NEET-XII-Physics
24: Kinetic Theory of Gases
- #3Find the number of molecules in 1 cm3 of an ideal gas at 0°C and at a pressure of 10-5 mm of mercury.Ans : Given:
Volume of ideal gas, V = 1 cm3 = 10-6 m3
Temperature of ideal gas, T = 0 °C = 273 K
Pressure of mercury, P = 10-8 m of Hg
Density of ideal gas, ρ = 13600 kgm-3
Pressure `` \left(P\right)`` is given by
P = ρgh
Here,
ρ = density of ideal gas
g = acceleration due to gravity,
Using the ideal gas equation, we get
`` n=\frac{PV}{RT}``
`` \Rightarrow n=\frac{\rho gh\times \,\mathrm{\,V\,}}{RT}``
`` \Rightarrow n=\frac{13600\times 9.8\times {10}^{-8}\times {10}^{-6}}{8.31\times 273}``
`` \Rightarrow n=5.87\times {10}^{-13}``
`` ``
`` ``
Number of molecules = N × n
= 6.023 × 1023 × 5.874 × 10-13
= 35.384 × 1010
= 3.538 × 1011