Kinetic Theory

Question : 6

Total: 14

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0m3 at a temperature of 27°C and 1 atm pressure.

Solution:

Here, volume of air molecules, V=25.0m3
Temperature of air molecules, T=27°C=27+273=300K
Pressure of air molecules, P=1‌atm=1.013×105Pa
Now, PV=nRT
P=

nRT

n(Nk)T

[∵

=k=1.38×10−23JK−1=Boltzman‌constant]

(nN)kT

N′kT

[∵N′=nN=Total‌number‌of‌air‌molecules]

N′=

(1.01×105)×25

(1.38×10−23)×300

=6.10×1026

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