A typical value for the atmospheric pressure on Earth is 101 kPa. The surface area of the Earth A, is related to its mean radius R by the expression A = 4piR^2, where R has the value 6400 km.
Calculate the number of molecules in the atmosphere, assuming that the mass of a mole of air is 30 g.
The pressure on the earth is applied by the weight of air in the atmosphere.
`P = F/A`
`P = 101kpa`
`A = 4piR^2 = 4xxpixx(6400xx10^3)^2 = 5.147xx10^14m^2`
`F = 1.01xx10^5xx5.147xx10^14 = 5.2xx10^19`
If the mass of air is m the;
`F = mg`
`5.2xx10^19 = mxx9.81`
`m = 5.3xx10^18kg`
It is given that mass of 1 mole of air is 30g.
Amount of moles in air `= (5.3xx10^18)/0.03 = 1.77xx10^20 mol`
According to Avogadro 1mol of substance contain `6.022xx10^23 ` atoms.
Atoms in air `= 6.022xx10^23 xx1.77xx10^20 = 1.065xx10^44`
So there is `1.065xx10^44` atoms in air.
Gravitational acceleration is constant throughout the atmosphere.