How to Calculate the Mass of the Air in the Atmosphere

Image of a circle that says Earth.  The circle is surrounded by a blue layer that says Atmosphere.Earth's Shape: oblate spheroid
Diameter polar = 12719 km
Diameter equatorial = 12762 km
Diameter average = 12740.5 km
Atmosphere: 25 km
Radius of Earth: (12740)/2 = 6370 km = 6.37x106 m
Radius of Earth and air: (12740 + 50)/2 = 6395 km + 6.395x106m
Volume of sphere formula: 4/3 pr3
Volume of Earth: 4/3 pr (6.37 x 106m)3 = 1.0827 x 1021m3
Volume of Earth and air: 4/3 p (6.395 x 106m)3 = 1.0959 x 1021m3

Note: 97% of the atmosphere's weight is found within 25 km of Earth's surface.

Calculate the volume of air:
Volume of Earth and air: 1.0959 x 1021m3
Volume of Earth: 1.0827 x 1021m3

Image of a chalkboard diagram that has a formula to find the volume of air.  Please have someone assist you with this.

Density = Mass/Volume
Density x Volume = Mass
Average Density of Air = = 0.450 kg/m3 or 450g/m3

Important Note: With the density/height variation in mind we used a density averaged over the whole atmospheric layer under consideration -- zero to 25 km in this case. The density of air drops by a factor of 30 between the surface and 25 km altitude.

Calculate the mass of air:
Density = 450g/m3
Volume = 1.28 x 1019m3
Mass = 5.76 x 1021g of Air

Image of a chalkboard diagram that has a formula to find the mass of air.  Please have someone assist you with this.

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