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 :

__We have to consider the Ideal Gas Law with the__ __Boltzmann constant to solve this problem____.__

Given:

Volume of the room (V) = 25 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 also be written as

PV = k_{B}NT

(Where, K_{B} is Boltzmann constant = 1.38 × 10^{–23} m^{2} 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 × 10 ^{26}__

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