Graham diffusion

Thomas Graham studied the interdiffusion of gases by measuring the volume of a test gas that would replace a unit volume of atmospheric air when the gases were allowed to exchange through a porous plug (at constant temperature and pressure). Graham reported replacement volumes (volume of gas diffusing in divided by volume of air diffusing out) for a variety of gases; he called these ratios "equivalent volumes of diffusion." He related those equivalent volumes to the specific gravity (density) of the gas, again using atmospheric air as the standard. His results were:

gasequivalent vol.spec. gravity
hydrogen3.830.0694 [original had 0.694, a typo]
carburetted hydrogen1.3440.555
olefiant gas1.01910.972
carbonic oxide1.01490.972
nitrogen1.01430.972
oxygen0.94871.111 [original had 0.111, a typo]
sulphuretted hydrogen0.951.1805
protoxide of nitrogen0.821.527
carbonic acid0.8121.527
sulphurous acid0.682.222

(Download a spreadsheet file containing Graham's data by clicking here.)

Is there a relationship between equivalent volume and density? If so, what is it? Try plotting the equivalent volume V vs. the density ρ, then ln V vs. ρ, and then ln V vs. ln ρ. Is the result of any of the plots a straight line? If so, note the slope m and y-intercept b, and write the resulting equation y = mx + b in terms of V and ρ. Finally, solve that equation for V as a function of ρ; that is the relationship between equivalent volume and gas density.

Reference

Thomas Graham, "On the Law of Diffusion of Gases," Philosophical Magazine 2, 175-190, 269-276, 351-358 (1833)
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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