Mean Free PathThe mean free path or average distance between collisions for a gas molecule may be estimated from kinetic theory. Serway's approach is a good visualization  if the molecules have diameter d, then the effective crosssection for collision can be modeled by using a circle of diameter 2d to represent a molecule's effective collision area while treating the "target" molecules as point masses. In time t, the circle would sweep out the volume shown and the number of collisions can be estimated from the number of gas molecules which were in that volume. The mean free path could then be taken as the length of the path divided by the number of collisions.

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Refinement of Mean Free PathThe intuitive development of the mean free path expression suffers from a significant flaw  it assumes that the "target" molecules are at rest when in fact they have a high average velocity. What is needed is the average relative velocity, and the calculation of that velocity from the molecular speed distribution yields the resultThe resulting mean free path is The number of molecules per unit volume can be determined from Avogadro's number and the Ideal gas law, leading to Calculation 
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Mean Free Path Calculation

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Mean Free Path PerspectiveYou may be surprised by the length of the mean free path compared to the average molecular separation in an ideal gas. An atomic size of 0.3 nm was assumed to calculate the other distances.

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