|HOW MANY MOLECULES OF AIR ARE IN THE ATMOSPHERE?
METEOROLOGIST JEFF HABY
Molecules are extremely small. Much of the air is composed of Nitrogen and Oxygen but there is also Argon, Carbon Dioxide, Water Vapor
and many other trace gases. The number of molecules in Earth’s atmosphere must be incredibly large. This writing aims to estimate the
amount of air molecules.
First we start by finding the mass of the atmosphere
Pressure = Force / Area
Pressure = 101,325 Pascals
Area = Area of Earth
The earth is a near sphere. A sphere has an area of 4*PI*radius^2. Earth has a radius of 6,371 km = 6,371,000 meters.
Area of Earth = 4*PI*6,371,000^2 meters^2 = 5.1 * 10^14 m^2
Force = Pressure * Area
Force = (101,325 Pascals * 5.1 * 10^14 m^2) = 5.17 * 10^19 Newtons
Force = mass * gravity
mass = Force / gravity
mass = 5.17 * 10^19 Newtons / 9.8 ms^-2 = 5.27 * 10^18 kilograms
Now that we have a mass in kilograms, we need to convert this number into grams
(5.27 * 10^18 kilograms) * (1000 g / 1 kg) = 5.27 * 10^21 grams
The molar mass of air is around 29 grams / mole
(5.27 * 10^21 grams) * (1 mole / 29 grams) = 1.81 * 10^20 moles
Finally, multiply by Avogadro ’s number to convert moles to molecules
(1.81 * 10^20 moles) * (6.02214179*10^23 molecules/mole) = 1.09 * 10^44 molecules
Written out and rounded, there are about this many molecules of air in the atmosphere:
That is a lot of molecules!!