Question
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 $27°C$ and $1$ atm pressure.
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Answer
Volume of the room, $\mathrm{V}=25.0 \mathrm{~m}^3$ Temperature of the room, $\mathrm{T}=27^{\circ} \mathrm{C}=300 \mathrm{~K}$ Pressure in the room, $\mathrm{P}=1 \mathrm{~atm}=1 \times$
$1.013 \times 10^5 \mathrm{~Pa}$ The ideal gas equation relating pressure ( P ), Volume ( V ), and absolute temperature ( T ) can be written as, $\mathrm{PV}=\mathrm{k}_{\mathrm{B}} \mathrm{NT}$ Where, $\mathrm{K}_{\mathrm{B}}$ is Boltzmann constant $=1.38 \times 10^{-23} \mathrm{~m}^2 \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{k}^{-1} \mathrm{~N}$ is the number of air molecules in the room $\therefore \mathrm{N}=\frac{\mathrm{PV}}{\mathrm{K}_{\mathrm{B}} \mathrm{T}}=\frac{1.013 \times 10^5 \times 25}{\left(1.38 \times 10^{23} \times 300\right)}=6.11 \times 10^{26}$ molecules Therefore, the total number of air molecules in the given room is $6.11 \times 10^{26}$
$1.013 \times 10^5 \mathrm{~Pa}$ The ideal gas equation relating pressure ( P ), Volume ( V ), and absolute temperature ( T ) can be written as, $\mathrm{PV}=\mathrm{k}_{\mathrm{B}} \mathrm{NT}$ Where, $\mathrm{K}_{\mathrm{B}}$ is Boltzmann constant $=1.38 \times 10^{-23} \mathrm{~m}^2 \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{k}^{-1} \mathrm{~N}$ is the number of air molecules in the room $\therefore \mathrm{N}=\frac{\mathrm{PV}}{\mathrm{K}_{\mathrm{B}} \mathrm{T}}=\frac{1.013 \times 10^5 \times 25}{\left(1.38 \times 10^{23} \times 300\right)}=6.11 \times 10^{26}$ molecules Therefore, the total number of air molecules in the given room is $6.11 \times 10^{26}$
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