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!! |