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 Subject: Diffusion of gases Category: Science > Chemistry Asked by: brittanyl-ga List Price: \$10.00 Posted: 20 Jul 2005 18:39 PDT Expires: 19 Aug 2005 18:39 PDT Question ID: 546023
 `Which gas will diffuse fastest Ne, Ar, Kr, or Cl2? Why?`
 ```Hi brittanyl-ga. The theory behind your question goes back to Graham's law of gases. This states that the speed of each particle (atom or molecule) of a gas has a speed which is proportional to the 1 / M^0.5 (i.e., one over the square root of the molar mass of the gas). The molar mass is the atomic mass of the particle expressed in grams. Here's an example: For Neon (Ne), the atomic mass is 10 daltons, so the molar mass is 10 grams. This means that one mole (Avogadro's number of particles, 6.02 x 10^23) has a mass of 10 grams. For hydrogen, with an atomic mass of 1 dalton for it's single proton, the molar mass would be 1 gram. For Neon, this means that the speed of the individual Neon atoms is proportional to 1 / sqrt(10). Why is this so? Graham's law is not just arbitrary. Imagine two containers, each with one of two gases at the same given temperature. Temperature is a bulk measure of the kinetic energy of individual particles in a material. At the same temperature, the average energy of the particles in each container will be the same. But... the particles in each container have different masses. Let's say the first container has Neon and the second has Argon (Ar). On average, then, we have the following: KE(Ne) = KE(Ar) 1/2 M(Ne) v(Ne)^2 = 1/2 M(Ar) v(Ar)^2 [KE = 1/2 mv^2] simplifying: M(Ne) v(Ne)^2 = M(Ar) v(Ar)^2 v(Ne)^2 / v(Ar)^2 = M(Ar) / M(Ne) taking the square root of each side: v(Ne) / v(Ar) = sqrt [M(Ar)/M(Ne)] So, as stated in Graham's law, the velocity of individual particles in gasses at the same temperature is proportional to the reciprocal of the square root of the molar mass. In simpler terms, the heavier each particle is in a gas, the slower it moves to have the same kinetic energy. So, the lightest gas particles will need to move the fastest to have equal kinetic energies, from the equation above. The faster a gas particle moves, the faster the gas will disperse overall. Think of the gas particles moving towards the edges of the container... if the particles there are moving faster, the volume of the gas will expand faster. So, the molar masses of the gasses you list are as follows: Neon (Ne): 10 grams Argon (Ar): 39.9 grams Krypton (Kr): 83.8 grams Chlorine gas (Cl2): 71 grams (35.5 x 2) So, Neon is the lightest and will therefore move the fastest if all of these gases are at the same temperature. For this reason, Neon will diffuse the fastest. Here is a page that further describes the diffusion of gasses, including a lab: http://chemmovies.unl.edu/chemistry/smallscale/SS028c.html A nice discussion of the motion of particles in gasses can be found at this site from the Oklahoma State introductory chemistry course: http://intro.chem.okstate.edu/1314F97/Chapter10/Fri1212971.html Best of luck in your studies. Please feel free to request any clarification. -welte-ga```
 brittanyl-ga rated this answer: `This was a very helpful answer!`