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Q: Diffusion of gases ( Answered 5 out of 5 stars,   0 Comments )
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?
Subject: Re: Diffusion of gases
Answered By: welte-ga on 20 Jul 2005 19:06 PDT
Rated:5 out of 5 stars
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]
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:

A nice discussion of the motion of particles in gasses can be found at
this site from the Oklahoma State introductory chemistry course:

Best of luck in your studies.  Please feel free to request any clarification.

brittanyl-ga rated this answer:5 out of 5 stars
This was a very helpful answer!

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