Graham's Law of Effusion and Diffusion
 Root-mean-square velocities of gas molecules are sometimes directly useful, but the comparison of velocities explains the results of, and is useful in, studies of effusion of molecules through a small hole in a container or diffusion of molecules through porous barriers. The comparison between two gases is most conveniently expressed as: vrms(1)/vrms(2) = (M2/M1)1/2 = (d2/d1)1/2 This equation gives the velocity ratio in terms of either the molar mass ratio or the ratio of densities. The ratio of root-mean-square velocities is also the ratio of the rates of effusion, the process by which gases escape from containers through small holes, and the ratio of the rates of diffusion of gases. This equation is called Graham's law of diffusion and effusion because it was observed by Thomas Graham (1805-1869) well before the kinetic-molecular theory of gases was developed. As an empirical law, it simply stated that the rates of diffusion and of effusion of gases varied as the square root of the densities of the gases. Graham's law is the basis of many separations of gases. The most significant is the separation of the isotopes of uranium as the gases 238UF6 and 235UF6. Fluorine has only one isotope, so the separation on the basis of molar mass is really a separation on the basis of isotopic mass. Example. The ratio of root-mean-square velocities of 238UF6 and 235UF6 can be calculated as follows. The molar mass of 238UF6 is 348.0343 and the molar mass of 238UF6 is 352.0412. The mass ratio is 1.011513 and the ratio of root-mean-square velocities is 1.00574. Although the difference is small, many kilograms of 235U have been separated using this difference in the gas-diffusion separation plant at Oak Ridge, Tennessee, U. S. A. This plant prepared the uranium for the Manhattan Project of the Second World War and produced the uranum used in the uranium atomic bomb dropped on Japan in 1945.