Estimate the total number of air molecules

cbse
kinetictheoryofgases

#1

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.


#2

Given , V = 25.0 ${{m}^{3}}$, T = 273+ 7 = 300 K
${ k }{ B }$ = 1.38 x ${{10}^{-23}}$ J${{K}^{-1}}$
Now, pV = µRT
pV = µ(${ N }
{ A }$ kb)T
pV = N’ ${ k }{ B }$T (N’ is total number of molecules)
N ’ = pV / ${ k }
{ B }$T = 1.01 x ${{10}^{5}}$ x 25 / 1.38 x${{10}^{-23}}$ x 300 = 6.10 x ${{10}^{26}}$