• id: JTHERM-02-N14
• title: Rate of Diffusion and Effusion
• tags: graham, diffusion, effusion

Graham's law states that the rate of diffusion (or effusion) of a gas is inversely proportional to the square root of its molar mass: $r \propto 1/\sqrt{M}$. For two gases at the same temperature and pressure: $r_1/r_2 = \sqrt{M_2/M_1}$. This follows directly from kinetic theory since the average speed $v_{\text{avg}} \propto 1/\sqrt{M}$, and the rate of effusion through a small hole depends on how fast molecules arrive at the hole. Effusion is the escape of gas through a tiny opening (smaller than mean free path). Diffusion is the spreading of gas through another gas. Graham's law applies exactly to effusion and approximately to diffusion.