Gas Molecules

I recall an atmospheric problem example in my general chemistry textbook from about 45 years ago. The example was intended to offer a sense of the number of gas molecules in each breath of air. At first, the problem solution is compound but not difficult. The results are intended to be a little surprising.

I think that there are other derivative problems that make this a little more interesting.

Assume a standard breath of air inhaled to be about 500 cc (or ml) and at the conditions applicable for the ideal gas, e.g. sea level (1 atm etc).
Calculate the number of gas molecules in the breath of air - easy to do.

Next figure out the distribution of those gas molecules if they were equally diffused in the atmosphere.

The solution comes out to one molecule of gas for each breath inhaled over the entire planet atmosphere. Seems intuitively reasonable.

The textbook, if I recall, made the point that this meant that in the pure molecular distribution sense, with each breath of air that we all breathe in, we are statistically breathing in a molecule that was breathed in by anyone who lived on planet earth in the past, so long as time and distance allowed for full diffusion. One breath has a molecule from confucious, siddharthra, jesus, mohammed, attila the hun, julius caesar, ghengis khan, chairman mao, adolf hitler etc.

Well, it's not really true, of course. We metabolize those oxgen molecules. The nitrogen gets caught up in amino acids and nucleic acids. The molecules aren't just marbles that don't change.

But wait. What if my memory is faulty? What if the book was referring to Argon? Argon is inert and it could be true! Argon makes up about 0.934% of the earth's atmosphere. What happens if we run the numbers then?

There are corollary questions: What about water molecules? What about the atoms of our bodies?

For now, I'm just curious if anyone cares to run the calculations for argon to see if the concept holds.

Why don't I do it? Well, I'm a little troubled by the atmospheric distribution. I suppose I could readily determine the median altitude for atmospheric pressure and calculate the total volume of the atmosphere from there. That would work. But then, How does argon distribute in the altitude gradient?

I'm just curious and thought I'd toss this out there for a fun excerise in case it interests others.

Originally posted by billyray
I recall an atmospheric problem example in my general chemistry textbook from about 45 years ago. The example was intended to offer a sense of the number of gas molecules in each breath of air. At first, the problem solution is compound but not difficult. The results are intended to be a little surprising.

I think that there are other derivative problem ...[text shortened]... just curious and thought I'd toss this out there for a fun excerise in case it interests others.

I deal with argon daily at my job in the semiconductor industry and argon and the oxidation
number is zero so it forms compounds with almost nothing else so it can be considered a marble, marble in, marble out. If that is any help. It's been more like 50 years for me since chem 101🙂

I should amend that to talking about neutral argon.

In my field, we ionize argon with RF in a vacuum system, and ionized argon has a nice feature for us. You are probably aware of sand blasters or bead blasters, used to clean metal parts of surface contamination.

Ionized argon is like a molecular sand blaster. It hits the surface of stuff and bits of that stuff gets whacked into the vacuum system and conveniently, if you happen to have some kind of substrate in the way of that cloud of ionized argon and neutral stuff coming off what we call the 'target', then some of that cloud of neutral stuff will coat whatever you have nearby, in our case, a substrate of alumina with electronics crap on it🙂 The stuff in our case is SiO2 (Glass), Aluminum, Silicon Carbide, Titanium-tungsten, Silicon-Chrome, pure Chrome and so forth.

One at a time of course.

Anyway, that is all due to the very reactive argon ion, relatively heavy, AMU of 40 so it is like a molecular battering ram, whatever surface it hits, that surface will be disrupted on an atomic scale, a few atoms or molecules at a time get whacked away from the surface of the target and into the cloud of ionized argon which then makes its way to the substrate of the day, whether that be silicon wafers, sapphire, gallium arsenide, aluminum, alumina, doesn't matter what the substrate is, some of that target material will find its way to the substrate.

The secondary problem is whether the stuff of the target is low stress material, or high stress. If it is low stress, it has a better chance of sticking to the substrate but high stress material like Silicon Carbide has a better than average chance of just flaking off the surface to be coated so it may require an interstitial layer, say SiO2 as a low stress material capable of making better contact between the substrate and the SIC layer.

Anyway that is my 50 cent tour of our industry. Hope you didn't get TOO bored🙂

A similar popular claim is that every glass you drink contains at least one water molecule that was once also drunk (and subsequently urinated) by Napoleon during his lifetime (or any other famous figure long ago).

It would be interesting to know with your air version just how quickly molecules of air really do disperse. If we were to trace every molecule from one breath how long would it take for at least one molecule to reach the far side of the earth?

Originally posted by twhitehead
A similar popular claim is that every glass you drink contains at least one water molecule that was once also drunk (and subsequently urinated) by Napoleon during his lifetime (or any other famous figure long ago).

It would be interesting to know with your air version just how quickly molecules of air really do disperse. If we were to trace every molec ...[text shortened]... one breath how long would it take for at least one molecule to reach the far side of the earth?

I would assume that would depend on what trade wind you were immersed in. If you were, say, already at McMurdo in Antarctica, you would probably see your breath molecules spread around Antarctica but not much else.

Originally posted by sonhouse
I would assume that would depend on what trade wind you were immersed in. If you were, say, already at McMurdo in Antarctica, you would probably see your breath molecules spread around Antarctica but not much else.

I think that's about right. In other words, pure equal distribution would likely take millennia - just guessing, largely due to southern and northern hemisphere atmospheric rotations. For the atmospheric gas science wonks, it's a great question: We open a bottle of some scent, e.g., perfume, on the south pole. How long before one molecule reaches the north pole? How long, too, before we shuffle the deck of molecules thoroughly? I have no idea but I'm absolutely certain that the answer is already quite well known and the problem considered to be trivial. We'll see.

Originally posted by sonhouse
I deal with argon daily at my job in the semiconductor industry and argon and the oxidation
number is zero so it forms compounds with almost nothing else so it can be considered a marble, marble in, marble out. If that is any help. It's been more like 50 years for me since chem 101🙂

I should amend that to talking about neutral argon.

In my field, w ...[text shortened]... he SIC layer.

Anyway that is my 50 cent tour of our industry. Hope you didn't get TOO bored🙂

Thanks so much for the fun esoterica about argon. I was, indeed, working on the presumption that atmospheric argon was our metaphorical marbles.

Originally posted by twhitehead
A similar popular claim is that every glass you drink contains at least one water molecule that was once also drunk (and subsequently urinated) by Napoleon during his lifetime (or any other famous figure long ago).

It would be interesting to know with your air version just how quickly molecules of air really do disperse. If we were to trace every molec ...[text shortened]... one breath how long would it take for at least one molecule to reach the far side of the earth?

Great nuance to the question. Thanks.

Originally posted by twhitehead
A similar popular claim is that every glass you drink contains at least one water molecule that was once also drunk (and subsequently urinated) by Napoleon during his lifetime (or any other famous figure long ago).

It would be interesting to know with your air version just how quickly molecules of air really do disperse. If we were to trace every molec ...[text shortened]... one breath how long would it take for at least one molecule to reach the far side of the earth?

Not long, really, given the speed that molecules travel and the number of them. That, however, is purely theoretical. We can't "tag" a hydrogen molecule to track it and identify it showing up at the south pole. Alas, it's just an interesting theortical concept -that one molecule travel concept. Statistically, it would take a long time for the gases to diffuse evenly. That's the real time challenge, if one cares to ponder it at a global level.

Originally posted by coquette
Not long, really, given the speed that molecules travel and the number of them. That, however, is purely theoretical. We can't "tag" a hydrogen molecule to track it and identify it showing up at the south pole. Alas, it's just an interesting theortical concept -that one molecule travel concept. Statistically, it would take a long time for the gases to diffuse evenly. That's the real time challenge, if one cares to ponder it at a global level.

We can I believe measure some types of diffusion. I believe the radio activity of sea water as a result of Fukushima can be measured over quite large distances giving reasonable estimates as to how fast radioactive atoms spread. Other gasses can be detected by satellites and we can measure to some degree how they travel from their sources.

Originally posted by twhitehead
We can I believe measure some types of diffusion. I believe the radio activity of sea water as a result of Fukushima can be measured over quite large distances giving reasonable estimates as to how fast radioactive atoms spread. Other gasses can be detected by satellites and we can measure to some degree how they travel from their sources.

The difficulty with radioactive tagging, since coquette used hydrogen as her example I'll stick with that, is that if one uses tritium one increases the relative molecular mass of the hydrogen molecule by a factor of about two if it's tritium hydride and 4 if it's di-tritium (*), so the physical characteristics of the molecules change. Even with the radioactive oxygen they use in PET scans the mass change is of the order of about 5%. So one can demonstrate diffusion from a source of di-tritium into a container which already has hydrogen in it, but one has to extrapolate to predict the rate of mixing of the hydrogen from our source (nozzle say) and the hydrogen already in a container.

(*) I'm not sure of the correct name for a molecule with two tritium atoms, di-tritium sounds about right.

Originally posted by coquette
Not long, really, given the speed that molecules travel and the number of them. That, however, is purely theoretical. We can't "tag" a hydrogen molecule to track it and identify it showing up at the south pole. Alas, it's just an interesting theortical concept -that one molecule travel concept. Statistically, it would take a long time for the gases to diffuse evenly. That's the real time challenge, if one cares to ponder it at a global level.

What screws that up is the 'mean free path' of molecules. It doesn't take much of a vacuum to get that free mean path movement to centimeters or more but at 15 PSI, the free mean path is measured in microns.

With that in mind, think of a crowd of people trying to get out of a theater. There is a number of people, 2 or three at a time maybe getting out but look at the people in the seats and isles, all vying to get out after the show.

Remove the seats and now watch a big crowd, they will jostle about and if you tracked the foot movements of each person they may move left a bit, right, forwards, back a bit and so forth so while each person can move relatively quickly in an empty building, with all those other people around, they might move a kilometer to get ten meters ahead.

The same with molecules. They in fact are moving very fast at room temperature but the general movement in a particular direction is pretty small bouncing around like the balls in a snooker tournament. Magnify that snooker situation by a trillion trillion and you can see an individual molecule won't get very far.