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.
We have to consider the Ideal Gas Law with the Boltzmann constant to solve this problem.
Volume of the room (V) = 25 m3
Temperature of the room (T) = 27°C = 300 K
Pressure in the room (P) = 1 atm = 1 × 1.013 × 105 Pa
The ideal gas equation also be written as
PV = kBNT
(Where, KB is Boltzmann constant = 1.38 × 10–23 m2 kg s–2 K–1 and N is the number of air molecules in the room)
∴ N = =
⇒ N = 6.11 × 10 26 molecules
The total number of air molecules in the given room is 6.11 × 1026
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