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Air in gaseous form occupies a certain volume at certain temperature and pressure. To measure density of air first fix temperature and pressure. Once you determine the weight (mass) occupied by unit volume, the density of air mass per unit volume. The standard air density is 1.293 kilograms per normal cubic meter (Mn3). A "normal cubic meter" a cubic meter of volume at 1 atmosphere pressure and 273 degrees Kelvin temperature (0 Centigrade).

The process of "weighing" air is a little bit tricky because some of the usual methods for measuring mass or weight do not work because one must account for the buoyancy of the measuring vessel and the buoyancy of the volume which holds the air or vacuum etc.

Obviously, to know density, one must normally know a mass and a volume because the average density of an object is equal to its mass divided by its volume.

We will assume that one can easily measure volume and concentrate on measuring mass. We will assume that we know the gravitational acceleration and so measuring the weight of air is enough to give us the mass. There are two approaches, you can add mass or subtract mass.

1. Subtract

There is a common demonstration of the mass of air that is made by taking a rigid container and weighing it and then evacuating the container and weighing it again and determining that the container without air is lighter. If one knows that the evacuated container has essentially zero pressure, then all of the air has been removed and the change in weight is the weight of the air that was originally in the container. This approach requires that one can measure the pressure accurately.

2. Add

If one can measure pressure one can also add air to a container and increase the mass. One would assume that by doubling the pressure, one would double the mass. (This may not be true of there is enough water vapor such that it might condense.) It is easier to measure pressure above atmospheric pressure than below, but this method does mean that you need to know what the starting atmospheric pressure is. If you double the pressure, then you double the mass and the increased weight in the container gives the density of air. (Conversely, at half the pressure you can assume half the mass.)

Note: These measurements assume the temperature is held constant and the volume is held constant and known accurately. In the "add method", one is also treating air as an ideal gas and assuming double pressure means double mass which is pretty good.

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Q: How could you measure the density of air?
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