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As we all know, air consists of many gases including oxygen and carbon dioxide. I found that carbon dioxide is heavier than O2. Does the volume difference neglect the mass difference? Is it same for all other gases in air or is there another force that keeps all of these gases together?

If I take a breath of a fresh air, will the exhaled air be heavier because of its higher CO2 content? Will it fall on the floor?

Qmechanic
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Markus von Broady
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  • Even the smallest initiation of disturbance stimulates positive entrophy change and chaos. Making different things merge. When you spray perfume in middle of a room, it diffuses even if theres no convection. – huseyin tugrul buyukisik Aug 22 '12 at 19:37
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    Yes, Tuğrul, but pouring oil to a cup with water won't make them diffuse, so this is not always the case, question is why it is with air. – Markus von Broady Aug 23 '12 at 06:03
  • You are right Marcus, maybe the activation energy for displacement into foreign fluid is too high and its probability is very low. But still there is very very small fraction that can for the water and oil. – huseyin tugrul buyukisik Aug 23 '12 at 09:23
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    I asked another question that is similar. Not about what happens to the gas you exhale, but the general distribution of equilibrium mixture of ideal gases of different formula masses. Although part of the picture, convection is so important for Earth that the minute vertical stratification due to mass difference is unlikely to matter for everyday life. http://physics.stackexchange.com/q/34785/ – Alan Rominger Aug 23 '12 at 13:00

3 Answers3

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From your comments it seems that effectively you are asking about "why do gases mix so easily?"

If a system such as a mixture of gases is kept under constant temperature in a constant volume, the equilibrium state corresponds to the minimum of Helmholtz free energy:

$$A = U - TS$$

As you see, for $A$ to reach the minimum either the energy $U$ should decrease or the entropy $S$ should increase (or both in reality).

Minimizing energy. Most of the energy of common gases at normal conditions comes from their kinetic energy defined by the temperature. Energy due to intermolecular potential is negligible. So the only possibility to lower the energy is to lower the gravitational energy. In essence it would require the mixture to perfectly separate --- heavy gases at the bottom, light gases up.

Maximizing entropy Maximum entropy for the system in hand (under specified conditions) would imply perfect mixture, the state of most disorder. That's actually what drives the diffusion.

So as you see, the equilibrium state is a compromise between low energy and high entropy. For gases the entropy wins, because there isn't much energy difference between a mixture and a separated state (apart from gravity, which is still small).

As for your example with oil and water the situation is opposite. Unlike gases considerable amount of energy in liquids comes from intermolecular forces. Thus there is a huge differences in energy of interaction water-water or water-oil, so it is more preferable do separate to considerably minimize the energy.

Yrogirg
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    +1 spot on. Intermolecular forces are more important in liquids because the average intermolecular spacing is much shorter. – John Rennie Aug 23 '12 at 08:55
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    Do I understand it - lowering gravitational pull will make gases stratify? It would explain why air is stratified in higher layers of atmosphere, as data linked by Zhermes. But it doesn't make sense to me, as gravity is the force that make substances stratify in the first place! – Markus von Broady Aug 23 '12 at 10:07
  • "to lower the gravitational energy" --- meant to lower energy of the gas in the gravitational field by gas stratifying, $g$ doesn't change, it is gas configuration that changes. It's just like saying lowering the gravitational energy of a rock by moving it down from a hill. – Yrogirg Aug 23 '12 at 10:22
  • Oh, sorry, I had a hard time understanding gravitational energy, until I searched it on wiki and found it's what I know by "potential energy". Maybe I should point out that I'm a physics ignorant :D. Thank You for Your answer, but I'm accepting the one of Zhermes. I wished I could accept both, though. – Markus von Broady Aug 23 '12 at 22:40
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CO2 will, on average, equilibrate slightly lower than O2 in a gravitational field. But the difference in the force of gravity is very small compared to the random thermal motion of the molecules, thus the effect is effectively negligible in day to day life.

In the context of the atmosphere as a whole this can be a non-negligible effect (e.g. this link), and in astrophysical contexts, this can be very important (e.g. this paper or this one).

Emilio Pisanty
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DilithiumMatrix
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  • So, as I understand it, there are random factors, like wind, heated surface, chemical reactions on/near surface, that make air below mesosphere mixed? I also wonder, If I took two empty (only vacuum inside) containers, opened them on opposite sides of my room, and then closed them and checked for gases in laboratory, would they both compare nearly perfect, or the differences could be actually substantial? – Markus von Broady Aug 23 '12 at 06:09
  • Your right, but the biggest factor keeping gases mixed is their thermal energy---every molecule is flying around at random because its hot (even in the 'cold' upper atmosphere, its still moving rapidly), and this keeps things well mixed. If you did the containers experiment on opposite sides of the room, they would always be incredibly near identical (no device could measure a difference). There are, about $10^33$ particles that would be captured -- the statistics to have them mixed are very strong. – DilithiumMatrix Aug 23 '12 at 14:34
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The exhaled air is lighter, because it is hotter, and this swamps the CO2 density difference. But if you have pure CO2, it will fall down before diffusing into the air around it--- there is a common demonstration of pouring CO2 on a candle to snuff it out, you can do it as if you were pouring water, the CO2 displaces the oxygen and the candle dies.

Ron Maimon
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