Question

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

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

$$\begin{gathered} n=\frac{PV}{RT} \\ \Rightarrow n=\frac{\rho gh\times \mathrm{V}}{RT} \\ \Rightarrow n=\frac{13600\times 9.8\times {10}^{-8}\times {10}^{-6}}{8.31\times 273} \\ \Rightarrow n=5.87\times {10}^{-13} \end{gathered}$$

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