but that's not the point of a thermodynamic model.

 

[Drakkith]

Thanks, guys.

On a related note, what does "cavitation" mean in the following context:

The ideal gas law is often introduced in its common form:

where P is the cavitation pressure of the gas, V is the cavitation volume of the gas, n is the cavitation amount of substance of gas (measured in moles), R is the ideal, or universal, cavitation gas constant, and T is the cavitation temperature of the gas.

 

[Bystander]

"cavitation"

This is from some larger discussion regarding bubble formation in liquids? Never heard the word being used in any other context, and wouldn't think it's any sort of general discussion of boiling if it's using an ideal gas model.

 

[Drakkith]

It's right out of the top paragraph on wiki's Ideal Gas Law article: http://en.wikipedia.org/wiki/Ideal_gas_law

 

[Bystander]

Thankee --- and, at the bottom of the article, under "external links" we find "diving medicine." "Cavitation" shows up nowhere else in the article, suggesting it's Frankenstein's monster stitched together from two or three other discussions. Woonta thunk Wiki would be that flaky on PV = nRT.

Getting back to your original "?" long ago memories of a religious distinction between Dalton's law of partial pressures for mixing (non)ideal gases and somebodies approach of adding the volumes of pure components, have surfaced; sometime in my early education, there was an instructor who really thought there should be a difference --- he never could demonstrate a difference, produce a reference, or explain himself, but we all had to do a little mindreading on exams to discern which he wanted applied --- then we all promptly forgot it.

 

[Borek]

Edited these 'cavitations' out, they looked nonsensical.

There is a slight chance that in some context they make sense, but never in a general article on the IGL.