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The mean distance traversed by a gas molecule before collision with another is called its mean free path, L. This can be calculated from the viscosity of the gas, η, by the formula: L = 1.25 η / √(pD). It is greater the lower the pressure, because the molecules are then less crowded together and their jostling is reduced. In oxygen at S.T.P., L is very nearly 10-5 cm.; it is double this in hydrogen.
The mean free path of the oxygen molecule at atmospheric pressure is equal to the thickness of the thinnest gold-leaf. At low pressures such as exist in the spaces between the walls of "thermos" flasks, the free path is several cm. A molecule rebounds from opposite walls of such a flask many times without encountering another.
During one second a molecule describes as many free paths as it makes collisions, and the sum of the paths is equal to the mean speed Ω. Thus the collision frequency, or the number of collisions per second, is Ω/L. In oxygen, this is 4.25 x 104/10-5 = 4.25 x 109. At very low pressures the mean free path is 1 cm., but even then there will be 105, or 100,000 collisions per second.
The area exposed by the surfaces of all the molecules, assumed spherical, in 1 c.c. of oxygen at S.T.P, 4Nπr2, is about 7 square metres.
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