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I know that technically two or more gases in one container should have different volumes. But when you imagine the gas molecules being mixed together, it look sorta like the two gases have the exact same volume, that is the volume of the container.

Also, in one of the questions I did on gas laws, wet hydrogen and hydrogen are shown to have the same volume in a container. Given the barometric pressure, I subs tract the vapor pressure at the certain temperature from it. Then I sub the pressure of dry hydrogen gas into the ideal gas law along with the volume of the container to find the number of mole of hydrogen gas.

enter image description here This is the part in my textbook that I am confused about. It shows how partial pressure fraction is equal to the corresponding mole fraction. But this is all under the assumption that the volume and other things are constant. I am lost right here, because Avogadro's theory states the volume and mole number of a gas are directly proportional. ( wait...wouldn't this mean that pressure, mole and volume are all directly proportional to one another???)

Can anyone give a answer, along with a proof/ a source?

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Your second idea, that they have the same volume, is correct. Each gas in a mixture of gases stored in the same container has the volume of that container. Remember that gases are mostly empty space, so it is not a problem that their volumes overlap.

As is implied by your comment about subtracting the vapor pressure of water from the pressure of wet hydrogen, the gases in a mixture can have different partial pressures. Perhaps that is your point of confusion.

The only case where they would have different volumes would be in a more accurate gas model than ideal gases, something like the Van der Waals model, where gas volume is corrected by a small amount to account for the portion of space that is taken up by the gas particles.

In short, each component of a mixture of gases stored in a given container shares the same volume and temperature and may (or may not) have different partial pressures and number of moles.

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  • $\begingroup$ Wait even partial pressure of ideal gas depends on their mole ratio which is volume ratio. So you mean they all got the same pressures? $\endgroup$
    – most venerable sir
    Commented Oct 31, 2014 at 3:13
  • $\begingroup$ @Doeser No, that's not what I meant. If I take 2 moles of oxygen and 2 moles of nitrogen and put them in the same container, they will have the same pressure and volume. However, if I have 1 mole of oxygen and 2 moles of nitrogen and I put them in the same container, the gases will have different partial pressures but will have the same volume (the volume of the container.) Mole ratios for gases aren't measured by volume, they're measured by pressure. Check out Dalton's Law of Partial Pressures for more information. $\endgroup$
    – Jason Patterson
    Commented Oct 31, 2014 at 13:21
  • $\begingroup$ But they are proportional according to Avogadro $\endgroup$
    – most venerable sir
    Commented Nov 2, 2014 at 17:07
  • $\begingroup$ @Doeser Avogadro's Law only applies if pressure and temperature are kept constant. That is not the case here, where volume and temperature are constant; that's why they could be canceled in the image from your book. A real life example: I fill a tire with nitrogen until it is at 100kPa pressure. If I then put in an equal number of moles of oxygen, the tire's volume won't increase (much), but the pressure inside the tire will double. The oxygen is filling the same space as the nitrogen. They share a volume, and each has the same partial pressure, 100kPa, and the total gas pressure is 200kPa. $\endgroup$
    – Jason Patterson
    Commented Nov 3, 2014 at 2:18
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    $\begingroup$ Van der Waals made a model that involved gases that were slightly more real. His model accounted for the volume of the gas particles and the attraction between them. That's all there is to it. Any real gas is a van der Waals system. $\endgroup$
    – Jason Patterson
    Commented Nov 12, 2014 at 2:17

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