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.
Volume of the room, V=25.0m3 Temperature of the room, T=270C=300K Pressure in the room, P=1atm=1×1.013×105Pa The ideal gas equation relating pressure (P), Volume (V), and absolute temperature (T) can be written as: PV=kBNT Where, kB is Boltzmann constant =1.38×10−23m2kgs−2K−1. N is the number of air molecules in the room. ∴N=kBTPV =1.38×10−23×3001.013×105×25 =6.11×1026 molecules Therefore, the total number of air molecules in the given room is 6.11×1026.
