### Q.6:- 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.

**Answer:-**

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

∴ *N* = *PV* / *k _{B}T*

= 1.013 × 10

^{5}× 25 / (1.38 × 10

^{-23}× 300)

= 6.11 × 10

^{26}molecules

Therefore, the total number of air molecules in the given room is 6.11 × 10

^{26}.