 0

# How much does a cubic foot of air weigh?

According to the CRC Handbook of Chemistry and Physics, the density of dry air at 20 degrees C at 760 mm of mercury (one atmosphere of pressure) is 1.204 milligrams per cubic centimeter.1 cubic foot = 28,316.8467 cubic centimeters.

So, dry air weighs 34,093.48 mg per cu.ft.

Which is about 1.2 ounces per cu.ft.

Observation:I think the above is what you would find if you weigh the air in a vacuum (the air is in a container of known weight, and the container is being weighed in a vacuum). The above was probably determined with knowledge of physics and mathematics, but the idea is the same. Practically speaking on earth's surface, at 20 degrees C and one atmosphere, the air would weigh nothing at all; perhaps more accurately the air 'weighs' its own displacement in the air itself. It would be perfectly buoyant. Think about weighing 1 cubic foot of lake water, with the water completely submerged under the surface of the lake... quite a different result from weighing it on dry land. Unless you are studying buoyancy, it might be more useful to use things like atmospheric pressure, or the mass of a sample of gas and its temperature and pressure within the sample, depending on your need. The question demonstrates the importance of knowing the standard conditions (stp) used in research. There is no universally established set of standard conditions, so attention is absolutely necessary. See discussion. Follow-up to observation:If you had a container with a volume of one cubic foot and evacuated it, it would weigh less than if it were full of air at standard temperature and pressure. You would not need to weigh it in a vacuum, unless its weight in vacuum is what you want.

By comparing the weights of the evacuated and the full container, you can determine the weight of the air, essentially, in a vacuum. The weight of the air "in air" remains zero. This seems odd, because we are weighing the container "in air", and the weight goes up when we add the air. I think this does not mean that the air weighs something as it hangs out in the air. [see discussion]

I think what is happening is that the observed weight of the perfectly evacuated container at one atmosphere will be less than the weight of the container itself, because to find the container's weight we would need to subtract the weight of the volume of air the whole container is displacing. So putting mass into the container serves the purpose of bringing us closer to the weight of the container, and doesn't demonstrate that the air has weight while suspended in itself. [see discussion]

Any chemist will tell youthat the molar volume is 22.4 liters at STP - Standard Temperature and Pressure (1 atmosphere, 32 F). The mass of a mole is equal to the molecular weight of the molecule it's made of, multiplied by 1 gram.

Air doesn't have a standard definition as to composition, but it's generally about 78% nitrogen, 21% oxygen, and 1% other stuff. Since nitrogen has a molecular weight of about 28 and oxygen has a molecular weight of about 32, the molecular weight of air is about 28.8 and a mole has a mass of 28.8 grams.

Dividing 28.8 grams into 22.400 liters, you get 1.286 grams per liter, which isn't far from the 1.2 grams per liter quoted above, which is not at STP.

Arguing that air "weighs nothing" in ordinary conditions ignores the fact that air may be used to displace other fluids, and ignores the fact that air's weight gives air momentum.

Or consider the lift of a hot air balloon. If the temperature of the air in the balloon is 200F and you are ballooning on a winter morning when it's 40 out, how much lift does the balloon produce. You need to use absolute temperatures so adjusting to Rankin scale, the air inside the balloon only weighs 499/659 as much as the air outside the balloon. That's about 75% as much - and so the lift of that balloon is about 25% of the weight of the air that would normally be in that balloon. Hmmm. A back-of-the-envelope calculation reveals that 25% of nothing is still nothing - and yet hot air balloons DO rise.

One might as well assert that you only weigh 85 pounds, because you're only 85 pounds over the Metropolitan Insurance tables, but you'll still have to buy your clothes in the Big & Tall store.