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It is difficult to weigh air, since air has a buoyancy that is exactly equal to its own weight (being surrounded by more air) - sort of like trying to weigh water while you are underwater. However, if you had a vacuum chamber in which you could work (wearing a spacesuit so you could breathe) then you could weigh air, inside a container (you would also have to weight the container separately, of course). A triple beam balance is sensitive enough for this job, if you use a large container.

Alternatively, you could weigh a light weight can, and then evacuate it and weigh it again. It will weigh less by the quantity of air excluded. But it is important that the can remains the same shape after evacuation, but your vacuum need not be particularly good for a reasonable measurement.

The mass of dry air is approx 0.0012 grams per cm3. Or about 1.2kg per m3. (check my math.)

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Q: Can you get the mass of air with the triple beam balance?
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