Graham's Law of Effusion
Diffusion is the spontaneous intermingling of one substance with another. This occurs with perfumes and aftershaves and also with the fragrance of irate skunks.  Diffusion is over when the molecules of the fragrance are evenly spread within a container, be it a room or a gas flask.  Another way to look at it is to describe the process using partial pressures.  Diffusion is over when the partial pressures of all the gases involved become identical in all parts of the container.  When a fragrance is more or less concentrated in a corner of a room, its partial pressure is higher there.
 
Another necessary term is the gradient.  A gradient is used to describe how the concentration or partial pressures change from one place to another.  When sugar is added to coffee it sinks to the bottom.  If left alone, (and the coffee stayed hot), the sugar would dissolve and gradially spread on its own accord throughout the coffee.  ( Of course, we stir it because the time involved here is quite long.)   At the bottom of the cup we have a lot of sugar.  At the top of the cup we have zero dissolved sugar.  A concentration gradient is set up from bottom to top.  Sugar will gradually move down this gradient until it is evenly spread out.  When a freshly skunked pet comes into the room, it brings with it a high concentration of skunk perfume molecules.  Where the pet enters the house there will be a high conentration.  Everywhere else in the house there will be a zero concentration of skunk molecules. (Unless of course, this is not your pets first time, or your a skunk rancher!)   The point is, one of the great facts about natural processes is that "Nature abhors a vacuum."  Another way to say this is that nature abhors gradients.  Given the chance, gradients in nature tend to disappear, some rapidly and some only over eons of time, until there is as much an evenness as possible.
 
The effusion of a gas is its movement through an extremely tiny opening into a region of lower pressure.   The term diffusion really only speaks to the direction of gas movement. Effusion speaks for not only the direction but the rate that a change occurs.
 
An English scienetist, Thomas Graham (1805-1869), studied the rates at which various gases effuse, and he found that the more dense the gas is,  the slower it effuses.  The exact relationship between rate and gas density, d, is called Graham's Law of Effusion.
 
(effusion rate)A  X  (dA)1/2  = (effusion rate)B X (dB)1/2
 
Finding the densities of gases at various temperatures is often difficult to do.  With a little chemical slight of hand we can get a formula for a much simpler answer.
 
(effusion rate)A  X  (molecular massA)1/2  = (effusion rate)B X (molecular massB)1/2
 
Example:  Under the same conditions of temperature and pressure, does hydrogen iodide or ammonia effuse faster? Calculate the relative rates at which they effuse.
 
 molecular mass of HI = 128           molecular mass of NH3 = 17.04

 ( effusion rate of NH3 )  X  (17.04)1/2  = ( effusion rate of HI ) X (127.91)1/2

This rearranges to    rate for NH3(127.91)1/2
                                   rate for HI         (17.01)1/2

This rearrange into  rate for NH3 = (127.91/17.01)1/2
                                             rate for HI
                                                       = 2.74
Thus ammonia effuses almost three times as fast as hydrogen iodide.
 

As a general rule the more a molecule masses the slower it moves.  To find a mathematical value to this rate use Graham's Law.

 
           Go to the Effusion Law Worksheet