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 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:

109,000,000,000,000,000,000,000,000,000,000,000,000,000,000

That is a lot of molecules!!