Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m3 at a temperature of 27 °C and 1 atm pressure.

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Solution

Given, the volume of the room is V=25 m 3 , temperature is T=27 °C and pressure is P=1 atm.

The ideal gas equation is given as,

PV= k b NT N= PV k b T

Here, k b is the Boltzmann constant which is 1.38× 10 −23 m 2 ⋅kg/ K⋅ s 2 and N is the number of air molecules.

Substitute the values in the above expression.

N= 1.013× 10 5 ×25 1.38× 10 −23 ×300 ≈6.10× 10 26 molecules

Hence, the total number of air molecules is 6.10× 10 26 molecules.

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