Ambedkar Nagar Collision frequency and mean free path Molecule–Wall Collisions: Let’s call Z w the rate of collisions of gas molecules with a section of wall of area A. I. Z w should be proportional to the area A II. Z w should be proportional to the average molecular speed, v avg III. Z w should be proportional to the number of mole, n/V ∝ × × The proportionality constant can be calculated from a complete analysis of the directions from which molecules impinge on the wall; it turns out to have the value 1/4 . So the wall collision rate is = 1 4 × × Collision rate per unit area Г = = 1 4 × = 1 4 × � 8 = √2 Diffusion Diffusion is the process by which the molecules of different substances mingle with each other. The atoms of two solids diffuse into each other when the two solids are in contact, but the process is very slow. The diffusion of a solid through a liquid solvent is much faster but mixing normally needs to be encouraged by stirring or shaking the solid in the liquid (the process is then no longer pure diffusion). Gaseous diffusion is much faster. Effusion Effusion is the process in which a gas escapes through a small hole into vacuum. This occurs if the diameter of the hole is considerably smaller than the mean free path of the molecules. Rate of Effusion = × ℎ = = Г × ∝ √ Graham’s law of effusion The rate of effusion of a gas through a small hole into a vacuum is inversely proportional to the square root of its molar mass. Assuming that different gases are studied at the same temperature and pressure, their number density, N/V, is the same, and the rate of effusion of each gas depends only on the factor 1/√ , exactly as observed by Graham.