Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity `25.0 m^(3)` at a temperature of `27^(@) C` and 1 atm pressure. (Boltzmann constant `= 1.38 xx 10^(-23) JK^(-1))`.

Explanation

Volume of the room,` V = 25.0 m^3`
Temperature of the room,`T = 27^(@)C = 300 K`
Pressure in the room,` P = 1 atm = 1 × 1.013 × 10^5` Pa
The ideal gas equation relating pressure (P), Volume (V), and absolute temperature (T) can be written as:` PV=K_(B)NT`
Where,

`K_B " is Boltzmann constant" = 1.38 × 10^(–23) m ^(2 )kg s^(–2) K^(–1)` N is the number of air molecules in the room
`therefore N=(PV)/(K_(B)T)`
` (1.013 xx 10^5xx 25)/(1.38 xx 10^(-23)xx 300)= 6.11 × 10^26` molecules
Therefore, the total number of air molecules in the given room is` 6.11 × 10^26`.