In my post from Jan 18, 2017,<\/a> I define effuse<\/em>: it means to escape from a container through a porous boundary.<\/p>\n Graham’s Law of Effusion compares the rate at which two different gases will effuse, based on their comparative molecular masses. If eA<\/sub> is the effusion rate of gas A, and eB<\/sub> that of gas B, then<\/p>\n eA<\/sub>\/eB<\/sub> = (MMB<\/sub>\/MMA<\/sub>)1\/2<\/sup><\/p>\n where MMA<\/sub> is molecular mass of gas A, and MMB<\/sub>, that of gas B.<\/p>\n The reasoning behind the formula is that effusion depends on molecular motion, which is quantified by kinetic energy, KE:<\/p>\n KE = 0.5MMv2<\/sup><\/p>\n where, once again, MM means molecular mass, while v means velocity.<\/p>\n Two gases of the same temperature have the same kinetic energy:<\/p>\n 0.5MMA<\/sub>vA<\/sub>2<\/sup>=0.5MMB<\/sub>vB<\/sub>2<\/sup><\/p>\n Dividing both sides by 0.5MMA<\/sub>vB<\/sub>2<\/sup> gives<\/p>\n vA<\/sub>2<\/sup>\/vB<\/sub>2<\/sup> = MMB<\/sub>\/MMA<\/sub><\/p>\n square rooting both sides gives<\/p>\n vA<\/sub>\/vB<\/sub> = (MMB<\/sub>\/MMA<\/sub>)1\/2<\/sup><\/p>\n Since effusion is motion through pores, the ratio of velocities is the ratio of effusion:<\/p>\n eA<\/sub>\/eB<\/sub>=vA<\/sub>\/vB<\/sub> = (MMB<\/sub>\/MMA<\/sub>)1\/2<\/sup><\/p>\n Example: Compare the effusion rate of methane, CH4<\/sub>, with that of propane, C3<\/sub>H8<\/sub>.<\/p>\n Solution: the ratio of effusion should be<\/p>\n eA<\/sub>\/eB<\/sub>=(MMB<\/sub>\/MMA<\/sub>)1\/2<\/sup><\/p>\n Note that methane, CH4<\/sub>, has MM=16, while propane, C3<\/sub>H8<\/sub>, has MM=44. Therefore, <\/p>\n emethane<\/sub>\/epropane<\/sub>=(44\/16)1\/2<\/sup>=1.66<\/p>\n Methane should escape from a porous container 1.66 times the rate that propane escapes.<\/p>\n Note that, in a more general sense, this is a law of diffusion<\/em>. Therefore, if propane and methane are released at one end of a room, methane should reach the other end 1.66 times as quickly as propane.<\/p>\n HTH:)<\/p>\n Source:<\/p>\n Mortimer, Charles E. Chemistry<\/u>, sixth ed. Belmont: Wadsworth, 1986.<\/p>\n White, J. Edmund. Physical Chemistry<\/u>, College Outline Series. New York: Harcourt Brace Jovanovich, 1987.<\/p>\n