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Graham's Law of Effusion

According to the kinetic molecular theory, the average kinetic energy of any sample of gas molecules, 1/2 mu2, has a particular value at a given temperature.  Thus a gas composed of light molecules, such as He, will have the same   average kinetic energy as one composed of heavier molecules, such as Xe, provided the two gases are at the same temperature.  In order for this to be true, the molecules of the lighter gas must have a higher rms (average) speed, u, than the heavier one.  The speed of gas molecules is inversely proportional to the molar mass.   The dependence of molecular speeds on mass has some interesting results.  One of these is effusion, which is the escape of gas molecules through a tiny hole into a vacuum.  A second is diffusion, which is the spread of one substance throughout a space or a second substance.

In 1846 Thomas Graham discovered that the effusion rate of a gas is inversely proportional to the square root or its molar mass.  If the rate of effusion or two gases, at the same temperature and pressure, are r1 and r2, and their respective molar masses are M1 and M2 Graham's law states:

GRAHAMEQ.jpg (2888 bytes)

This equation compares the rate of effusion of two gases under identical conditions, and it indicates that the lighter gas effuses more rapidly.

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