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Home » Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity at a temperature of and 1 atm pressure.
Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 \mathrm{~m}^{3} at a temperature of 27^{\circ} \mathrm{C} and 1 atm pressure.
CBSE | Class 11 | Kinetic Theory | NCERT | Physics
Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 \mathrm{~m}^{3} at a temperature of 27^{\circ} \mathrm{C} and 1 atm pressure.

Volume of the room is given as V=25.0 \mathrm{~m}^{3}

Temperature of the room is given as T=27^{0} \mathrm{C}=300 \mathrm{~K}

Pressure in the room will be P=1 \mathrm{~atm}=1 \times 1.013 \times 10^{5} \mathrm{~Pa}

The ideal gas equation can be written as:

P V=\left(k_{B} N T\right)

Where,

\mathrm{K}_{\mathrm{B}} is Boltzmann constant having value
\left(1.38 \times 10^{-23}\right) \mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}

\mathrm{N} is the number of air molecules in the room

Therefore,

\begin{array}{l} N=\left(P V / k_{B} T\right) \\ =\left(1.013 \times 10^{5} \times 25\right) /\left(1.38 \times 10^{-23} \times 300\right) \end{array}

We get,

=6.11 \times 10^{26} molecules

As a result, 6.11 \times 10^{26} is the total number of air molecules in the given room.

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