I If air is a mixture, why don't the gases separate?

[Chestermiller]

My professional judgement tells me to prefer some quantitative parameters rather than just intuition.
I have no direct experience with gas separation.
I just said that the non-separation of N2 - O2 does not necessarily implies non-separation in all cases.

Wouldn't you think that the magnitude of the gravitational contribution would be roughly proportional to the difference in molecular weights. So if the segregation of N2 and O2 is zilch, the segregation between air (mw 29) and CO2 (mw 44) at equilibrium would be about 15/4 = ~ 4 times zilch.

 

[sophiecentaur]

What do you mean with "the distributions of heavy and light molecules would have the same effect on each other"? I would say diffusion can't happen in absence of collisions.

--
lightarrow

My wording was really poor, wasn't it?
I was thinking of partial pressures and that the gradients would be expected to be different. Yes, the diffusion will be slowed by collisions (as in a porous medium) but I am sure that the final gradients should turn out to be different for different gases, and the same that you would get if each gas were in isolation around a less massive planet (?).

 

[nasu]

Wouldn't you think that the magnitude of the gravitational contribution would be roughly proportional to the difference in molecular weights. So if the segregation of N2 and O2 is zilch, the segregation between air (mw 29) and CO2 (mw 44) at equilibrium would be about 15/4 = ~ 4 times zilch.

Are you sure it is a linear effect?
Do you have some quantitative basis for this? That will be interesting.

 

[anorlunda]

Let me propose a laboratory experiment that I bet Chet would agree on after some thought.

Take a vertical cylinder container of height L and cross-sectional area A. Let R=L/A.

We will fill it with 1/3 He (1/3 by volume), 1/3 air, and 1/3 CO2.

Now, if there are stratified layers, then mixing will occur at the boundaries between layers because of thermal agitation, or diffusion, or turbulence. But mixing efficiency decreases with A.

So for small values of R, agitation dominates and there will be no measurable layering (zilch layering). But as R increases, mixing efficiency becomes arbitrarily small. Something else must begin to dominate. What candidates are there other than buoyancy? For high values of R, buoyancy dominates and there will be measurable stratified layers in the steady state.

In the lab, rather than directly modifying R, we could start with a pipe, L=10 m, A=$1cm^2$. Then place 2 gate valves to partition the cylinder into 3 equal volume regions. The valves would initially be fully open. The experiment would then be to very gradually close the valves over a period of weeks or months while measuring the proportions of He, air, and CO2 in the regions.

 

[Chestermiller]

Here is a simple calculation that quantifies the effect. I have air (MW =29) and He (MW =4) in a room at 1 atm and room temperature. Such a mixture can be treated as an ideal gas mixture. In an ideal gas mixture, the different gases behave as separate entities. Let:

p_ao= partial pressure of air at the floor
p_h0= partial pressure of He at the floor
L= height of room (nominally 3 m)
z = distance measured upward from the floor
T = absolute temperature
R = ideal gas constant
M_a=molecular weight of air
M_h=molecular weight of helium

For each gas in the ideal gas mixture, the barotropic equation tells us that:

$$\frac{dp}{dz}=-\frac{Mg}{RT}p$$
So as a function of height z in the room, the partial pressures of air and of helium are given, respectively, by:
$$p_a=p_{ao}\exp{\left(-\frac{M_agz}{RT}\right)}$$
$$p_h=p_{ho}\exp{\left(-\frac{M_hgz}{RT}\right)}$$
So the ratio of the partial pressures (and mole fractions) at the ceiling are related to the ratio of the partial pressures (and mole fractions) at the floor by
$$\frac{p_h}{p_a}=\frac{p_{ho}}{p_{ao}}\exp{\left(\frac{(M_a-M_h)gL}{RT}\right)}$$
The term in parenthesis in this equation is equal to ~ 0.0003.

Therefore, the ratio of the mole fractions at the ceiling is equal to the ratio of the mole fractions at the floor times about 1.0003 (i.e., a variation of 0.03%). That's the big stratified separation that occurs.

For a small typical value of the expression in parenthesis like 0.0003, the relationship becomes:

$$\frac{p_h}{p_a}=\frac{p_{ho}}{p_{ao}}\left(1+\frac{(M_a-M_h)gL}{RT}\right)$$

So, to answer nasu's equation in post #33, yes I do have evidence that the change is essentially linear in the molecular weight difference.

Chet

 

[anorlunda]

Here is a simple calculation that quantifies the effect.

My knees quiver to argue with Chestermiller, but here goes.

That partial pressure calculation assumes that the gasses are well mixed. It can't be used to establish the mixing ratios. The NASA paper linked by Russ uses those types of equations for the Homosphere where turbulence guarantees well mixed gases. http://ruc.noaa.gov/AMB_Publications_bj/2009%20Schlatter_Atmospheric%20Composition%20and%20Vertical%20Structure_eae319MS-1.pdf The figure below from the same paper shows the mixing ratios of different gasses. They are highly nonlinear, and not even monotonic. It is unclear from the paper exactly how they define mixing ratio. They discuss it using units ppmv (parts per million volume?) Nevertheless, note that the mixing ratio for O2 is $10^4$ to $10^{10}$ times bigger than the ratio for H. I take that to mean that H is much more reluctant to mix than O2.

The caption says that the ratio for nitrogen is not shown because it is always well mixed.

 

[Chestermiller]

My knees quiver to argue with Chestermiller, but here goes.

That partial pressure calculation assumes that the gasses are well mixed. It can't be used to establish the mixing ratios. The NASA paper linked by Russ uses those types of equations for the Homosphere where turbulence guarantees well mixed gases. http://ruc.noaa.gov/AMB_Publications_bj/2009%20Schlatter_Atmospheric%20Composition%20and%20Vertical%20Structure_eae319MS-1.pdf The figure below from the same paper shows the mixing ratios of different gasses. They are highly nonlinear, and not even monotonic. It is unclear from the paper exactly how they define mixing ratio. They discuss it using units ppmv (parts per million volume?) Nevertheless, note that the mixing ratio for O2 is $10^4$ to $10^{10}$ times bigger than the ratio for H. I take that to mean that H is much more reluctant to mix than O2.

The caption says that the ratio for nitrogen is not shown because it is always well mixed.

In atmospheric science parlance, mixing ratio is the same thing as what we call mole fraction.

Except for oxygen, CO2, and Argon, all the other gases in this figure are strongly affected by the photochemistry. CH4 decreases with altitude because of its reaction with OH radicals, and N2O decreases with altitude because of photolysis and reaction with O¹D. Of course ozone, O atoms, and H atoms are all very highly active photochemically. And water up to the tropopause is controlled by condensation processes at the very low temperatures in the upper troposphere. So the only gases in this figure that have relevance to our discussion are O2, CO2, and Ar. And these gases are seen to have constant mixing ratios all the way up to 80 km. This is a little higher than the 3 meter room I was talking about.

I guess if you were going to use a figure from Guy Brasseur's paper, you should have at least read the paper. I was a very active worker in the atmospheric transport and chemistry area for a number of years when I worked for DuPont. (Incidentally, I knew Guy Brasseur and his frequent co-work Susan Solomon personally during that period). Here are a few of my papers that you may be interested in reading:

Miller, C., Meakin, P., Franks, R.G.E., and Jesson, J.P., The Fluorocarbon-Ozone Theory – V. One Dimensional Modeling of the Atmosphere: The Base Case, Atmospheric Environment, 12, 2481-2500 (1978)

Miller, C., Filkin, D.L., and Jesson, J.P., The Fluorocarbon-Ozone Theory – VI. Atmospheric Modeling: Calculation of the Diurnal Steady State, Atmospheric Environment, 13, 381-394 (1979)

Glasgow, L.C., Jesson, J.P., Filkin, D.L., and Miller, C., The Stratospheric Abundance of Hypochlorous Acid (HOCl), Planet. Space Sci., 27, 1047-1054 (1979)

Miller, C., Steed, J.M., Filkin, D.L., and Jesson, J.P., Two-Dimensional Model Calculations of Stratospheric HCl and ClO, Nature, 288, 5790, 461-464 (1980)

Bass, A.M., Glasgow, L.C., Miller, C., Jesson, J.P., and Filkin, D.L., Temperature Dependent Absorption Cross Sections for Formaldehyde: The Effect of Formaldehyde on Stratospheric Chlorine Chemistry, Planet. Space Sci., 28, 675-679 (1980)

Miller, C., Steed, J.M., Filkin, D.L., and Jesson. J.P., The Fluorocarbon Ozone Theory – VII. One-Dimensional Modeling – An assessment of Anthropogenic Perturbations, Atmospheric Environment, 15, 5, 729-742 (1981)

Miller, C., Filkin, D.L., Owens, A.J., Steed, J.M., and Jesson, J.P., A Two-Dimensional Model of Stratospheric Chemistry and Transport, J. Geophys. Res., 86, C12, 12039-12065 (1981)

Steed, J.M., Owens, A.J., Miller, C., Filkin, D.L., and Jesson, J.P., Two-Dimensional Modelling of Potential Ozone Perturbation by Chlorofluorocarbons, Nature, 295, 5847, 308-311 (1982)

Owens, A.J., Steed, J.M., Miller, C., Filkin, D.L., and Jesson, J.P., The Atmospheric Lifetimes of CFC 11 and CFC 12, Geophys. Res. Lttrs., 9, 6, 700-703 (1982)

Owens, A.J., Steed, J.M., Miller, C., Filkin, D.L., and Jesson, J.P., The Potential Effects of Increased Methane on Atmospheric Ozone, Geophys. Res. Lttrs., 9, 9, 1105-1108 (1982)

Owens, A.J., Hales, C.H., Filkin, D.L., Miller, C., Steed, J.M., and Jesson, J.P., A Coupled One-Dimensional Radiative-Convective, Chemistry-Transport Model of the Atmosphere, 1. Model Structure and Steady State Perturbation Calculations, J. Geophys. Res., 90, D1, 2283-2311, (1985)

Now, I provided an analysis of the problem we have been discussing concerning air and helium in a room in post #36. You claimed that there would be a significantly larger concentration of helium near the ceiling than near the floor, and I showed that there would only be a 0.03% difference. If you have found any flaws in my analysis, please identify them.

Chet

 

[anorlunda]

I stand corrected. Should have known better.

 

[nasu]

So, to answer nasu's equation in post #33, yes I do have evidence that the change is essentially linear in the molecular weight difference.

Chet

I hope you understand that I was rely curious about some quantitative estimate and not challenging you without reason.

 

[Chestermiller]

I hope you understand that I was rely curious about some quantitative estimate and not challenging you without reason.

You rascal. You baited me into it. I figured it out while I was out walking the dogs.

Chet

 

[Mike Bergen]

Look up Dalton"s Law and it will explain how these separate gasses will spread out equally in a container. In this case the atmosphere is pretty big and with half the air we have between sea level and 40.000 ft. The atmosphere never really stops but after 100 miles up the molecules are pretty few and far between

 

[rcgldr]

There have been instances where large amounts of carbon dioxide was released, and initially it stayed close and/or descended to the ground due to being about 1.5 times as dense as normal atmosphere.

 

[PWiz]

There was a really nice answer on Stackexchange as to why the separation of gases in air is not as prominent as a mixture of liquids. I can't say it better in my own words, so here it is:

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 to reach the minimum either the energy should decrease or the entropy 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.

(Here's the link if you want to view other answers to that question too: http://physics.stackexchange.com/questions/34733/why-does-air-remain-a-mixture )

 

[Mike Bergen]

I wonder if the propane example is more pronounced because it is more a Vapor than Gas and certainly much heavier than air. Water vapor is interesting because it is lighter than air.

Also the distribution of the mixed gases seems subject to the gravitational effect at that altitude So does it seem that percentage of gas at each altitude is subject to how much of the whole is left at those higher altitudes

 

[Chestermiller]

I wonder if the propane example is more pronounced because it is more a Vapor than Gas and certainly much heavier than air. Water vapor is interesting because it is lighter than air.

You are aware that a vapor is just a gas above its dew point, right?

Also the distribution of the mixed gases seems subject to the gravitational effect at that altitude So does it seem that percentage of gas at each altitude is subject to how much of the whole is left at those higher altitudes

In case you didn't notice it, this effect is addressed quantitatively in post #35.

 

[Mike Bergen]

Chester Miller, My HVAC Trade understanding of Vapor/ Gas is that vapor- liquid is easier to accomplish with less heroic methods than Liquefying gas like O2 Or is it how well they follow the Ideal Gas Laws.
I am a Tradesman and not a Physicist, But I am finding a lot of the discussion interesting

Yes I saw that Fig 2 Mixing Ratio Data and found the N2 omission because it was "well mixed and the O2 and CO2 graphs interesting along with the water vapor H2O

Thanks for the clarification Mike

 

[klimatos]

If the global atmosphere were in a condition of equilibrium (which it most definitely is not), then Dalton's Law would explain the distribution of the individual molecules of the various non-reacting gases quite well. As it is, Dalton's Law does not do a bad job. It produces a very good first approximation. The real free atmospheric distribution of gas molecules is also influenced by fluid flow (winds and currents) which change the local distribution somewhat, and by precipitation--which affects the concentration of water vapor. I think that you will find that Dalton's distribution is approached more closely in the polar areas (where both strong convective storms and precipitation are less common) than in the tropics--where both strong convective storms and water vapor are much more common.

 

[Mike Bergen]

Seems Dalton works on small samples that are not unduly affected by Gravity. That Mixing Ratio Fig 2 , I guess shows the effect of gravity on certain gases like NOX's or H

I believe I read where the height of Atmosphere is lower at Poles along with water vapor so you are right the winds and a lot of other factors are really making this an interesting topic

Thanks for thoughts, Mike

 

[Chestermiller]

Seems Dalton works on small samples that are not unduly affected by Gravity. That Mixing Ratio Fig 2 , I guess shows the effect of gravity on certain gases like NOX's or H

I believe I read where the height of Atmosphere is lower at Poles along with water vapor so you are right the winds and a lot of other factors are really making this an interesting topic

Thanks for thoughts, Mike

Mike,

Please use discretion when you submit posts to Physics Forums. These Forums are not for speculation or guessing. If you're not sure, please do not guess. Your recent posts are bordering on misinformation. For example, Fig. 2 does not show the effect of gravity on certain gases like NOX or H. I know this because I worked in this area and am familiar with how these results were obtained.

Saying that the height of the Atmosphere is lower at the poles is also incorrect. The height of the troposphere, which is the lower part of the atmosphere, is lower at the poles, because the temperature inversion occurs at lower altitudes near the poles than near the equator.

I'm not going to issue warning points this time, by my warning finger is getting itchy.

Chet