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 atmospheric pressure. ( k = 1.38 x 10 ^2–3 J/K).

Solution

The ideal gas equation is given by,
PV = nRT
Therefore,
n =

\frac{PV}{RT}

\frac{PV}{nKT}

So, total number of air molecules in volume V is given by

nN = \frac{PV}{KT}

Here,
Pressure, P = 1 atm = 1.01

\times 10^{5} N m^{- 2}

Volume, V = 25 m³Temperature, T = 27^o C = 300 K
Boltzman constant, k = 1.38

\times

10^-23 J/K

So, total number of air molecules is given by,

nN = \frac{PV}{kT} = \frac{1.01 \times 10^{5} \times 25}{1.38 \times 10^{- 23} \times 300} = 6.10 \times 10^{26} molecules

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