Answer to Question #245233 in Physics for raviraj

Question

The mean free path of CO2 molecules in a vessel is 790 Å, density is 1.7 kg/m3.Calculate the diameter of CO2 molecule

Answer 1

The mean free path can be expressed in terms of pressure and diameter:

$$l=\frac{k_BT}{\sqrt2\pi d^2p},\\\space\\ d=\sqrt{\frac{k_BT}{l\pi p\sqrt2}}=3.4\text{Å}.$$

We took the temperature of 300K and pressure of 101325 Pa.