Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# P Find the Number of Molecules in 1 Cm3 of an Ideal Gas at 0°C and at a Pressure of 10−5mm of Mercury. - Physics

Sum

Find the number of molecules in 1 cm3 of an ideal gas at 0°C and at a pressure of 10−5mm of mercury.

Use R = 8.31 J K-1 mol-1

#### Solution

Given:
Volume of ideal gas, V = 1 cm3 = 10-6 m​3
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

$n = \frac{PV}{RT}$

$\Rightarrow n = \frac{\rho gh \times V}{RT}$

$\Rightarrow n = \frac{13600 \times 9 . 8 \times {10}^{- 8} \times {10}^{- 6}}{8 . 31 \times 273}$

$\Rightarrow n = 5 . 87 \times {10}^{- 13}$

Number of molecules = N × n
= 6.023 × 1023×5.874 × 10−13
= 35.384 × 1010
= 3.538 × 1011

Concept: Kinetic Theory of Gases and Radiation - Introduction of Kinetic Theory of an Ideal Gas
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 2 Kinetic Theory of Gases
Q 3 | Page 34