Ncert Exercises & Solutions

13.6 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.

The 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}

The ideal gas equation is:

PV = N

k_{B}

Where

k_{B}

= Boltzmann constant = 1.38 ×

x 10^{- 23} m^{2} kg s^{- 2} K^{- 1}

The number of air molecules in the room is given by,

N = \frac{PV}{k_{B} T}

= \frac{1.013 \times 10^{5} \times 25}{1.38 \times 10^{- 23} \times 300}

= 6.11 ×

10^{26}

molecules

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

10^{26}

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