# Q13.6 Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity $25.0m^{3}$ at a temperature of $27^{0}C$ and  $1atm$ pressure.

S Sayak

The volume of the room, V = 25.0 m3

Temperature of the room, T = 27oC = 300 K

The pressure inside the room, P  = 1 atm

Let the number of moles of air molecules inside the room be n

$\\n=\frac{PV}{RT}\\ n=\frac{1.013\times 10^{5}\times 25}{8.314\times 300}\\ n=1015.35$

Avogadro's Number, $N_{A}=6.022\times 10^{23}$

Number of molecules inside the room is N

$\\N=nN_{A}\\ N=1015.35\times 6.022\times 10^{23}\\ N=6.114\times 10^{26}$

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