Estimate the total number of molecules inclusive of oxygen, nitrogen, water vapour and other constituents in a room of capacity `30m^(3)` at a temperature of `30^(@)C` and 1 atmosphere pressure.

Explanation

As Boltzmann's constant,
`K_(B)=(R )/(N) therefore R=K_(B)N`
Now, `PV=nRT=nK_(B)NT`
The number of molecules in the room
`=nN=(PV)/(TK_(B))=(1.013xx10^(5)xx30)/(303xx1.38xx10^(-23))=(1.013xx30xx10^(5)xx10^(23))/(303xx1.38)`
`=(1.013xx30xx10^(28))/(418.14)=(30.39xx10^(28))/(418.4)=0.0726xx10^(28)=7.26xx10^(26)`