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A typical value for the atmospheric pressure on Earth is 101 kPa. The surface area of...

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lak-86 | Student, Undergraduate | Salutatorian

Posted June 16, 2013 at 3:12 AM via web

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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.

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted June 16, 2013 at 3:36 AM (Answer #1)

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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.

 

Assumption

Gravitational acceleration is constant throughout the atmosphere.

Sources:

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