Have you ever wondered how much breathable air is on Earth?
In this article, I will demonstrate how to calculate the mass of oxygen in the atmosphere. Calculating how much oxygen in the air is relatively easy. The challenge is that atmospheric science is complicated, and the numbers are estimates based on current theories and knowledge. Afterward, we’ll explore nine reasons why the accepted amount of oxygen in the atmosphere might not be accurate, including my fishbowl theory. If you want to skip the math, you can see the answers highlighted in yellow below.
For the record, we will measure only the breathable oxygen in the atmosphere, also known as molecular oxygen, which is two molecules of oxygen — O2. After iron, oxygen is the second most abundant element on Earth. It is part of almost half the upper crust of the Earth and more than half of the sea, but, of course, we can’t breathe dirt or water.
Our calculation will be in two steps. 1) We need to know how big the atmosphere is. 2) Then, we can figure out the percentage and mass of the atmosphere’s different gases.
Okay, let’s get started.
What is the mass of the Earth’s atmosphere?
Because the atmosphere is composed of gases and the volume of gases changes with temperature, we will calculate the mass of the atmosphere instead. To arrive at this number, all we need to do is calculate the Earth’s surface area and then multiply that by the pressure the atmosphere exerts on the surface. This simple formula will get us very close to the accepted value, which according to the National Center for Atmospheric Research, is 5,148,000,000,000,000,000 kilograms. We’ll discuss this number more below.
First, we need to calculate the surface area of the Earth. We can use simple high school geometry.
The formula for the area of a sphere is 4 x pi x radius squared. A search online gives the Earth’s radius as 6.371e6 meters. Plugging this into our formula gives:
A = 4 x π × (6.371e6)2
Area of the Earth = 5.100644e14 m2
Again, I’m using CalculatorSoup to help. (More about how I do my math.) And I double-check all my answers with reputable sources online. Wikipedia says that the surface area of the Earth is “about 510 million km2,” which is the same number. This assumes the Earth is a perfect sphere, but it is squished a little, like someone sitting on a yoga ball. I’m assuming the difference in surface area is insignificant. Still, it is the first hint of something being off.
Now we need to know what the atmospheric pressure is at sea level. We are under tremendous pressure. 14.696 pounds of pressure per square inch. Imagine putting a 15-pound weight on one square inch of your body. It would leave a big dent. Fortunately, we don’t notice because the pressure is equal all over inside and out.
Anyway, we need to convert that number to something more useful. We can measure the atmospheric pressure as pounds per square inch, Pascals, bars, millimeters of mercury, et cetera, etc. (The hard part of all this math is converting the numbers and units. Sheesh! If only humanity could agree on something.) Cheating a little bit and looking it up online, the unit of measure and the number I need is Newton/meter2.
So, converting 14.696 psi, the pressure the atmosphere exerts on the Earth’s surface = 101,325 Newton/meter2.
But that is the pressure at sea level; the pressure on top of mountains is much less. Now, let’s do a rough calculation of the average elevation of both land and sea. If I trust the internet, the average elevation of all the continents is 841 meters, and the Earth is covered by 71% ocean and 29% land. So:
841 meters × 29% = 244 meters
The average elevation of the Earth = 244 meters
The atmospheric pressure at that elevation per this website equals 98,416 N/m2.
So, the total force the atmosphere exerts on the surface of the Earth is:
98,416 N/m2 × 5.100644e14 m2
= 5.019849e19 Newtons
To convert force (Newtons) to mass (kilograms), we use the equation for the force of gravity.
Force = mass × gravity. Solving for mass gives:
Mass = Force ÷ gravity
Mass = 5.019849e19 N ÷ 9.81 N/kg
Mass of the atmosphere = 5.117073e18 kilograms or 5,117,073 gigatonnes.
Double-checking this number again, Wikipedia says the mass of the atmosphere is about 5.1480e18 kg. So, my number is very close. Far less than a 1% difference. And, now that we know the mass of the Earth’s atmosphere, we can calculate the mass of its parts.
How much oxygen is in the atmosphere?
Below is a chart of the five most common gases in our atmosphere. You’ll notice almost all of it is oxygen and nitrogen. Carbon dioxide, the gas everyone is worried about, is not even close. (To be fair, it may not seem like a lot of CO2 but if it doubles, that’s a big problem.) And, the water vapor varies greatly, so it is subtracted before measured.
|Gas||Symbol||Volume %||Molar Mass||Weight %|
Here is something I didn’t know: it is commonly said that oxygen is 21% of the air. That means oxygen is about 21% of the volume or 21% of the number of molecules, but oxygen is about 23% of the atmosphere by weight. Confusing? Yes!
So the mass of oxygen in the atmosphere is:
0.2314% × 5.117073e18 kilograms (mass of the atmosphere per my math)
= 1.184090e18 kilograms or 1,184,090 gigatonnes
That’s pretty good for an artist. Maybe I should have been an atmospheric scientist. But, seriously, how can it be this simple to figure out how much oxygen is in the atmosphere? It makes me wonder if something is wrong.
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Possible errors in measurement
Okay, I was so surprised at my accuracy that I had to consult a real research scientist. They didn’t seem surprised. They said, “This is how science works. Doing science is like following a recipe. Anyone can duplicate the process and arrive at the same answer.” They also said that hundreds if not thousands of scientists came before me to help make this process very easy, like Newton and Avogrado. That being said, if one theory, one scientist or one piece of data collected is wrong, our recipe fails. The good news is that science is meant to be scrutinized. If a theory breaks, that is an opportunity to see how the world really works.
At this point, I should admit that I have a bias — let’s call it a theory. I believe that the real driving force behind climate change is NOT carbon dioxide emissions but oxygen depletion. So, as part of my investigation, I’m looking to see if there is some measurement error. Is there less oxygen than believed?
So far, the science has held up to my scrutiny. But I have found some potential gaps. Below I will give a brief introduction to each idea. Perhaps in the future, I will investigate each idea thoroughly. However, I have learned that one can only go so far with the existing scientific literature. At some point, these ideas may require novel, in-the-field research studies.
I’m going to start with the simple ideas first and save my best for last.
My first idea is circumstantial evidence. As I mentioned, it was just too easy to calculate the mass of oxygen in the atmosphere. I used nothing more than high-school-level geometry, chemistry and physics. Think of all the complicating factors that should have made this calculation far more complex: calculating the average landmass (Is this done by satellite measures or theory?), accounting for seasonal variations in water vapor and temperature, differences in pressure (wind), the oblate spheroid shape of the Earth, and many more factors, some that I’m guessing are still unknown to science. My ideas below are more complicating factors. I don’t know if they are new, but I did think of them myself or brainstorm them with friends, like the Fishbowl Theory.
Weight versus Volume
As I mentioned, we calculated the mass of oxygen in the atmosphere, not volume. The volume of oxygen in a given parcel of air is 20.946%, but its weight is 23.14%. Arguably this is the same amount of oxygen any way you look at it. But practically, it is very different. For example, I rode my bicycle to Mount Everest Base Camp. It got very hard to breathe. It was the same percentage of oxygen but in very thin air. It takes a lot of acclimatization to survive at this altitude and some never can. The thin air is an example of Boyle’s law: as the pressure decreases, the volume of air increases. So, on the ground level, the percentage may remain the same, but the air could be getting thinner or thicker due to unknown factors. For example, wouldn’t global warming cause the air to expand and get thinner?
The water vapor problem
In the above chart of the five most common gases in our atmosphere, what should have ranked as third is water vapor. According to many sources online, the percentage of water vapor in the atmosphere varies from 0.2% to 4%.
Measurements of the atmosphere are done with “dry air.” The water is condensed or frozen out of the sample before measurement. Now I understand that scientists are using this method to achieve consistent numbers despite the weather, but what does this mean under practical circumstances? Does water vapor displace the oxygen or the nitrogen? On a very humid day, does that mean there is only 17% percent oxygen? Do internal combustion engines perform worse? Does it get harder to breathe?
I think air pollution, which is also subtracted from the measures, has much the same effect as water vapor. So, imagine a smoggy and a humid day combined. The oxygen levels would drop even further. Now imagine a smoggy, humid day while living at a high altitude. Now imagine it got really hot! You can understand how the practical amount of breathable oxygen can get quite low.
Measuring non-breathable forms of oxygen.
I am doubtful this is a problem, but I will mention it anyway. When scientists measure oxygen, what kinds of oxygen are they measuring? There are three forms: atomic oxygen (O), molecular oxygen (O2) and ozone (O3). And there are a lot of gases that have oxygen as part of their makeup: carbon dioxide (CO2) and carbon monoxide (CO) and water vapor (H2O).
Atmosphere shape and size.
This also doesn’t seem to be a problem, but worth mentioning. The Earth is not round and the atmosphere less so. Our math above assumed the Earth and atmosphere are perfect spheres and that the pressure around the world is constant, but it is a much more complicated place. However, it appears to all average out. If the pressure drops in one area, gases will flow into the hole. We call this weather. And, as you can see in the illustration, the atmosphere (bottom of the troposphere) is shorter at the poles and taller at the equator. It would seem that the pressure is much greater at the equator, but this air is warm and moist, thus less dense. And if the air does change, it will circulate. It doesn’t seem to be a problem; still, I think there may be areas left to study. Consider the next point.
Doldrums and dead zones
Pictured in the illustration are the doldrums (Inter-Tropical Convergence Zone), where sailboats can get stuck in the windless waters. There are many zones that may act as walls, similar to those heaters that blast hot air in front of a cold door.
Also, given that there are high and low-pressure systems, and deserts (no oxygen production), and forests (oxygen-producing), and urban areas (burning oxygen), there have to be high and low areas of oxygen, much like the dead zones in the sea. Do scientists measure these invisible dead zones as they float around? Do planes fly through them? Do the Himalayas block the jet streams and create a pocket of dead air?)
I’m reminded of the classic book, On the Beach by Nevil Shute. In this nuclear holocaust, the superpowers in the Northern Hemisphere have destroyed themselves. However, the weather patterns have temporarily delayed the spread of the deadly radiation. Earth’s last survivors in Melbourne, Australia, await their fate.
Okay, this is my favorite idea and what seems like the biggest possible error when measuring the mass of oxygen in the atmosphere. It’s super simple to understand, but first, a little background.
Per this article about air composition and molecular weight, “Air is usually modeled as a uniform (no variation or fluctuation) gas with properties averaged from the individual components.” That means if you put a bunch of different gases in a box and close the lid, all the gases will mix evenly because all the molecules are in constant motion. But, of course, the Earth is not a box. It is more like an open fishbowl with temperature and gravity diminishing towards the top.
So imagine the water inside the fishbowl is nitrogen; now we pour in some oxygen, which is heavier (see the chart above), and it falls to the bottom like sand. You can even imagine that as oxygen gets burned and turned into other pollutions that these heavier molecules are like rocks that fall to the bottom. In other words, we should expect a greater density of oxygen at ground level. Evidence of this stratification of layers is very obvious. You see it almost every day — clouds. Water vapor is lighter than both nitrogen and oxygen. (If it wasn’t, the Earth would be a very different place.)
This subject requires a lot more research. I haven’t found much yet to disprove it. In fact, the same article we just quoted also says, “The composition of air is unchanged until [an] elevation of approximately 10.000 m.” Unfortunately, there is no mention of what the composition of the atmosphere is above this altitude (10 kilometers).
And this article about the exosphere lends further proof. It says, ”The exosphere layer is mainly composed of extremely low densities of hydrogen, helium and several heavier molecules including nitrogen, oxygen and carbon dioxide closer to the exobase. The atoms and molecules are so far apart that they can travel hundreds of kilometers without colliding with one another. Thus, the exosphere no longer behaves like a gas, and the particles constantly escape into space.”
The other layers of the atmosphere also have slightly different compositions, but their weight pressing down on the surface of the Earth is still part of the formula above.
Oxygen depletion in the ocean has been researched a lot more. Below, we see an example of dead zones in the ocean. We can see the levels are affected by weather patterns, continents and the depth of the ocean. Measuring oxygen levels at the surface would yield much different results. I think that this graph models what we would expect to see in the atmosphere in different locations and different altitudes.
How is oxygen measured?
I was going to stop here, but I uncovered another clue during my research for this article. I wanted to learn how oxygen is actually measured. The Scripps O2 Program is the organization that collects air samples from 9 locations worldwide and measures changes in atmospheric oxygen concentration. (Per their data, oxygen is going down step by step, matching the rise in carbon dioxide.) Two points interest me:
One) Per their website: “Measuring the changes in O2 is challenging because the changes are so small. The data reported on this website are measured using a technique developed by the project leader (R. Keeling) as part of his Ph.D. thesis back in the 1980s. The technique involves detecting changes in refractive index of air via a very precise measurement method known as interferometry. The data are reported as changes in the O2/N2 ratio in ‘per meg’ units.”
Two) Then, they compare this ratio to a sample of air they collected in the mid-1980s.
Okay, wow! So, the reference sample of oxygen is only about 35 years old. This is well after the industrial revolution when fossil fuels began being burned. What’s more surprising is that the Scripps Institute only measures a change in the ratio between oxygen and nitrogen, not a change in the actual amount of oxygen. This raises so many questions:
- How did they measure the total mass of oxygen? (Their measure is almost the same as mine and presumably also 35 years old.)
- Was this method accurate in the 1980s?
- Where does nitrogen come from or go? (If this has changed, then the ratio is off.)
- And, again, not only are water vapor and pollutants subtracted from the equation but so are three of the top five gases, argon, carbon dioxide and neon.
Update: Coincidentally, I found another paper by the same scientist above. It reports that the ocean is currently losing about 1.5−3.1 gigatons (1.5−3.1 billion tons) of oxygen each year (Keeling and Garcia, 2002; Schmidtko et al., 2017). So, my first question is: where does the oxygen go? If it is evaporating into the air, then it is offsetting the loss and the measurements are wrong. Perhaps we can assume the melting glaciers are releasing an equal amount of oxygen into the atmosphere.
Well, figuring this all out could take a long time!
Okay, whew! We calculated the mass of the atmosphere to be about 5,117,073 gigatonnes and the mass of the oxygen to be 1,184,090 gigatonnes. We can feel given the current understanding of climate science that these numbers are fairly accurate. Then we discussed nine reasons why there might be less oxygen than believed. This is part of my series exploring the theory that it is actually oxygen depletion NOT carbon dioxide emissions that is the major factor in climate change.
If you can think of any more reasons, or you find any flaws in my thinking, please leave a comment below. Thanks.
See links in above the article. Plus the following.
The Mass of the Atmosphere: A Constraint on Global Analyses.