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Graham’s law of diffusion states the rate of diffusion between two gases is inversely proportional to their molar masses. Now, this is helpful when we are focused on two gases. But that is rarely the case in a beaker or even the atmosphere.

So how do you measure the rates of diffusion of many gases moving at once? Do you measure each rate of effusion (inversely proportional to molar mass) and just order them, then use stoichiometry to determine which one will be dispersed quickest based on the amounts present?

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  • $\begingroup$ If the gases can be regarded as ideal then the diffusion of each one is treated as independent of any other. $\endgroup$ – Buck Thorn Apr 16 at 16:02
  • $\begingroup$ @BuckThorn So a few comments: (1) an ideal gas is that which meets the criteria for kinetic/particle molecular theory; (2) if treated as independent of any other, then its diffusion rate can be compared in an ordered list; (3) once you have that list together, you can compare each to one another. Is that all correct? As a result, that’s why we have Graham’s law — because if effusion is inversely proportional to the molar mass, then you would just divide the inverse of the molar mass of one to the inverse of the molar mass of another. $\endgroup$ – Alex Apr 16 at 16:45
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    $\begingroup$ If I understand you correctly, you seem to be wondering if the relationship is transitive, and the answer would be yes. $\endgroup$ – Buck Thorn Apr 16 at 17:52
  • $\begingroup$ @BuckThorn Yes, it’s a transitive relation. Assuming the gases are ideal, then we order them in a list. If we can order them in a list, then we can compare them. And that’s how we got Graham’s law, which clarifies things, thanks. $\endgroup$ – Alex Apr 16 at 19:27
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If the gases in a mixture are ideal then their diffusion is independent*.

The relationship described by Graham's law is transitive, therefore the relative effusion rate of multiple substances with respect to a reference substance also provides a ranking of their relative diffusion coefficients (an ordered list).

*Outside of condensed or supercritical phases it seems unlikely that two fluid substances would display sufficiently strong interactions to alter the relative order of their diffusion coefficients.

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