Question

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

Answer 1

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